1

Thèse

Présentée à

L’Université Bordeaux 1

Ecole Doctorale des Science Physiques et de l’Ingénieur

par

Preeti Gaikwad

Pour obtenir le grade de

Docteur

Spécialité: Laser, Matiere et Nanosciences

Matériaux poreux multi-échelles pour la diffusion multiple/localisation de la

lumiere et les lasers aléatoires

English translation:

Multi-scale porous materials designed for multiple light

scattering/localization and random lasing

Soutenue le 13 Décembre 2012

Après avis de: DR Patrick Sebbah

Prof. Reinhard Höhler

Devant la commission d’examen formée de:

M. Bernard Pouligny DR, CNRS, CRPP Président

M. Patrick Sebbah DR, IL, ESPCI, Paris Rapporteur

M. Reinhard Höhler Professeur, INSP, UPMC, Paris Rapporteur

M. Peter Hesemann DR, Univ. Montpellier 2 Examinateur

M. Renaud Vallée CR, Habilitation, CRPP Directeur de thèse

M. Rénal Backov Professeur, Univ. Bordeaux 1 Codirecteur de thèse

Matériaux poreux multi-échelles pour la diffusion multiple/localisation de la lumiere et les lasers aléatoires

Résumé : Des matériaux poreux à architecture complexe et de couleur blanche ont été synthétisés, en combinant la physico-chimie des fluides complexes (émulsions, mésophase lyotropes) avec la chimie sol-gel. Ce procédé est connu sous le nom de chimie intégrative. En contrôlant la taille des objets diffusants (diamètres des pores) et en augmentant l’indice de réfraction, nous souhaitons augmenter le caractère diffusant de ces matériaux, générant ainsi diffusion et localisation de la lumière. Toutes les caractérisations structurales et optiques ont été réalisées. En utilisant des modèles physiques, nous avons analysé les résultats et obtenu les paramètres critiques de transport (transport moyen, longueur d’onde d’adsorption et constante du diffusion). Ces matériaux présentent un fort comportement multidiffusif et éventuellement de localisation de la lumière. Ces matériaux très diffusants sont des candidats pour la génération de lasers aléatoires. Dans cette optique, nous les avons infiltrés avec de la rhodamine-6G (chromophores) et quantifié leurs propriétés comme lasers aléatoires.

Mots clés : matériaux poreux multi-échelles, systèmes à diffusion multiple et lasers aléatoires

Multi-scale porous materials designed for multiple light scattering/localization and random lasing

Abstract : Disordered, porous, white, hierarchical materials have been synthesized using a sol-gel process combined with the physical chemistry of complex fluids (emulsion, lyotrope mesophase). The whole process is known as integrative chemistry. By tuning the size of the scatters (pore diameters) and increasing the refractive index contrast, we want to increase the scattering strength of our materials, thus promoting light scattering/localization. The structural and optical characterizations have been performed. By using well established theories, we have analyzed our results and obtain the transport parameters (transport mean free path, absorption length and diffusion constant). The materials exhibit a strong multiple-diffusive behavior and an eventual localization of light. These strongly scattering materials would be of potential interest for random lasing applications. Therefore, we infiltrated them with Rhodamine 6G laser dyes and quantified their random lasing performances.

Keywords : multiscale porous materials, multi-diffusive systems and random lasers

Equipe d’accueil : Univ. Bordeaux, CNRS, CRPP, UPR 8461, F-33600 Pessac, France.

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Contents 3

Acknowledgement 7

Chapter I State of the Art 13

I Introduction 15

I.1 Light propagation through disordered media 15

I.2 Disorder materials as random lasers 20

I.3 Material aspects 23

II Problems and goals 29

III Description of the subsequent chapters 30

Chapter II Syntheses of Porous Materials and Structural

Characterisations 31

I Introduction 33

II Porous materials definition and their overall syntheses 34

II.1 Type of porosity 34

II.2 Dimension aspects 36

II.3 Porous materials syntheses 36

II.4 Inorganic polymerization; Sol-gel process 37

II.5 Soft templates using emulsion 38

II.6 Syntheses of SiO2(HIPE) 40

II.7 Syntheses of SiO2/TiO2 (HIPE) 41

III Structural characterizations 42

III.1 Macroscopic length scale: SEM 43

III.2 Mesoscopic and macroscopic length scale: Mercury porosimetry 44

III.3 Mesoscopic and macroscopic length scale: TEM-TED

and EDXS 45

III.4 Microscopic length scale: XRD 46

IV Conclusion 47

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Chapter III Fundamentals of Scattering/diffusion/localization and random

lasing with their Optical Characterizations Tools 49

I Introduction 51

II Light propagation through disordered media 51

II.1Scattering of light 52

II.2 Multiple light scattering 53

II.3 Anderson localization of light 54

III How to probe the light propagation behavior? 55

III.1 Transmission versus Length (T (L)) measurements 55

III.2 Time of flight measurements 57

IV Theoretical approach 59

IV.1 Classical diffusion approximation 59

IV.1.1 Stationary solution of the diffusion equation 62

IV.1.2 Dynamic solution of the diffusion equation 64

IV.2 Pre-localized regime 65

IV.2.1 Stationary solution 65

IV.2.2 Dynamic solution 66

V.1 Dye Infiltration and Thermogravitometric analysis (TGA) 67

V.2 Experimental setup for random lasing 69

VI Conclusion 70

Chapter IV SiO2 (HIPE) for multiple scattering/localization

and random lasing 71

I Introduction 73

II Results and Discussion: All Characterizations 73

II.1 Structural Characterizations 74

II.1.1 Macroscopic Length Scale: SEM Image Analysis 74

II.1.2 Mesoscopic and macroscopic Length Scale: Mercury porosimetry 76

II.2 Optical Characterizations 77

II.2.1Transmission versus length measurements 77

II.2.1Time of flight experiments 80

III Random Lasing 86

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III.1 TGA 87

III.2 Results and Discussion for random lasing 87

IV Conclusion 91

Chapter V SiO2/TiO2 (HIPE) for multiple scattering /localization and

random lasing 93

I Introduction 95

II Results and Discussion: All Characterizations 96

II.1 Structural Characterizations 96

II.1.1 Macroscopic Length Scale: SEM Image Analysis 96

II.1.2 Mesoscopic Length Scale: Mercury porosimetry 97

II.1.3 Mesoscopic Length Scale: TEM-TED and EDXS 99

II.1.4 Microscopic Length Scale: XRD 101

II.2 Optical Characterizations 102

II.2.1 Transmission versus length measurements 103

II.2.1 Time of flight experiments 106

III Random Lasing 108

III.1 TGA 108

III.2 Results and Discussion 109

IV Conclusion 114

Chapter VI Conclusions and perspectives 115

References 123

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Acknowledgement

For their kind co-operation to the completion of my thesis work, I would like

to gratefully acknowledge the enthusiastic supervision of Dr. Renaud Vallée

and Prof. Rénal Backov and, also, for providing me financial support in the

Ph. D. fellowship. It has been an honor to be their Ph.D. student. On one

hand, Dr. Vallée taught me how good experimental optics can be performed

and, always taught me to double-check the obtained results, in order to

ensure reproducibility and, also to ensure that obtained results are correct in

all respects. On the other hand, Prof. Backov trained me with the skills for

chemical synthesis and helped me to understand ‘Integrative Chemistry’. Out

of his very busy schedule, Prof. Backov was frequently visiting all of his

students to motivate and support them for quality research work, which

remains one of his speciality. I appreciate their contributions in terms of

their valuable time, innovative ideas, to make my Ph.D. experience

productive and stimulating. The joy, enthusiasm, and dedication they have

for their research was contagious and motivational for me. They have real

qualities to furnish and/or polish a student. I am also thankful for the

excellent example they have provided as a successful scientist, teacher and

motivator.

I am really grateful to DR Patrick Sebbah for his kind help/guidance and his

kind permission to carry-out random lasing experiments in his laboratory. I

have never seen such a kind and generous scientist like him.

I also greatly acknowledge all jury members DR Bernard Pouligny, DR.

Patrick Sebbah, Prof. Reinhard Höhler, Prof. Peter Hesemann, Dr. Renaud

Vallée, and Prof. Rénal Backov. All jury members were so kind and

supporting and they really suggested me to improve the quality of presented

thesis.

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The members of the NICE group have contributed immensely to my personal and

professional time at CRPP. This laboratory has been a source of friendship as well

as good advice and scientific discussions. I am especially grateful to Prof. Serge

Ravaine for his help/suggestions to better understand various chemical processes.

I am also thankful to all the members of NICE group, especially Béatrice

Agricole, Laurent Maillaud, Céline Leroy, Simona Ungureanu for their kind co-

operation.

I am also grateful to the Director of the CRPP lab, DR. Philippe Richetti, for his

kind permission to work in his laboratory. I am grateful to him to provide a very

positive and encouraging environment in his laboratory.

I am also very grateful to Isabelle Ly for her continuous help in extracting

beautiful SEM images of my samples. Without her dedication my thesis would

not be so attractive.

I am also thankful to the members of the Service Informatique especially Anne

Faq and Jean-Luc Laborde, for their constant help during my Ph. D. time. Their

help made me familiar to solve all software related problems. Special thanks to

Anne Faq for being kind friend whenever I needed her.

I am also grateful to the Mechanical Department of CRPP, especially Philippe

Barboteau and Jean-Yves Juanico, for their valuable contribution for

manufacturing all kinds of optical supports and stages. They were all the time

available to help us while we were setting up our optics laboratory.

Of course, without the library support, research work and thesis writing are not

possible and I am really grateful to Nadine Laffargue for her constant help for

providing journals/books when I needed them.

For my thesis, I have used various user facilities such as TGA, Mercury

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porosimetry, TEM-TED and XRD etc. And, for that, quite a number of people

were involved. I am thankful to all of them: Marc Birot, Alain Derré, Frédéric

Louërat, Elisabeth Sllier.

I believe that, without friends, any good or bad things are not possible and for this

long journey I really was with many friends namely - Hrshita, Usha, Anirban ,

Shri bharani, Vivien, Richa, Indrani, Dalice, Besira, Sapana, Parantap, Rupali,

Sudha and many more. I really cannot list all of them and thank them for being

with me and making my journey easy and enjoyable.

Last but not least, my loving dad and, both of my brothers (Anand and Kapil),

who were a source of constant inspiration for this long journey…but it was my

dad’s dream to see me as a ‘Doctor’. I am really thankful to GOD that I am

daughter of you dad.

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11

Dedicated

To

My Dad

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13

Chapter I State of the Art

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I. Introduction:

Electromagnetic radiation (light) shows a dual nature. It either consists of

waves (Christian Huygens) or particles (Isaac Newton). In the beginning of the

18th century, Young's double slit experiments showed clear evidence of the wave-

like nature of light (1). In the 19th century, the propagation of light was described

as a wave phenomenon. Through the work of Max Planck, Albert Einstein, Louis

de Broglie, Arthur Compton, Niels Bohr, and many others, it appeared that all

particles have a wave nature (and vice versa). From then, people started to explore

the benefits of light (photons) over the electrons for various applications. Since

the photon is a mass-less particle and can move faster than the electron, it is better

to use photons instead of electrons for various applications, i.e.

telecommunication purposes. The control of the light flow on a microscopic level

may equally well open a new era in the realms of computation, quantum

electronics, photonics, optical chips, and functional devices. E. Yablonovitch said

that everything we have done with the semiconductor will be done with the light

(2). Therefore, the aim is currently to control photons in the way that electrons

were controlled in microchips, or in integrated circuits. In 1987, E. Yablonovitch

and Sajeev John introduced the idea of photonic crystals where a control of the

propagation of light is possible (2, 3). These ordered (periodic) arrangements can

modify the transport of light and give rise to a photonic band-gap similar to the

electronic band-gap in semiconductors (2, 4). Due to the presence of the band-gap

in a photonic crystal, the propagation of light is inhibited at certain wavelengths

depending on the refractive index contrast and the geometry of the structure.

However, considering that the diversity of modern optical devices has

dramatically increased, there is now a plethora of new challenges in our quest for

new ways of controlling light.

I.1 Light propagation through disordered media:

Light can also be controlled in a non-periodic medium. Each non-periodic

medium is in a sense a unique structure. While, at first glance, it seems that no

‘universal behavior' can be traced with respect to light propagation in such a

medium, the definite laws of light propagation resulting from random scattering

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can still be evaluated. There are analogies between the length-dependent

resistance (and conductivity) of a conductor, coherent backscattering and

Anderson localization of light. Furthermore, there are well-identified classes of

aperiodic media featuring definite geometrical regularities, like e.g. fractal media

with self-similar geometry. Some 'universal behaviors' of light propagation

through such aperiodic media with well- defined geometrical algorithms have

been discovered to date and are still an issue of current research.

When a pulse of light passes through a photonic crystal without scattering, it will

generally emerge from the crystal in much the same shape (with some broadening

of the pulse owing to dispersion). But if the pulse encounters defects in the

crystal’s structure, they will cause its photons to scatter. This can cause a

transition on the propagation of light through the crystal from a predominantly

ballistic to a diffusive regime. In this regime, the photons entering the crystal as a

short pulse will leave as a drawn-out exponential. The duration of this exponential

(characteristic time) is directly linked to the diffusion constant. Diffusive transport

of light energy allows for light ray trajectories to be implied in the consideration

of light propagation. If light scatters so frequently that light rays have no chance

to be plotted between two scattering events, i.e. if diffusive transport is no longer

possible since even a single oscillation cannot be performed by a wave between

successive scattering events, the wave appears to be confined within a portion of

space with a characteristic size of the order of the wavelength. This ultimate limit

is known as the Ioffe–Regel (localization) criterion for mean free paths versus

wavenumber k = 2π/λ: kl < 1 and means that the wave localizes in a random

medium.

In 1958, P. W. Anderson arrived at the conclusion that electrons cannot diffuse in

a strongly disordered potential (5). This phenomenon is among the cornerstone

concepts of the theory of disordered solids and its place in solid-state physics has

been recognized by the Nobel Prize awarded to P. W. Anderson in 1977. It is

referred to as the Anderson localization. While being first introduced for electron

conductivity processes, Anderson localization is possible for all types of waves

provided the localization criterion is fulfilled in terms of sufficiently strong

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fluctuations of the physical parameters determining the speed of waves. For

electrons, fluctuation of potential is the proper physical parameter, whereas for

electromagnetic waves refractive index fluctuations are the relevant counterpart.

Generally, localization occurs more readily in space with lower dimensionality.

This is always the case for one-dimensional space provided a negligible disorder

is present. This is because there are no independent scattering processes in a one-

dimensional problem. In two dimensions, localization occurs under a certain

degree of disorder (depending upon system size and direction of observation),

whereas in three dimensions the disorder should be even stronger for localization

to occur. S. John was the first to outline the possibility of Anderson localization of

electromagnetic waves in 1984 (6). This report was followed promptly by the

elegant comment by P. W. Anderson (7) and since then localization of light has

become a challenge for experimentalists. However, experimental observation of

the Anderson localization of light is hard to perform and no straightforward report

on the observation of light localization has been reported up to now. The

principal obstacle is the relatively low refractive index of materials in the

optical range.

Experimental studies on Anderson localization of light have been reported in the

microwave regime (8-10), the near infrared regime (11), and the visible regime

(12-14).

For the near infrared, the highest refractive index values are inherent in Ge (n =

4), Si (n = 3.4), and GaAs (n = 3.37); for the visible these are GaP (n = 3.31),

ZnTe (n = 2.98), and TiO2 (n = 2.8). Not all of the above materials are readily

available in the form of a sub-micrometer powder. Not all of them are actually

suitable for experiment. For example, Si and Ge smaller particles readily acquire

an oxide shell in air.

D. Wiersma et al. (11) used GaAs powder samples with different average particle

diameters. A laser wavelength λ = 1064 nm was used, at which the absorption

coefficient of pure GaAs is α < 1 cm−1 and the refractive index is 3.48. Upon

reducing the average particle diameter, these authors found three distinctive

regimes of light propagation. The first one was the known T ∝ 1/L behavior

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inherent in typical diffusive light transport (for 10 μm particles). The mean free

path evaluated from the backscattering data and from the T ∝ l/L dependence had

the same value l=9.8 μm. A deviation from this law for thicker samples (L > 500

μm) was interpreted as a signature of absorption and estimated to have a

characteristic length labs ≡ α −1, with an absorption coefficient value α < 0.13 cm−1.

When the particle mean diameter goes down to 1 μm, the T ∝ l/L law was no

longer valid. Instead, a quadratic dependence T ∝ L −2 emerged. This type of

behavior was predicted by the scaling theory of localization at the localization

transition (7, 15). Finally, for smaller particle diameters of about 0.3 μm, an

exponential transmission versus length law was observed: T (L) ∝ exp (− L/lloc),

which is a distinctive manifestation of the light localization regime. The

characteristic scaling length parameter lloc appearing in this exponential decay is

called the localization length, which in the case under consideration was found to

be lloc = 4.3 μm. However, this exponential law formally coincides with the Beer-

Lambert-Bouguer law inherent in inelastic (absorptive) losses, expressed in the

form T (L) = exp(−L/labs ) to emphasize this similarity.

After the GaAs paper (11) came out, comments were raised by Scheffold et. al.

(16) to question whether these phenomena were purely related to absorption in the

sample.

Scheffold et al. examined the behavior of samples of large GaP particles. In this

case, the absorption coefficient was found to be rather small. However, an

increase of this absorption coefficient for sub-micrometer powder entities could

not be excluded. These comments were countered in a reply (17) by pointing at

inconsistencies in the arguments used by Scheffold et al. In experiments with Ge

powders (with n =4.1 in the near infrared, Ge is the best candidate for light

localization experiments), this material exhibited a non-negligible absorption

which did influence the transmission of light and partially contributed to the

exponential T (L) law observed (18). Therefore the issue of absorption and

localization in GaAs powders was difficult to resolve by only performing T(L)

measurements.

Further signatures of light localization are to be searched for. An important

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experiment would be to perform time-resolved transmission in which a drastic

reduction of the diffusion constant at the Anderson localization transition is

expected.

In the simulation done by Conti et al. (19) in the case of an inverse opal, for

moderate amounts of disorder above a certain value, the decay strongly deviates

from a single exponential and the distribution of characteristic times of the

emerging light splits into separate components with two different time constants.

The first component results from the expected delays induced by scattering. The

second component corresponds to a more pronounced critical slowing down of

photons arising from the population of localized states. Surprisingly, one finds

that this critical component only arises within a certain range of disorder, with the

localization length reaching a minimum at some optimal value and then

increasing once more with increasing disorder.

Back to experiments, Maret et al. (12, 20) performed experiments with dense TiO2

ground beads of a size close to the optical wavelength packed in dense layers of

1.2–2.5 mm thickness. They observed and reported increasing deviations at long

time from the exponential time dependence predicted by the diffusive transport

theory. For a sample with large kl value (as checked by coherent backscattering

experiments), the temporal profile of the output light pulse featured good

agreement with the theory of diffusive transport and exhibited an exponential tail

at long times. For smaller kl values, a discrepancy with the diffusive transport

theory manifested, which increased while kl was getting smaller and smaller. In

these cases, the transmission tail was found to be reasonably well described by a

modified diffusion equation taking into account a time-dependent diffusion

coefficient D (t). They found that D (t) beared witness to a decrease with time as

1/t, as expected from the theory of the localization regime.

The above results indicate that time-resolved light flight measurements offer

further insight towards discrimination of light propagation regimes near the

localization threshold.

Very recently, Beek et. al. showed that both the continuous wave and time-

resolved transports of light through GaAs powders can be fully described using

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the diffusion model (21). They observed very small absorption length (6.1 ± 1.9

μm) and transport mean free path (0.6 ± 0.2 μm). These results shed new light on

the absorption and localization debate from more than two decades ago (16, 20).

The scattering strength, expressed by the product of the wave vector and the

transport mean free path ‘l’ kl = 5.5 is, according to the Ioffe-Regel rule, not in

the regime where a transition into the Anderson localization is expected to take

place. They have used more than two types of samples: powder samples, porous

homogenous and inhomegenous ones. The homogenous sample has an average

pore size of 5 μm. Their time-resolved transmission profiles were exponential

decay curves, suggesting the absence of Anderson localization in the GaAs

ground samples. In their second step, they scratch the homogenous porous sample

(at the center of about 40 μm) to create the inhomogeneity. By using a position-

dependent time-resolved setup, they observed the scratched area of the

inhomogeneous sample. The obtained results showed a non-exponential decay at

long time scale and the value of the diffusion constant was varying (between 64

and 37 m2/s).

Therefore, up to now, only dense sample of TiO2 beads showed visible light

localization in three dimensional systems due to its high refractive index contrast

and absence of absorption in the visible. Our concern is to find other materials

suitable for light diffusion/localization purposes. In order to fulfill the Ioffe-Regel

criterion, material engineers should design materials with a strong scattering

strength which are non-absorbing.

I.2 Disordered materials as random lasers:

Scattering medias can be used to generate random lasing. To understand

the physics underlying the functioning of a random laser, fundamentals of

conventional lasers are required.

A conventional laser is typically constructed from two basic elements: a

material that provides optical gain via stimulated emission and an optical cavity

providing resonant feedback in order to trap light. When the total gain of the

cavity is larger than the losses, the system reaches a threshold and lases. The

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cavity determines the modes of a laser, i.e. induces the directionality of the

emission and its frequency.

Coherence of a laser emission and its strong dependence on the properties

of the cavity present a severe drawback for certain applications where high spatial

uniformity of illumination and high stability of the emission wavelengths are

desired. The frequency of the laser emission mode is sensitive to optical

alignment, thermal expansion of the resonator, mechanical vibration, and so on.

In order to overcome these issues and other disadvantages caused by the spatial

coherence of a laser beam, Letokhov et.al. have proposed in 1966 a new type of

laser where a non-resonant feedback occurred via reflection off a highly scattering

medium used in place of the optical cavity (22).

In 1967, Letokhov made one step further and theoretically predicted the

possibility of generating laser light through multiple scattering media in which the

light wavelength is much smaller than the dimension of the system (23). In the

proposed system, the scattering material at the same time played the role of an

active laser medium and an effective resonator providing nonresonant feedback.

Letokhov found that the solution of the diffusion equation for propagation of

emitted photons in an amplified medium diverges at some critical value of the

gain ‘g’ depending upon the characteristic size of the pumped medium B (B is

different for different shapes of the pumped volume) and the diffusion coefficient

D, g=DB2. Therefore by increasing either D or B, the gain will increase. The

critical value of g is associated with the threshold of stimulated emission in a

medium with gain and scatterers. That was probably the first report of what we

now call a random laser or powder laser. The proposed applications of an

incoherent random laser include a highly stable optical frequency standard and

express-testing of laser materials, which could not be easily produced in the form

of homogenous large crystals.

Experimentally, the first random laser like emission and properties were observed

by Markushev in 1986 in the powder of neodymium-activated luminophosphors

(Nd:La 2O3, 24). He found that above a certain pumping energy threshold, the

duration of the emission pulse shortened by approximately four orders of

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magnitude (this was at liquid nitrogen temperature). An approximately equally

strong enhancement was found in the intensity of the strongest spectral

component of the 4F3/2-4I11/2 emission transition (approx 1.06-1.08 µm), the line

width of which narrowed significantly (25). Only one narrow line is observed in

the spectrum above threshold (see Fig 1.1(b), (a) is the spectrum below

threshold). The intensity of this emission line plotted versus the pump energy

resembled the input-output characteristics of a conventional laser (fig 1.1 (c)).

Fig 1.1: Emission spectrum of Nd3+ transition at T=77k (a) below and (b) above threshold (c)

input-output power dependence curve of stimulated emission in Na5La1-x powder.

By increasing the scattering strength of a diffusive medium, one can enhance the

path of the pump light. These long paths are responsible for many of the salient

features of light in random media, such as enhanced backscattering and ultimately

light localization. In most cases, the light intensity is distributed throughout the

sample and the modes are extended. In others, light interference can lead to

Anderson localization for which the multiple scattering processes themselves are

inhibited. The average spatial extent of these localized modes defines the

localization length. Such localized states trap light and can lead to intense lasing

modes. Near the Anderson light localization, localized modes of the passive

system act like regular modes of a conventional cavity. They are not modified by

the presence of gain. By introducing local pumping to the system, selective

excitation of an individual localized mode is possible. Therefore, the emission

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spectrum is quite narrow at a very low lasing threshold. Such observation

constitutes in fact another approach to determine the scattering strength of the

investigated system.

In the case of 3D system, the multiple scattering of the pump light restricts the

excitation to the proximity of a sample surface. The emitted photons readily

escape through the sample surface, giving a high lasing threshold. In such systems

lasing is an issue. Many lasing modes appear at discrete frequencies, in spite of

tight focusing conditions. Therefore, the overall emission spectrum is broadened

and sharp peaks will not be clearly visible above threshold. Also, in case of

moderately absorbing materials, the non-uniform distributions of gain and

absorption could result in spatial localization of lasing modes in the pumped

region. In other words, local pumping in an absorbing medium creates a

“trapping” site for lasing modes.

Our concern is to observe the random lasing characteristics in 3 dimensional

disordered systems in order to complement the characterization of

diffusion/localization regime exhibited by our materials, performed by other

techniques.

I.3 Material aspects:

The idea of material comes from the natural sources, where we have

variety of disorder materials. One such type of system is the foam/porous

materials, containing gaseous voids surrounded by a denser matrix. These

materials have been widely used in the variety of applications, for example,

insulation, cushioning, absorbents, and weight-bearing structures (26). Depending

on the composition, cell morphology, and physical properties, polymer foam can

be categorized as rigid or flexible foams. Solid foams have cellular structures: the

word cell derives from the latin word cella, which means small compartment.

Cellular structures are common in nature; diatoms, lumbar vertebra, lungs, cork,

wood, sponge, and coral are example of this type of materials. Some of the natural

porous materials are shown in Fig 1.2 (a and b are the Biddulphia reticulate and

Diatoms which is the species of algae and c is the glass sponge which is the

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Fig.1.2: Biddulphia reticulate (a), Diatoms (b), glass sponge (c)

sponge with a skeleton made up of four and/or six-pointed SiO2 spicules (tiny

spike like structures). Mankind has used these natural cellular materials for

centuries and more recently has made its own cellular materials; polymers are the

most common, but now there are techniques allowing metal and ceramics to

fabricate in the cellular forms. The main areas of application of solid cellular

materials are buoyancy, thermal insulation, packaging, and structural uses,

catalysis, water cleaning, etc (27). Polymer foams represent a group of

lightweight materials that have been widely used in a variety of industries.

However, applications of foam are limited by their inferior mechanical strength,

poor surface quality, and low thermal and dimensional stability. Cellular polymers

are usually prepared by chemically-induced (effervescence), air injection foaming

or using biliquid foams as templates (28). In these cases, the control of the cell

size leads generally to the preparation of fully open-cell structures. Based on our

experience in air-liquid or biliquids foams used as templates we can estimate that

solid foams emerging from air-liquid foams are much more mechanically fragile

than the ones obtained though the use of biliquid foams. Therefore, the emulsion-

template approach to prepare polymer foam could represent an interesting

alternative. High internal phase emulsions (HIPEs) are an interesting class of

emulsions usually characterized by an internal phase volume fraction exceeding

0.74, the critical value of the most compact arrangement of uniform, undistorted

spherical droplets. Consequently, their structure consists of deformed (polyhedral)

and/or polydispersed droplets separated by a thin film of continuous phase, a

structure resembling gas-liquids foams. The internal or dispersed phase of HIPEs

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can be either polar or nonpolar. Therefore they can be, as ordinary emulsion,

classified into two categories: water-in-oil and oil-in-water (29). Fig 1.3 shows

the hierarchically synthesized porous materials under the laboratory environments

by using emulsion-template. A SiO2 photonic crystal of pore diameter of about 1

µm has been shown in Fig 1.3 a, synthesized by emulsion templating (30). As

emulsions are made of liquids, the droplets are easily removed by evaporation or

dissolution after the templating has been accomplished. They propose a method to

synthesize quite polydisperse macroporous materials of titania, silica and zirconia

with pore sizes ranging from 50 nm to several micro-meters. This technique can

be applicable to a wide variety of metal oxides, as far as the sol-gel chemistry is

well controlled, and even organic polymer gels. The method takes advantage of

the fact that the oil droplets are both highly deformable and easily removable. The

high deformability allows the inorganic gel to accommodate large shrinkage,

which prevents cracking and pulverization during ageing and drying. These

materials with the pore diameter comparable to the optical wavelength are

predicted to have a unique and highly useful optical properties, e. g. - photonic

bandgap and optical stop bands (31). Owing to the sol-gel chemistry and direct

emulsion template F. Carn et. al. synthesized SiO2 monoliths type material with

controlling pore diameters from nm to several microns (Fig 1.3 b) (32). They

obtained a hierarchically organized porosity and high internal surface area. By

increasing the oil volumic fraction of the starting emulsion above the typical value

of 0.74, they increase both the polydisperse emulsion viscosity and the shear

strength, so minimizing both the macroscopic cell sizes and the external junction

sizes while keeping the window cell diameters almost constant. Due to the high

internal surface area in porous materials with dense inorganic walls, gives rise to

maximal contrast of the refractive index between the matrix and the pores of the

material, which is an important characteristic for reaching high-performance

photo-band gap properties. There are a number of reasons why porous materials

are important and are used in various application(s) starting from photonics

(band-gap materials) (31), soft chemistry (shape selective catalysis) (33),

chromatography (34), batteries (35, 36) and bone implants (37) etc. Moreover,

26

many physical properties of porous structure such as density, thermal

conductivity, the mechanical resistance, or the permeability, are closely related to

Fig 1.3: Porous materials synthesized under the laboratory environments (a) SiO2

photonic crystal, (b) poly-HIPEs of SiO2 by Carn et al (32).

the solids. Thus, the control and/or the hierarchisation of porosity represent a

fundamental challenge for making of band-gap materials, catalysts, adsorbents, or

electrodes. Due to high internal surface area porous materials can be used in bulk-

chemistry applications e. g. - catalysis, in which reactant molecules need to be

readily access the interior pore structure but at the same time the internal surface

area is maximized, a ramified pore structure with large pores leading to smaller

and smaller pores is desired (similar to the structure of human lungs). Indeed, it

can be shown that the largest pores should form a 3D grid with the grid sections

subdivided by a sub-grid of smaller pores, and so on. Consequently, there is a

need to have complete control not only of the pore sizes at each dimension but

also the interconnectivity of these pores. Furthermore, for bulk applications it is

important that the preparation of such materials is straightforward, scalable and

eventually fairly inexpensive. Recently Brun et. al. have designed enzyme-based

biohybrid foams for continuous flow heterogeneous catalysis and biodiesel

production (38). In this context, they prepared the functional ordered macro-

mesoporous materials according to the concept of ‘‘integrative chemistry’’ (39).

They prepared the long monolith (Fig 1.4 d) using stainless column (b, c) and the

set up (a) shown for continuous flow. Those features, when applied to

transesterification (biodiesel production) via enzyme catalysis, provide among the

27

top enzymatic activities displayed by the bio-hybrid catalysts bearing

unprecedented endurance of continuous catalysis for a two month of period.

Fig.1.4 (e) shows the SEM image of monolith. This has an advantages of covalent

Fig.1.4: Pictures of: (a) the continuous flow set-up; (b, c) the as-synthesized column after 60 days

stabilization of the enzymes, together with a low steric of continuous flow transesterification

catalysis within the stainless steel canister; (d) the biohybrid macrocellular column extracted from

its canister after 60 days of continuous flow esterification catalysis. The two set of columns used

in this study are labelled col [CCR- lipase]@gGlymo-Si(HIPE) and Col[C-TL-lipase]@gGlymo-

Si(HIPE), (e) shows the SEM image of monolith.

hindrance between proteins and substrates, optimized mass transport due to the

interconnected macroporous network and simplicity with regard to the column in

situ synthetic path. The concept of immobilized biocatalysts, and have designed a

new series of biohybrid materials.

Another important application of these materials has been addressed by

Brun. el. al group in heterogeneous catalysis, separation techniques, absorbers,

sensors, optics. By using the above synthetic route (Integrative Chemistry), they

prepared macro-mesocellular hybrid foams (Eu3+@Organo-Si(HIPE)) (Fig 1.5)

28

and characterized their optical properties (absorption and emission) (40). From

this work, it is clear that these materials are quite useful for light emitting device.

Therefore, synthesizing this SiO2 (HIPE) and using it for optics is quite

reasonable from on the above facts. Using the same strategy, they combined with

foams (Lipase@Organo-Si(HIPE)), showed high catalytic performances. There

are several pathways that intend to synthesize ordered and disordered porous

materials. The integration of the sol-gel process with lyotropic mesophases,

supramolecular architectures, air–liquid foams, bi-liquid foams, external fields,

organic polymers, nanofunctionalization and nanotexturation, are an emerging as

a broad area of research and offers the possibility of achieving new architectures

Fig 1.5: Synthesized Organo-Si(HIPE) monoliths. (a) Eu3+@gβ- diketone-Si(HIPE)

(bearing the yellow color of the β-diketone silane derivative) and Eu3+@gmalonamide-

Si(HIPE) (white as malonamide silane derivative is colorless), (b)

Eu3+@gmalonamide-Si(HIPE) when irradiated under UV light (350 nm), and (c)

Eu3+@gβ-diketone-Si(HIPE) when irradiated under UV light (350 nm).

at various length scales and with enhanced properties. Current approaches to

hierarchically structured inorganic materials include coupling of multi-scale

templating that make use of self-assembled surfactant with larger templates as

emulsion droplets (41), air-liquid foams (42), latex beads (43), bacterial threads

29

(44), organogelators (45), controlled phase segregation (46), and nano- and

macromolding (47) etc.

II. Problems and goals:

From the “state of the art” literature survey, we know that there is

currently no experimental proof of Anderson light localization in the visible light

spectrum for 3D systems, the reason being mainly the lack of available materials

fulfilling the requirements of the Ioffe-Regel criterion. Main hurdles are to

construct non dispersive, high refractive index materials. While different scientific

groups have presented various arguments in favour of a localization behaviour,

like i.e. the quadratic dependence of the inverse transmittance as a function of the

sample using semiconductor materials (in transmission versus length

measurements), it was realized later that this behavior could be due to absorption.

Due to the lack of optical materials able to localize light in the visible range of the

spectrum, this field is still being explored and new materials are probed. In the

same context, we have hunted some potential disordered materials for light

localization purposes and the idea of such material comes from the natural source,

presenting a variety of disordered materials. Carn et al. showed a potential method

to synthesize porous, disordered, white, hierarchical materials by using integrative

chemistry (a sol-gel process combined with the physical chemistry of complex

fluids (emulsion, lyotrope mesophase). This method gives rise to a full control of

the morphology of the structure. Also, by mixing high refractive index metal

oxides, it is possible to enhance the refractive index contrast in these materials.

In this thesis, we aimed to and have synthesized 3D SiO2 (HIPE) and SiO2/TiO2

(HIPE) materials with a given control of the pore diameters, by varying the oil

volumic fraction. We expect these materials to have a large scattering strength,

thus promoting light scattering/localization. Strongly scattering materials would

be of potential interest for random lasing applications. These materials are like

white paints, can be successfully applied for various applications such as display

and or integrated chip technologies. We have quantified their diffusive regime and

random lasing performances by infiltrating them with Rhodamine 6G dyes. The

30

investigation of the light diffusing and or random lasing properties of these new

materials are reported here for the first time.

III. Description of the subsequent chapters:

Chapter II presents an introduction to porous materials and the various

methods used to synthesize disordered porous materials. The procedures to

synthesize SiO2 (HIPE) and SiO2 /TiO2 (HIPE) are described in detail. All

structural characterization tools (SEM, mercury porosimetry, TEM, TED, EDXS,

and XRD) are then discussed.

In chapter III, we first provide a basic theoretical description of light propagation

in disordered media via scattering/diffusion/localization. Then we describe the

experimental tools (time of flight measurements, transmission versus length

measurements) used to probe such phenomena. Finally, we discuss the

fundamentals of regular lasers and random lasers and the experimental setup used

to measure the laser characteristics.

In chapter IV, we describe all results obtained from the structural and optical

characterizations of pure SiO2(HIPE), using the characterization tools described in

chapter II and III. These results are fitted/analysed by the appropriate theories.

Finally, random lasing experimental results are described and discussed in detail.

In chapter V, we describe all results obtained from the structural characterizations

(SEM, mercury porosimetry, TEM, TED, EDXS, and XRD) of the

SiO2/TiO2(HIPE) composites. Then we describe results obtained from the optical

characterizations. Finally, we discuss the random lasing performances of these

composites.

In chapter VI, we conclude and present some future perspectives.

31

Chapter II Syntheses of Porous Materials and Structural

Characterisations

32

33

I. Introduction:

According to the first chapter, we can assume that disordered porous

materials can be the candidates of choice to trigger novel optical properties. In the

present chapter, we describe the fundamental questions, asked by the general

reader on the definition of porous materials and how can they be synthesized.

Beyond, the structural characterization techniques addressed to assess these

foams’ specific surface as well as bulk and skeleton densities are provided. The

properties of such solid state macrocellular foams are commonly dedicated to

heterogeneous catalysis, sensor, photovoltaic, drug delivery etc.(31-37) In the

present study we will use them for the first time for light their light transport

properties and more precisely for localization/diffusion and random lasing

applications. We have used some experimental techniques to structurally

characterize these porous materials such as Scanning Electron Microscope (SEM),

mercury porosimetery, Transmission Electron Microscopy combined with

Transmission Electron Diffraction (TEM-TED), and X-Ray Diffraction (XRD) to

obtain complementary structural information on the synthesized porous materials.

In the first step, a state-of-the-art bottom up approach (molecular chemistry

combines with the emulsion template) has been used to design polymerized High

Internal Phase Emulsion (poly-HIPEs) exhibiting a strong disorder in terms of

refractive index contrast. Owing to this approach, we are able to engineer silica-

based materials bearing controlled morphologies and textures (wall thickness,

wall curvatures, wall textural topologies, wall degree of mesoporosity, cell

diameter etc.). This emulsion-based templating route allows generating porous

hierarchical structures where photons can penetrate these solid foams internal

voids. The pores sizes, the pore monodisperse or polydisperse characters as well

as the wall density can be controlled through the adjustment of the oil volumic

fraction ‘f’ and the shearing rate. In the next step we have added 10 weight % to

15 weight % of Titania during the synthesis, with an objective of increasing the

refractive index contrast between the SiO2/TiO2 walls and the void spaces.

Thereby, by adding TiO2 in to SiO2 matrix, we intend to enhance the multiple

scattering. It is worth mentioning that titania exists in a number of allotropic

34

forms, the most important for optical applications are the ‘anatase’ or ‘rutile’

phases, the last being the TiO2 stable allotropic form. In order to assess which

form is present in the material, we have performed TEM-TED and XRD

analuyses. All structural characterizations technique(s) will be discussed hereafter.

II. Porous materials definition and their overall syntheses.

Porous materials are bi-phase medium which are composed of one continuous

phase (which can be solid or liquid) and while the dispersed phase is gazeous. A

simple example of the disordered porous material is shown in Figure2.1. The

cavities, containing gas, are named ‘pores’. The pores have small macroscopic

pore windows connecting to the porous template cells which are known as the

‘cell windows’. The volume occupied by the available porous environment, is

called apparent volume, and is composed of a solid part and it is denoted by Vs.

The volume of the porous network containing the gas phase of total volume is

denoted as Vp. In order to describe porous materials, several parameters are

necessary. Thus, one of the essential characteristics is related to the pore volumic

fraction, or internal porosity which is noted as φ, and defined as:

φ=Vp/Vs+Vp = (pore volume/ total volume)

II.1. Type of porosity:

Two types of porosities are described here at the macroscopic length scale.

The first one is known as “opened” or “connected” porosity where the cell walls

are broken and the structure consists of the ribs and struts. This type of porosity is

accessible to an external fluid. Other type of porosity is “closed” porosity where

the voids are isolated from each other and cavities are surrounded completely by

the cell walls. This type of porosity does not take part toward mass transport

properties. This topological distinction of porosity is intrinsically connected to the

type of applications when using these materials.

35

Fig 2.1: Represent the SiO2 disordered porous material (poly-HIPEs).

In the field of catalytic supports, the chromatographic filters, electrodes or

columns “open” porosity is useful. On the other hand, for their use as structural

material, where a “closed” porosity would be of use are - in soundproofing,

thermal or of mechanical energy absorption, and also for the light diffusion a

“closed” porosity would be of use. The second important parameter, directly

connected to the ratios of porosity, relates to the density of porous material.

Various type of densities, provide additional informations. The ‘skeleton’ density

is known as the real density of the materials. The skeleton density is defined as

the ration of the mass of the particle to the skeleton volume of the pores. Another

type of density is the bulk density, which is defined as the ration of the mass of

many particles of the material to the total volume they occupied. In this case, the

total volume includes particle volume, inter-particle void volume and internal

pore volume. Basically, each density is relative, and would represent different

values according to the characterization technique employed. Beyond the basic

concepts, it is of primary importance to define precisely the dimensional,

topological and morphological aspects of the pores, in order to be able to correlate

and capture the properties of materials.

36

II.2 Dimension aspects:

In natural porous materials the pore sizes can vary from angstroms (in zeolite

minerals) to nanometers (in leaf cellular structures) and to microns in diatom

skeletons for instance. The pores can be very uniform in shape and can cover a

wide range of pore sizes. The wall structure can be organized (crystalline) or

disorganized (amorphous). Finally, the chemistry (composition) of the wall can

vary enormously from oxide structures to functionalized polymers. According to

recommendations of International Union of Pure and Applied Chemistry

(IUPAC), three categories of the pores will be distinguished:

→The macropores, whose “diameter” is higher than 50 nm; and flow through the

macropores is described by the convection.

→ the mesopores, whose “diameter” lies between 2 and 50 nm; and flow through

mesopores is described by Knudsen diffusion (dispersion: a fluid is moving

through a weak convection in which molecules are diffusing).

→ the micropores, whose “diameter” is lower than 2 nm. Movement in

micropores is governed by activated diffusion (convection is negligible).

Our interest of pore sizes are lies in macroporous regime because our aim is to

enhance light-matter interaction for strong scattering. Therefore, we need a pore

diameter comparable to the light wavelengths.

II.3 Porous material syntheses:

Current approaches to synthesize hierarchically structured inorganic

materials include coupling of multi-scale templating that makes use of self –

assembled surfactant with larger templates as emulsion droplets, air-liquid foams

(41), latex beads(42), bacterial threads(43), organogelators (44), controlled phase

segregation(45) and nano macrmolding(46). Several synthetic methods to produce

hierarchical structures are multi-step processes and consequently there is an

impetus for low cost, one-pot, room temperature synthesis. In this regard, one

synthetic path was first published by Stucky and co-workers (47) using an

emulsion method to synthesize mesoporous silica. Using an emulsion method,

Imhof and Pine (30) has also reported the synthesis of ordered macroporous

37

materials. Subsequently, different research groups published various syntheses of

ordered macroporous materials using a mono-dispersed polystyrene monolith as a

template (48). Most of the methods allows producing an ordered macroporous

solid without meso- or microporosity or micro-mesoporous matter without the

macroporosity. The use of an emulsion makes the aim of producing materials

bearing hierarchical porosity (both macro-, meso and microporous) possible

where the macroscopic voids diameter falling into the range 50 nm - 50 μm (32).

II.4 Inorganic Polymerization: Sol-gel Process:

This reaction mechanism is quite popular in the polymerization of a silicon

alkoxyde and to control the morphology of the gel formed during the synthesis.

The latter point is of prime importance because it determines what will be the

final microporosity of the solid objects. The reaction pathways that we will

presents mainly are based on the work reported by Brinker et al (49). The sol-gel

process, as the name implies, involves the evolution of inorganic networks

through the formation of a colloidal suspension (sol) and gelation of the sol to

form a network in a continuous liquid phase (gel). The precursors for synthesizing

these colloids consists a metal or a metalloid element surrounded by different

reactive ligands. The starting material is processed to form a dispersible oxide and

forms a sol in contact with water or dilute acid. Removal of the liquid from the sol

yields the gel, and the sol/gel transition controls the particle size and shape. After

calcination of the gel to remove organic template we can produce the inorganic

oxides. Sol-gel processing refers to the hydrolysis and condensation of alkoxide-

based precursors such as Si(OEt)4 (TetraEthoxy-OrthoSiliane, or TEOS).

Materials prepared using this process when conbined with emulsions as template

are called, when dealing with silica, Si(HIPE) the acronym pending for High

Internal Phase Emulation (HIPE) due to high internal surface area. The reactions

involved in the sol-gel chemistry is based on the hydrolysis and condensation

reactions of metal alkoxides M(OR)z can be described as follows:

MOR + H2O → MOH + ROH (hydrolysis)

38

MOH+ROM→M-O-M + ROH (condensation)

Finally, resultant synthesis will provide metal oxides (M-O-M). Sol-gel method

of synthesizing nanomaterials is popular amongst chemists and is used to prepare

oxide materials. The sol-gel process can be characterized by a series of distinct

steps.

Step 1: Formation of different stable solutions of the alkoxide or solvated metal

precursor (the sol) where hydrolysis and condensation occurs.

Step 2: Gelation resulting from the formation of an oxide- or alcohol- bridged

network (the gel) by a poly-condensation reaction that results in a strong increase

in the viscosity.

Step 3: Aging of the gel, during which the poly-condensation reactions continues

until the gel transforms into a solid mass, accompanied by contraction of the gel

network and expulsion of solvent from gel pores. Ostwald ripening (also referred

to as coarsening, is the phenomenon by which smaller particles are consumed by

larger particles during the growth process) and phase transformations may occur

concurrently with aging. The aging process of gels can be completed, ranging

between 7-15 days and is critical for the prevention of cracks in gel(s) that have

been cast.

Step 4: Drying of the gel, when water and other volatile liquids are removed from

the gel network. This process is complicated due to fundamental changes in the

structure of the gel. The drying process has itself been broken into four distinct

steps: (i) the constant rate period, (ii) the critical point, (iii) the falling rate period,

(iv) the second falling rate period.

Step 5: Sintering of the gels at high temperatures (T>600°C).

Thus, depending on template, pore diameters greater than 100 microns can

be easily achieved. There are various hard and soft templates are discussed in the

literature such as phase separation, soft templates via emulsion, hard via polymer

beads (48) etc. Soft template approach(es) has been discussed in detail.

II.5 Soft templates: using emulsion:

39

An emulsion is a mixture of two or more liquids which are immiscible and

these are the part of a more general class of bi-phase systems of matter called

colloids. Although the terms colloids and emulsion are sometimes used

interchangeably, emulsion is used when both the dispersed and continuous phases

are liquids. In a direct emulsion, one liquid dispersed phase (oil) is dispersed in

the other continuous phase (water) (See Fig2.2 a). An emulsion is not

thermodynamically stable because of its high interfacial energy between the two

phases of water and oil. Several phenomenon as Ostwald ripening, coalescence,

Fig 2.2: Schematic representation of emulsion (a) and surfactant molecules (b).

drainage, will promote fast macroscopic phase separation between the oil and

water. Therefore, the stability of emulsions is defined kinetically, which means

that the rate of phase separation (relaxation) is slow in stable emulsions where

surfactant entities are used.

Indeed surfactant plays a significant role for the stability of an emulsion.

Surfactants are organic compounds that are amphiphilic, they contain both the

hydrophobic groups (in their tails) and the hydrophilic groups (in their heads)

(See Fig 2.2 b). The surfactant end with hydrophilic nature dissolves into the

water phase and the ends with hydrophobic nature dissolves into the oil phase.

Therefore, a surfactants are contains both water insoluble and oil soluble

components. Consequently, the hydrophilic and hydrophobic nature must be

balanced in the surfactant molecule and for this it has to work well as a good

40

emulsifier. Therefore, to obtain the stable emulsions without coalescence,

surfactant molecules must adsorb efficiently at the interface between the water

and oil phases. A good surfactant can lower the surface tension and the interfacial

tension between the two liquids. At low oil concentration the surfactant

molecules, if their concentration is posted above the critical micellar

concentration (C.M.C.), form micelles where oil droplets acts as a swelling agent.

The TEOS (TetraEthylOrthoSilane) will hydrolyse and condense and then will

bind to the swollen micelles so that the ultimate material is either a mesoporous

silica or a meso-cellular foam. There are various techniques to create templates

such as air-liquid foam, liquid-liquid foam etc. To prepare the monolith type

material, emulsion templates are quite promising and they can control the

morphology of the structure. Therefore, we have used emulsion template to

synthesize our porous materials.

II.6 Syntheses of SiO2(HIPE):

A sol-gel process has been used to obtain inorganic poly-HIPEs with a

procedure based on the use of both micelles and direct concentrated emulsion

templates (32). Tetraetoxy-orthosilane (Si(Oet)4, TEOS),

tretradecyltrimethylammonium bromide 98% (C14H29NBr(CH3), TTAB) were

purchased from Fluka, HCl 37% and dodecane 99% were purchased from

Prolabo. For the basic SiO2(HIPEs), typically 5 g of tetraethoxy-orthosilane

(TEOS) is added to 16.5 g of tetradecyltrimethyl ammonium bromide (TTAB)

aqueous solution at 35% in weight. The aqueous mixture is then brought to a pH

values close to 0 (by adding 6.7 ml of 37 % HCl). This aqueous phase was

continuously stirred for approximately 10 minutes in order to perform TEOS

hydrolysis. Then the emulsion was stirred manually using mortar by adding 35 g

of dodecane drop-by-drop in the as-prepared aqueous medium. This final

emulsion was then transferred into a long cylindrical container (or spread it to

obtain film) and left in this state for a period of one-week (shown in Fig 2.3). The

resulting material was then washed and calcined. To wash the monolith we have

used acetone/THF (1:1) mixture three times over a 24 hour period. Finally, to

41

remove the organic supramolecular-type templates, the hybrid organic-inorganic

materials were then calcined at 600°C for a period of six hours. The heating rate

was monitored at 2°C/min with a first plateau at 200°C for 2 hours. This basic

Figure: 2.3: One pot synthesis of HIPEs. (a) Adding oil drop by drop in continuous aqueous

phase (in mortar). (b) Spreading emulsion for condensation (c) Monolith of poly-HIPE sample.

materials are labeled as SiO2(HIPE). In this study we have performed the

syntheses of two pure SiO2(HIPE) foams emerging from the use of starting

concentrated direct emulsion at two different oil volumic fractions (f ) where 35 g

(f = 0.67) and 60 g (f = 0.78) of dodecane respectively are emulsified. Finally,

silica macrocellular foams are labeled as 35- SiO2(HIPE) and 60- SiO2(HIPE),

respectively.

II.7 Syntheses of SiO2/TiO2(HIPE):

In the second synthetic step, we have synthesized SiO2/TiO2(HIPE) by adding

titanium (IV) isopropoxide inorganic precursor with TEOS. The hydrolysis-

condensation reactions involved in silica polymerization are much easier to

control than that of SiO2/TiO2(HIPE). To obtain monolith-type material is the

difficult task for this composite material due to high shrinkage caused by sintering

effect in titania (discussed later). To prepare such hybrid structure, we have taken

a fixed oil volumic fraction (where f=0.67 means 35g of dodecane oil were used).

Titanium (IV) isopropoxide has been added in the aqueous solution of TTAB and

42

HCL and was stirred for minimum of 1 hour. Then TEOS was added in this

aqueous phase and was stirred for a minute and then emulsification process was

started by adding oil drop-by-drop. This final emulsion was then transfer into a

long cylindrical tube/ or spread like films and kept in this condition for more than

15 days in order to have condensation. We have applied thermal treatment to the

emulsion to enhance condensation process. We kept this cylindrical container in

an oil bath at 35° C for a period of 7 days prior to keeping it at room temperature

until completion. The resulting material was then washed with acetone and THF

(1:1) as mentioned above. Finally, to remove the organic supramolecular-type

templates, the hybrid organic-inorganic materials were calcined at 800 °C for a

period of 12 hours. The temperature used here is higher (800 °C) than the one

used for silica (600 °C), because we intend to obtain the rutile allotropic form of

titania. The main aim is to obtain rutile form is related to its refractive index.

Rutile form (2.6) of titania has higher refractive index than anatase form (2.4) of

titania. This higher refractive index material may improve multiple scattering. By

adding TiO2, we have synthesized two types of materials where 10 % and 15 % of

titanium (IV) isopropoxide weight added in 90 % and 85 % of TEOS weight

respectively. The samples are then labeled as 85/15-SiO2/TiO2(HIPE)and 90/10-

SiO2/TiO2(HIPE) where 85 and 90, 15 and 10 represents SiO2 and TiO2 weight

respectively. During the calcinations, these hybrid materials undergo strong

shrinkage. This high shrinkage is induced by the sintering effect, enhanced for

TiO2 by crystallization, where the amorphous microstructure switches towards the

ordered one. As we increase TiO2 in silica, shrinkage is further increased and it is

difficult to obtain a monolith or film after 15 % of TiO2. Therefore, we have only

synthesized upto 15 % of titania in 85% of silica matrix.

III. Structural characterization:

Structural characterizations have been performed on three scales: macroscopic,

mesoscopic and microscopic length scales. All the experimental techniques, used

for characterization of both type of HIPEs (SiO2 (HIPE) and SiO2/TiO2(HIPE))

are described in this section.

43

III.1 Macroscopic length scale; via Scanning Electron Microscopy (SEM):

A scanning electron microscope (SEM) is a type of electron microscope that

produces images of a sample by scanning over it with a high energy focused beam

of electrons. The electrons interact with electrons in the sample, producing

secondary electrons, back-scattered electrons, and characteristic X-rays (shown in

fig 2.4). Secondary electrons and backscattered electrons are commonly used for

imaging samples: secondary electrons are important for showing morphology and

topography on samples and backscattered electrons are important for illustrating

contrasts in the composition in multiphase samples (i.e. for rapid phase

discrimination via elemental analysis using EDAX). The electron beam is scanned

in a raster scan pattern, and the beam position is combined with the detected

signal to produce an image (shown inside computer in Fig 2.4). The electron

Fig 2.4: Schematic of scanning electron microscope.

beam can be focused on to a spot of approximately 1 nanometer in diameter, and

microscopes are able to resolve details ranging from 1–20 nm in size. To avoid

accumulating charge on the surface, samples must be electrically conductive; non-

conducting samples are often coated with an ultrathin coating of carbon or gold

44

materials. SEM analysis is considered to be "non-destructive"; that is, electron

beam generated by electron interactions do not lead to volume loss of the sample,

so it is possible to analyze the same materials repeatedly. We have performed

SEM observations with a Jeol JSM-840A scanning electron microscope, operating

at 10 kV. In our case, the specimens were carbon-coated prior to examinations.

We have also performed elemental analysis (using EDAX) along with SEM

observation on our silica/titania composites. All results are discussed in chapter V

and IV.

III.2 Macroscopic length scale; Mercury porosimetry:

In order to provide foams skeleton, bulk densities and to quantify the

macroscale void windows distributions, we have performed mercury intrusion

porosimetry (MIP) measurements. At this point we have to specify that this

technique measures the size of the macroscopic pore windows between the

emulsion template cells and not the diameter of the cells themselves. This

technique is based on the premise that a non-wetting liquid (one having a contact

angle greater than 90°) will only intrude pore windows under pressure. The pore

size can be determined based on the external pressure needed to force the liquid

into a pore against the opposing force of the liquid's surface tension. The

relationship between the pressure and pore windows diameter is described by

Washburn as:

P*=-4γ cosθ/d

Where P is pressure, g is surface tension of the liquid, θ is the contact angle of the

liquid and d is diameter of the pore windows. Total porosity is determined from

the total volume intruded. The MIP technique is widely used because of its ease

and simplicity. Since the technique is usually done under the vacuum, the gas

pressure remains zero. The contact angle of mercury with most solids is between

135° and 142°. The surface tension of mercury at 20 °C under vacuum is 480

mN/m. Obtained values from MIP are given in chapter IV and V for all our

samples.

45

III.3 Mesoscopic length scale; TEM-TED, HR-TEM and EDXS:

High resolution transmission electron microscopy (HR-TEM) have been

performed on SiO2/TiO2(HIPE) composites. We have performed HR-TEM using a

JEOL JEM 2200FS microscope operating at an accelerating voltage of 200kV

with a resolution down to the nanometer scale (~ 0.19 nm). The samples for

electron microscopy were prepared by grinding and subsequent dispersal of the

powder in ethanol and applying a drop of very dilute suspension on carbon-coated

grids. The suspension was then dried by slow evaporation at ambient temperature.

In the transmission electron microscope (TEM), electrons are transmitted through

a thinly sliced specimen and form an image on a fluorescent screen or

photographic plate (Fig 2.5). Those areas of the sample that are more dense will

transmit fewer electrons (i.e. will scatter more electrons) and will therefore appear

darker in the image. TEM’s can magnify up to one million times and are used

exclusively in Biology and Medicine to study the structure of viruses and the cells

of animals and plants. The following diagram shows the basic structure of a

TEM. This HR-TEM has a resolution down to nanometer range and can form an

highly resolved image (shown on computer screen in Fig 2.5). This HR-TEM

provides two modes for obtaining diffraction patterns from individual crystallites.

This technique provides a two-dimensional pattern of diffraction spots, which can

be highly symmetrical when a single crystal is oriented precisely along a

crystallographic direction (see inset of Fig 2.5 shown on computer screen). This

HR-TEM utilizes a new, rotation-free image-forming optical system which not

only facilitates acquisition of TEM images and diffraction patterns but also

produces elemental analysis with higher accuracy than the SEM with EDXS.

From this HR-TEM we have performed elemental analysis on our samples using

Energy-dispersive X-ray spectroscopy (EDXS). It relies on the investigation of an

interaction of X-ray with the sample. Its characterization capabilities are due in

large part to the fundamental principle that each element has a unique atomic

structure as a unique set of peaks in its X-ray spectrum. To stimulate the emission

of characteristic X-rays from a specimen, a high-energy beam of charged particles

such as electrons, or a beam of X-rays, is focused onto the sample under

46

investigation. At rest, an atom within the sample contains ground state (or

unexcited) electrons in discrete energy levels or electron shells bound to the

nucleus. The incident beam may excite an electron in an inner shell, ejecting it

from the shell while creating an electron hole. An electron from an outer, higher-

energy shell then fills the hole, and the difference in energy between the higher-

energy shell and the lower energy shell may be released in the form of X-rays.

The number and energy of the X-rays emitted from a specimen can be measured

Fig 2.5: Schematic of Transmission Electron Microscope.

by an energy-dispersive spectrometer. As the energy of the X-rays is characteristic

of the difference in energy between the two shells, and of the atomic structure of

the element from which they were emitted, this allows the elemental composition

of the specimen to be measured. EDXS via TEM is much more accurate than the

EDXS with SEM because it has higher energy and really can deal with the atomic

levels.

III.4 Microscopic length scale; XRD:

X-ray diffraction techniques are a family of a non-destructive analytical

technique which reveals information about the crystal structure, chemical

47

composition, and physical properties of materials and thin films. These techniques

are based on observing the diffracted intensity of an X-ray beam hitting a sample

as a function of incident and scattered angle, polarization, and wavelength or

energy. In order to determine the allotropic form of titania in SiO2/TiO2(HIPE)

composites, we have performed XRD on these samples. The diffraction patterns

were collected on a PANalitycal X'pert MPD Bragg-Brentano θ-2θ geometry

diffractometer equipped with a secondary monochromator over an angular range

of 2θ = 8-80°. Each acquisition was completed in 34 minutes. The Cu-Kα

radiation was generated at 40 KV and 40 mA (lambda = 0.15418 nm). The

powder samples were kept on the sample holders made up of silicon wafer and

flattened with a piece of glass. Results are discussed in chapter IV and V.

IV. Conclusion

In the first part of this work, we have synthesized SiO2 (HIPE) and SiO2/TiO2

(HIPE)s using the so-called integrative chemistry synthetic path, combining sol-

gel process, emulsions and lytropic mesophases. Details on synthetic paths and

characterization tools have been described in this chapter. Results for all structural

characterizations performed on the materials are given in chapter IV and V.

48

49

Chapter III Fundamentals of multiple scattering/localization and random lasing with

their Optical Characterizations Tools

50

51

I. Introduction:

Experimental investigations of light propagation through disordered

materials are discussed in the current chapter. The various types of poly-HIPEs,

introduced in chapter II, are highly disordered, porous and poly-dispersed

materials. These materials are white and thus highly diffusive. To enhance

multiple scattering and promote localization of light, some fundamental

requirements have to be fulfilled such as i) scatters must have a size comparable

to the wavelength of light and ii) the refractive index contrast must be high

enough. We give in this chapter the details of the diffusion/localization theories

that will be used later to characterize our disordered materials. Two types of

characterizations have been performed: i) Transmission versus length (T(L))

measurements which allow us to determine the transport mean free path lt and

absorption length la of the material and ii) Time of flight measurements, which

allow us to determine the diffusion coefficient D0 of the material. Using our

dedicated code written in Octave/Matlab, we have analyzed/fitted the

experimental data with the expressions derived from the relevant

diffusion/localization theories and obtained ls, la, and D0 of the various materials.

In a subsequent section, we provide the details of the experimental setups that

have been used to perform the T (L) and time of flight measurements. Synthesized

materials have also been investigated for their potentialities in random lasing

applications. We finish this chapter with a description of the experimental setup

used for random lasing, experiments performed in the group of Dr. P. Sebbah at

ESPCI (Paris) and describe the analysis of the data obtained.

II. Light propagation through disordered media:

Non-periodic (disordered) structures can strongly affect light transport.

For particles that do not mutually interact (i.e. photons), transport through a

disordered medium is described by multiple scattering, due to the

inhomogeneities of the medium. Here are some fundamental processes described

to understand light propagation.

52

II.1 Scattering of light:

Scattering is a general physical process where some forms of radiation,

such as light, sound, or moving particles, are forced to deviate from a straight

trajectory by one or more localized non-uniformities in the medium through

which they propagate. Scattering of light will lead to diffraction or transmission

depending upon the medium characteristics (shape, size and arrangement of

particles). If radiation is only scattered by one localized scattering center, it is a

single particle scattering (see Fig. 3.1).

Fig 3.1: Schematic representation of single particle scattering. a is the size of the scatterer.

In general two types of scattering phenomena occur; one is elastic scattering and

the other one is inelastic scattering. In the process of elastic scattering, the kinetic

energy of the incident particle is conserved (no exchange of energy to or from the

electromagnetic fields) and only their direction of propagation is modified by the

interaction with other particles. However, in the case of inelastic scattering, the

kinetic energy of an incident particle is not conserved (i.e. there is exchange of

energy to or from the electromagnetic fields). In the later case, some energy of the

incident particle is lost or gained. Furthermore, scattering is characterized by two

important parameters: the size of the scatterer ‘a’ and the refractive index contrast

between the scatterer and the background medium. Depending upon the size of

the scatterers three types of scatterings process are described below.

1. Rayleigh scattering: Scattering of light by particles (i.e. atoms, molecules, and

53

very fine dusts) much smaller than the wavelength (a <<λ) is called Rayleigh

scattering. Its hallmark is the proportionality of the scattering cross section to

1/λ4. As is well known, scattering of light in the atmosphere is accurately

described by Rayleigh scattering. The strong dependence on the wavelength

causes blue light to be scattered more efficiently than red light, accounting for the

blue sky and the red sun at the sunset.

2. Mie scattering: Particles with a size of about a wavelength (a ~ λ) can produce

strong resonances due to interference in the scattered field.

3. Geometric optics: For scatterers much larger than the wavelength, geometric

(ray) optics can be used and light is pictured as a ray inside the material. This type

of scattering is witnessed by natural marvels like the rainbow.

II.2. Multiple light scattering:

When light travels through a disordered/inhomogeneous system, it is multiply

scattered. Straight or ballistic propagation cannot accurately describe the transport

of light in such a system. Anything turbid like e.g. clouds, fog, white paint, human

bones, sea coral, and white marbles scatter light multiply. The multiple scattering

process can be easily understood by the following picture (Fig 3.2) representing

the complicated path followed by light in a disordered medium (cloud). The

Fig 3.2: Light multiple scattering (a) and schematic representation of a disordered medium where

ls is the average distance between two scatters (b).

scattering strength depends upon various parameters such as the size of the

54

scatter, the wavelength of interest, and the average distance between two

scatterers (mean free path ‘ls’ shown in Fig 3.2 b). If the scatterers are identical

and can be characterized by a scattering cross-section σ, the mean free path is

equal to (N*σ)-1 where N is the scatterers concentration. White light undergoes a

random walk and, if the scattering strength is not very large (relatively low

refractive index contrast), the whole transport regime can be accurately described

as a diffusion process.

In our study, we aim to determine the transport parameters ls, and D pertaining to

our samples. From them, we will determine the transport regime followed by light

in these samples: multiple scattering in the case of weak scattering and

localization in the case of strong scattering.

II.3. Anderson light localization: This phenomenon is named after the American

physicist P. W. Anderson, who was the first one to suggest the possibility of

electron localization inside a semiconductor, in case of sufficiently large

randomness of the impurities or defects (5). Beyond the critical amount of

impurity, scattering, diffusion, zigzag motion of the electron is not just reduced, it

can come to localization and the conductivity vanishes. Therefore, the conductor

becomes an insulator. The key concept in that description was the mean free path

‘ls’, the average length over which an electron travels before it collides with an

ion. According to the classical theory, the electronic conductivity is directly

proportional to the electron mean free path. Thus, the larger the number of

impurities presents in the material, the smaller is the mean free path and,

accordingly, the lower is the conductivity. To distinguish diffusion and

localization on the basis of the scattering strength, Ioffe & Regel have given

limiting criteria. They predicted a localization to occur, featuring a transition from

metal to insulator when k*ls ≤ 1 (where k = 2π/λ) is satisfied (50). Anderson

localization is a general wave phenomenon that applies to the transport of any

kind of waves, would it be acoustic, spin etc. In the optical regime, anything

turbid scatters light diffusively. The scattering strength of natural disordered

materials is too weak to obtain Anderson light localization.

55

Our aim is thus to synthesize materials with a large scattering strength and

avoiding light absorption, in order to localize light. Up-to-now, this is a very

challenging and tricky task in case of three dimensional systems.

III. How to probe the light propagation behaviour:

There are various experimental techniques which allow one to investigate

light diffusion/localization behavior. In this section, we are describing two types

of experimental techniques: transmission versus length and time of flight

measurements. These techniques have been shown to be successful in

discriminating between diffusion, absorption, and or localization processes (12).

III.1 Transmission versus length T (L) measurements:

In such measurements, the static transmission through various samples of

different thicknesses is collected. Figure 3.3 schematically sketches the setup used

to perform the transmission versus length measurements. Material slabs with

different thicknesses are placed on the entrance aperture of an integrating sphere

and illuminated with a white light lamp (fiber coupled white light HL-2000-HP-

FHSA, Ocean Optics). The integrating sphere (fiber coupled integrating sphere

FOIS-1, Ocean Optics) consists of a hollow cavity with its interior coated for high

reflectance. The output is recorded by a spectrometer (fiber spectrometer

USB2000+VIS-NIR, Ocean Optics) and the data are sent to the computer. Fig

3.4.a shows the bare transmission signal S collected from L=1 to 10 mm sample

thicknesses for 1 second acquisition time. These samples are optically very thick.

It can therefore be assumed that only diffusive light comes out at any angle from

the sample and enters in the integrating sphere. This bare transmission S is

normalized by the reference (R) and dark signals (D) (shown in Fig 3.4.b) by

using the following formula

The reference signal is the signal of the white lamp used and the dark

signal the one recorded in absence of incidence light. Such signals are obtained

56

Fig 3.3: Schematic representation of the setup used to perform the static light measurements. A

slab of poly-HIPE with thickness L is placed at the entrance of an integrating sphere and

illuminated with white light. Diffuse light is measured at the detector, integrated over all angles.

Fig 3.4: a. Bare transmission S for various sample lengths (from L=1 to 10 mm) and b shows the

normalized transmission properly defined as T= S-D/R-D.

57

for all wavelengths extending from 450 nm to 850 nm. Taking two particular

wavelength (500 and 700 nm), we then plot the inverse transmission 1/T as a

Fig 3.5: Inverse transmittance for all sample thicknesses (from L=1 to 10 mm) at two wavelengths

500 (red stars) and 700 nm (blue stars).

function of thickness L in Fig. 3.5.

From such a plot, and by using the stationary solution of the classical

diffusion equation as a fitting equation (Section IV), we are able to obtain the

transport mean free path and absorption length of this type of diffusive samples.

III.2 Time of flight measurements:

In these measurements, the time-dependent transmission of the incident

pulse is collected through the sample. Our aim here is to determine the diffusion

coefficient. Fig 3.6 shows the schematic of the time-resolved system in which we

have used a combination of a femtosecond laser in the excitation path and a streak

camera in the detection path. The femtosecond laser source (from Amplitude

System) delivers pulses of 300 fs with a repetition rate of 10 MHz at a wavelength

of 1030nm.

58

Fig 3.6: Schematic representation of the experimental setup used to perform time-resolved light

measurements. A femtosecond laser pulse is sent to the sample. A spectrometer collects the pulse

temporally spread by the sample and sends it to the streak camera.

By doubling this wavelength of 1030 nm owing to a SHG (Second Harmonic

Generation) crystal, we can get the output in the visible range (at 515nm). The

laser beam is then focused onto the disordered material. Due to multi-diffusion in

our material, the output pulse is spread in time (depicted in Fig 3.6 inside the

computer image). The temporally spread pulse is then collected by the

spectrograph (from Princeton) and sent to the streak camera. The Hamamatsu

streak camera (HAMAMATSU Streak scope C10627), has a temporal resolution

of around 20 ps. From this geometry, we thus get the time of flight of outgoing

photons from the structures (a time profile is shown in Fig 3.7 for a diffusive

sample of Polystyrene beads of 1 micrometer diameter in solution in a 1 mm thick

cuvette in red circles). To obtain the material dynamic parameters, the

experimental data are fitted by the time-dependent solution of the classical

diffusion equation (in blue). Due to the experimental acquisition procedure, a

59

slight deviation appears at long times with respect to the behavior predicted by the

classical diffusion model, which is not a sign of pre- localization, since this type

of sample is not subject to localization.

Fig 3.7: Transmition versus time of a diffusive sample of PS beads in solution.

IV. Theoretical approach:

As explained in the previous sections, in order to determine the transport

parameters, the data originating from the T (L) and time of flight measurements

must be fitted. In order to provide the functions to be fitted, we describe in this

section two theories applying respectively to the multi-diffusive (or weakly

scattering) regime and to the pre-localization (or strongly scattering) regime. Both

theories are considered in static and dynamic perspectives. The goodness of the

fits originating from one or the other theory will give us an idea of the transport

regime obeyed by our samples.

IV.1 Classical diffusion approximation:

The multiple scattering of light is a very complicated solution of Maxwell

equations, when many scatterers have to be taken into account. The diffusion

approximation considers a random walk of photons and imposes a continuity

equation for the light intensity I(r, t) (where r is space and t is time), disregarding

the interference effects. Propagation of light can, therefore, be viewed as a

diffusion process such as gasses which diffuse in a partial pressure gradient. The

60

diffusion equation can be derived in a straightforward way from the continuity

equation, which states that a change in density in any part of the system is due to

inflow and outflow of material into and out of that part of the system. Effectively,

no material is created or destroyed:

where ϕ(r, t) is the density of the diffusing material at location r and time t and j

is the flux of the diffusing material. The diffusion equation can be obtained easily

from this when combined with the phenomenological Fick’s first law, which

assumes that the flux of the diffusing material in any part of the system is

proportional to the local density gradient:

3.2

If D (diffusion coefficient) is constant, then:

3.3

In the case of light diffusion, ϕ(r, t) is replaced by I (r, t), which is the light

intensity. In disordered materials, the light intensity will decay for various

reasons. The most important parameter is the scattering mean free path ‘ls’ which

is the average distance between two consecutive scattering events. This parameter

sets the limits of the diffusive approximation as λ<< ls<< L: many scattering

events occur before the light leaves the system, where L is the length of the

system while the medium is still diffuse. After several scattering events, the light

propagation is completely randomized. The transport mean free path ‘lt’ is defined

as the average distance after which the intensity distribution becomes isotropic

and is the characteristic length in the regime of multiple scattering. The transport

mean free path ‘lt’ is related to the scattering mean free path ‘ls’ as lt=ls/(1-cosθ)

61

where θ is the average angle between incident light and scattered light. If one

consider the transport of ballistic or un-scattered light in a medium at position (r)

and time (t), it follows the Lambert-Beer equation where the intensity is

maximum at r=0 and exponentially decaying with li, the absorption length

3. 4

By using Eq. 3.3, in a diffuse system, light propagates according to the diffusion

equation as follows:

3. 5

where S(r, t) is the light source (given later), νe is the energy velocity (velocity of

the transported energy given by the ratio of the energy flux to the energy density

at any point in the sample) and li is the absorption length, over which light is

attenuated by a factor e−1. This equation describes how light intensity spreads

through the system with a rate of transport dictated by the diffusion constant, D.

The larger the diffusion constant, the faster is the transport process. The whole

diffuse transport propagation will be truncated by an absorption term which

is the characteristics time over which light is absorbed in the system. Multiple

light scattering increases the interaction between light and the disordered medium.

The diffusive absorption length, la, is the distance light propagates diffusively

before being absorbed. Inside a diffusive and absorbing material, la is the

penetration depth of the diffuse light. Diffuse light propagates a greater distance

than in a homogeneous material to reach the same depth because of the random

walk performed by light. For this reason, la is shorter than li ( ).

The experimental systems treated in this work have a slab-like geometry which

imposes some boundary conditions on the diffusion equation: the system can be

considered infinite for x and y directions and limited between z = 0 and z = L.

Within the diffusion approximation, only diffusive light can be handled and,

62

therefore, an incident plane wave cannot be inserted as source in the diffusion

equation: it decays exponentially inside the system. The incoming coherent flux is

replaced by a source of diffusive radiation at the plane z = zp , where zp is the so

called penetration length. A common phenomenological way to introduce a source

(51) is to consider an exponentially decaying one,

or a delta function that is infinite at z=zp,

Two types of boundary conditions exist, Dirichlet and Neumann boundary

conditions. Dirichlet boundary conditions, imposed on either an ordinary or a

partial differential equation, specify the values a solution needs to take on the

boundary of the domain while Neumann boundary conditions specify the values

that the derivative of a solution is to take on the boundary of the domain. In our

case, Dirichlet boundary conditions are appropriate and imposed to the diffusion

equation as follows:

3. 6

where ze1,2 are the extrapolation lengths, of the order of ‘lt‘, which are the

positions where the diffusive light intensity would be zero if the light source

would be placed inside the system and, eventually, may be different at the front

and back surfaces (if their reflectivities are different).

IV.1.1 Stationary solution of the diffusion equation:

The stationary solution of the diffusion equation (3.5) with boundary

conditions as given in (3.6) and for a delta source leads to the total transmission of

light through a sample slab given by (52):

63

3.7

Where

and 3. 8

In the solution, α = 1/ li is the inverse absorption length and R is the

polarization and angular averaged reflectivity of the boundaries (53). Figure 3.8

represents a scheme of the light intensity versus distance I(z), assuming a delta

source (vertical black line) for a slab geometry system with the parameters related

to the diffusion equation such as ze and zp, which are typically set to be identical

(ze = zp).

A very important function to take into account is the total transmission of

light integrated over all angles, which is defined as the total flux at z= L divided

by the incident flux S(0):

3.9

In the absence of absorption and for L>>lt, we can expand sinh(x) in a Taylor

series limited to the first order term to obtain the total light transmission.

= 3.10

where ze ˜ lt since, by definition, lt at the order of the length for which the light

intensity is completely randomized.

Therefore the total transmission (equation 3. 10) reduced as:

3.11

64

Figure 3.8: Plot of the light intensity vs. distance in a slab of a poly-(HIPE). The dash line

represents the solution to the diffusion equation assuming a delta source placed at Z=Zp.

Extrapolation length Ze and penetration length Zp are shown.

The total light transmission through a multiple scattering slab in the

absence of absorption is directly proportional to the transport mean free path lt

and inversely proportional to the slab thickness. Doubling the thickness of the

(optical) conductor halves the transmission. This is known as the photonic Ohm’s

law.

In the case of an absorbing sample, by using Eq. 3.9 as the fit function of

the inverse light transmission versus sample thickness in T(L) measurements, it is

possible to obtain the absolute values of the transport mean free path lt and

absorption mean free path la.

IV.1.2 Dynamic solution of the diffusion equation:

The full solution of the time-dependent diffusion equation (eq. 3.5) with

boundary conditions is given by (54):

65

3. 12

where

and 3. 13

is the absorption or inelastic time. The rate of diffuse light transport in such a

disordered system is defined by the diffusion constant D, given by the Fick’s law

(55).

The dynamic solution of the diffusion equation including absorption is a sum of

exponentially decaying functions. Absorption in homogeneously absorbing

sample simply introduces a multiplicative exponential factor. The physical

meaning of the summation in equation (3. 12) can be understood as follows: light

which follows the shorter optical paths through the slab is transmitted at earlier

times while the light which performs longer random walks emerges much later.

The total transmission is therefore, given by the sum of all these contributions.

This produces a time-spread of the initial pulse, which depends on the diffusion

constant. This time dependent solution of the diffusion equation (Eq 3.12) is an

exponential decay at long time, with the asymptotic form:

3. 14

IV.2 Pre-localized regime:

In the case of a pre-localization (strong scattering) regime, the stationary

and dynamic solutions show different features. In this section, we describe the

solutions modified by the local scale theory of localization as introduced by

Berkovits and Kaveh (56).

IV.2.1 Stationary solution:

As discussed earlier, light diffusion in a disordered, non-absorbing multi-

66

diffusive dielectric slab, leads to the photonic Ohm’s law. In a moderately

absorbing system, Ohm’s law will not hold anymore. Furthermore in case of

strong scattering (k.ls ≥1) the system is predicted to exhibit a quadratic

dependence of inverse transmission (1/T ∝ L2) with respect to the system size,

according to the scaling theory of light localization at the localization transition

(16). The averaged transmission coefficient of a wave near the transition will thus

change from T = ls/L in the weak-disorder limit (ls >>λ) to

T=( ls/L)2 in strong-disorder limit, ls ~λ. 3.15

Observing such a quadratic dependence in the T(L) measurement could be the

signature of the light localization transition. However, moderately absorbing

sample may also show such kind of quadratic dependence. Therefore to

investigate the exact reason of an observed quadratic dependence of inverse

transmittance versus thickness, we must proceed to further investigate.

IV.2.2 Dynamic solution in the pre-localization regime:

In their local scaling theory of localization (56), Berkovits and Kaveh have

calculated the time dependence of transmitted pulses through the slab geometry.

The diffusion constant has been shown to be time-dependent and follows the law

(57-60)

3.16

where τ is the elastic scattering time ls/c, D0=(1/3)c*ls and ξ is the correlation

length.

According to this time-dependent diffusion constant, Berkovits and Kaveh

predicted a time dependence of the transmitted wave for an initial injected narrow

pulse of the form

3.17

An asymptotic form of T(t) near the transition is given by

3.18

This form features a departure from the single exponential decay at long time.

67

To analyze the time of flight experiments, we fitted the decay profiles with

both equations 3.14 and 3.18. If, at long times, the obtained decay profile is a

single exponential form, the scattering is weak and the sample is simply,

classically multi-diffusive. In that case, it is best fitted by the function 3.14. On

the contrary, if the long time decay presents a departure from the single

exponential behavior, it will be best fitted by function 3.18, as shown in chapter

IV and V. This departure from the single exponential law then points to as system

more likely to be in the pre-localization regime.

V.1 Dye infiltration and TGA for random lasing: For the sake of random lasing

investigations, we have infiltrated an active medium in our bare SiO2 and

SiO2/TiO2(HIPE)s. We have chosen Rhodamine 6G laser dyes (shown in Fig 3.9)

as a gain medium because its optical properties such as quantum efficiency,

emission and absorption spectra etc. are well-known. Rhodamine 6G is a laser dye

which is commercially available. This dye is pumped by the second (532 nm)

harmonic from a Nd:YAG laser. The dye has a remarkably high photo-stability,

high fluorescence quantum yield (0.95), low cost, and its lasing range has close

proximity to its absorption maximum (approximately 530 nm). The lasing range

of the dye is between 555 to 585 nm with a maximum at 566 nm.

In order to infiltrate dye molecules in our HIPEs, we have dipped our materials in

the dye solution. However, we have observed that their surfaces are only

absorbing the dye molecules but dye is not able to penetrate the material. When

we drop HIPEs in the dye solution, we have observed that the sample was lying

on the top of the solution. The main reason is that these HIPEs are full of air and

to infiltrate them by the dye first we have to extract the air. Therefore, we have

applied vacuum of 10 mbar for 2 hrs to extract the air from the HIPEs and allow

the out flow of the dye solution from material. To confirm HIPEs infiltration, we

have cutted our sample in two pieces (so that we can see an inner part of the

sample) and kept under the UV lamp to observed irradiance. We have taken fixed

initial concentration (2*10-3 Mol/liter) for all HIPEs. But different structure

absorb different amount of dye depending upon their bulk densities. Therefore, in

68

order to know the exact amount of dye molecules within the structure, we have

Fig 3.9: Rhodamine 6G dye molecule.

performed thermogravitometric analysis (TGA). Thermal gravimetric analysis is a

type of testing performed on samples to determine changes in weight in relation to

a temperature program in a controlled atmosphere. Such analysis relies on a high

degree of precision in three measurements: weight, temperature, and temperature

change. To determine composition and purity one must take the mass of the

substance in the mixture by using thermal gravimetric analysis. In the first step,

we heat our composite at high temperature so that one of the components

decomposes into a gas and dissociates into the air. It is a process that utilizes heat

and stoichiometry ratios to determine the percent by mass ratio of a solute. If the

compounds in the mixture that remain are known, then the percentage by mass

can be determined by taking the weight of what is left in the mixture and dividing

it by the initial mass. Knowing the mass of the original mixture and the total mass

of impurities liberating upon heating, the stoichiometric ratio can be used to

calculate the percent mass of the substance in a sample. In our case, increasing the

temperature Rhodamine molecule decomposes and SiO2(HIPE) or

SiO2/TiO2(HIPE)s materials remains indestructible. Therefore from the weight

loss (in percentage) caused by the dye molecules represent the amount of dye

within the structure. Using bulk density and weight loss, we are able calculate dye

molecules per unit volume. Results of thermogravitometric analysis have been

given in chapter IV and V.

69

V.2 Experimental setup for random lasing:

We have explained the working principle of random lasers as well as their

typical characteristics in chapter I. In this section, we will discuss the

experimental setup (Fig 3.10) used at IL-ESPCI to investigate random lasing. The

second-harmonic output of a nanosecond Nd3+: YAG laser (at wavelength: 532

nm, pulse duration: 6ns, repetition rate: 5 Hz) was focused at the front surface of

Fig 3.10: Schematic representation of the experimental setup used to perform random lasing. A

nanosecond laser pulse is sent to the poly-HIPE sample. The output emission is collected in the

backward scattering geometry using a fiber placed at 45 degrees with respect to the normal of the

spectrometer. A filter F is used to cut the pump beam.

the poly-HIPEs self standing film by a lens of 10.0 cm focal length to excite R6G

molecules embedded in the HIPEs. The sample is placed beyond the focal point

of the lens to avoid damage and/or bleaching of dye. The emission of the dye

molecules from the sample is then collected in the backward scattering geometry

using a fiber placed at 45 degrees with respect to the normal to the sample

surface, and recorded using an Ocean Optics HR4000 spectrometer. This

spectrometer has a peak-to-peak spectral resolution of about 0.11 nm. Before the

spectrometer, we have used the band pass filter F (to cut the line 532nm and allow

long-pass emission from 540nm) to cut the pump beam. Recorded spectra will

70

give us the output intensity counts versus wavelength. An energy meter

(resolution 5 µJ) has been used to record the input energy. Using this geometry we

have systematically investigated the occurrence of random lasing and the

input/output characteristics of the materials. The obtained experimental data of

output versus input intensities have been fitted to obtain lasing threshold (in

chapter IV and V).

VI Conclusion:

In this chapter, we have developed a fundamental understanding of how

light propagate through disordered materials. The first part of this chapter was

specifically devoted to the theoretical and experimental approaches for

investigating scattering/diffusion/localization and random lasing. We have shown

the experimental setups allowing us to collect the transmitted light in disordered

media. The obtained results are discussed in chapter IV and V.

71

Chapter IV SiO2 (HIPE) for multiple scattering/localization and random lasing

72

73

I. Introduction:

Among the various materials available for photonics, SiO2 is probably one of

the most promising and renowned candidate for various optical applications. It is

important because of its low cost, compatibility with electronics, and established

fabrication techniques (30, 31, 39, 61). This material can be grown in a ordered or

disordered form using various effortless procedures. In chapter II, we have described

the sol-gel process allowing us to synthesize porous disordered SiO2 structures.

Generally, this material is white and non-absorbing in the visible range of the light

spectrum. It is white for large enough thicknesses and thus is beneficial for

localization/diffusion processes. In the current chapter, we discuss the optical properties

of SiO2 (HIPE)s. Two type of materials, namely 35-SiO2(HIPE) and 60-SiO2(HIPE),

have been structurally and optically characterized. Structural information on these

materials was obtained on macroscopic length scales using SEM and mercury

porosimetry. Results are discussed in the current chapter. After reporting on the

structural characterization results, we report on the light transport parameters of these

materials. Optical measurement, combining steady-state and time-resolved detections,

in the far field, are used to characterize the photon transport parameters (e.g., mean free

path, absorption length, diffusion coefficient, etc.). We show that a reduction in size of

the pores and an increased monodispersity of their distributions occur as the oil volumic

fraction (f) is increased, leading to a decrease of the transport/absorption mean free

paths and diffusion coefficient. The stationary solution of the diffusion equation has

been used to fit the static experimental data and results are discussed in detail. Two

different theoretical approaches have been used to fit the dynamic experimental data:

one is the classical diffusion approximation and the other one is the scaling theory near

the localization transition. Both approaches were discussed in detail in chapter III. From

this study, we are able to understand/characterize our highly complex disordered

materials. In a next step, we have used these materials for random lasing investigations.

By minimizing the transport mean free path and diffusion constant, we expected to

lower the random lasing threshold. Performance on random lasing and complete set of

results are shown in the subsequent sections.

II. Results and discussion; All characterizations:

74

Two types of materials (35-SiO2 (HIPE) and 60- SiO2 (HIPE)) are characterized

structurally and optically. Experimental details of the characterization setups are

described in chapter II and III. The experimental results are fitted using the theories

discussed in chapter III.

II.1 Structural characterizations:

Structural characterizations were performed using SEM and mercury

porosimetry. Both types of structural characterization are given in this section in detail.

II.1.1 Macroscopic length scale via SEM:

Owing to scanning electron microscopy (SEM), we have obtained structural

information, mainly the pore size distributions. The SEM has been described in chapter

II. Obtained SEM images are shown in Fig 4.1. An inorganic film-type material (Fig.

4.1.a) depicts the polymerized (HIPE) type interconnected macroporous texture with

poly-disperse cellular sizes within the micrometer range (4.1. b and 4.1.c). At this point,

we would like to mention that we call “windows” the holes, which separate two

adjacent macroscopic cells. To measure the pore diameters distribution, SEM image

analyses have been performed. As we increase the starting emulsion oil volumic

fraction (f), the macro-cellular cell sizes diminish drastically (see Fig. 4.1 b to c) and

the size, mono-dispersity of their distributions is reduced from 10 − 40μm to 1 − 3.5μm

(shown in Fig. 4.2, SEM image analysis data). In fact, considering the emulsion

rheology, it is well known that the viscosity of the direct emulsions increases

dramatically when the oil volumic fractions access the value 0.74 (62, 63). For the

starting emulsions of the materials 35-SiO2(HIPE) and 60- SiO2(HIPE), this

phenomenon increases the shear applied on the oily droplets minimizing thereby their

sizes.

Furthermore, as seen in Figs. 4.1 b, the macroporous monolithic texture resembles

aggregated hollow spheres. Indeed, in such low pH (0.035) conditions, the

polycondensation is strongly Euclidian (49) (dense) and starts at the oil/water interface.

In fact, the oil-water interface is promoting silica condensation by minimizing the

nucleation enthalpy, acting so as a defect (64). We may argue that this feature is valid at

75

FIG. 4.1: SEM micrographs of the 35-SiO2(HIPE) (b) and 60-SiO2(HIPE) (c).(a) shows a 35- SiO2(HIPE)

monolith.

the micelles interface too, but the Euclidian character of the on growing network is

addressed with solubilization-reprecipitation, the recipritation (nucleation) will occur at

Fig 4.2: Normalized size distributions (dotted red lines: 60-SiO2(HIPE); solid black lines: 35-

SiO2 (HIPE)) of pore diameters.

76

the interface bearing the lower curvature, this is to say the oil/water interface droplets

and not the micelles interfaces, if working above the critical micellar concentration

(CMC). Also, it the oil-water interface of an emulsion is associated to a higher

surfactant concentration than the core of the continuous aqueous phase (64). In our case,

this specific region of high surfactant concentration is also enhancing silica

condensation through minimizing electrostatic repulsions or achieving faster inorganic

precursors electroneutrality favoring the nucleation. As a consequence of the reduction

of the macroporous void space diameters from the 35- SiO2(HIPE) foam to the 60-

SiO2(HIPE), we expect the light transport parameter to decrease in the 60-SiO2(HIPE)

structure with respect to those of the 35-SiO2(HIPE) .

II.1.2 Macroscopic length scales via mercury porosimetry:

In order to provide foam skeletal, bulk densities and to quantify the

macroscale void windows distributions, we performed mercury intrusion

porosimetry measurements. At this point we have to specify that this technique

measures the size of the macroscopic pore windows between the emulsion

template cells and not the diameter of the cells themselves. Overall, if we increase

the condensation at the interfaces by minimizing the oil droplet diameters and by

optimizing the droplets number, we increase the number of cell walls per unit of

volume, leading to formation of a material with a larger bulk density (Table 4.1)

Materials Oil volumic Porosity Skeleton Bulk

fraction (%) density density (g/cm3) (g/ cm3)

35-SiO2(HIPE) 0.67 91 1 0.083

60-SiO2(HIPE) 0.78 77 0.98 0.23

TABLE 4.1: Mercury intrusion porosimetry data of two samples (35-SiO2 (HIPE) and 60- SiO2 (HIPE)).

and larger shrinkage. The skeleton densities are smaller than 1.2 (silica density)

77

because the foam walls are indeed bearing a large degree of meso-porosity (Fig.

4.1b, spheres have small pores). Increasing the oil volumic fraction, the porosity

of the material is reduced in 60-SiO2(HIPE) as compared to 35-SiO2(HIPE). The

60-SiO2(HIPE) is thus denser than the 35-SiO2(HIPE). For denser sample, a

stronger multiple scattering is expected. Furthermore, due to the the high bulk

density of the denser sample, this material will also absorb more dye molecules,

i.e. the amount of gain medium to promote random lasing.

II.2 Optical characterization:

Two types of materials (35-SiO2 (HIPE) and 60- SiO2 (HIPE)) are

characterized on the steady-state level and dynamically. Results are reported in

this section. Experimental details of the setups are described in chapter III. The

experimental results are fitted with the equation originating from the various

theories mentioned in chapter III.

II.2.1 T(L) experiments:

White light transmission versus length experiments, T (L), have been

performed on the two types of samples with more than 20 thicknesses ranging

between 1 and 10 mm. Figs 4.3.a and b exhibit the conductance versus thickness

behavior for the (35-SiO2(HIPE) and 60-SiO2(HIPE)) samples at two different

wavelengths (blue stars: 500nm and red stars: 700 nm). These experimental

results have been fitted by the stationary solution of the diffusion equation (Eq

3.9) including absorption (blue and red solid lines in Fig. 4.3). Using this fitting

function, we obtained the transport mean free path lt and the absorption length la

for the full range of wavelengths displayed by the white light illumination (from

500 to 800nm). The obtained values of lt and la are plotted in Fig 4.4 and 4.5. The

transport mean free paths at 515 nm of 35-SiO2(HIPE) and 60-SiO2(HIPE) are 86

μm and 19 μm respectively. Their absorption mean free paths at 515 nm are 2.9

and 1.5mm, respectively. A common behavior for transport mean free path is to

vary with frequency. However, both Fig. 4.4.a and 4.5.a exhibit a rather flat

dependence of lt on wavelength (especially around 515 nm, which we will use

78

Fig 4.3: Inverse transmittance versus thickness behavior for 35-SiO2(HIPE)(a) and 60-

SiO2(HIPE)(b) at λ=500 nm (blue circle) and at λ=700 nm (red circle) fitted by the stationary

solution of diffusion equation (blue and red solid line respectively) as well as by the 1/T∝ L2 law(

dotted lines). Inset shows the residuals of the fits.

79

Fig 4.4: Wavelength dependent transport mean free path (a) and absorption length (b) of 35-SiO2(HIPE).

later as excitation wavelength for dynamic measurements and random lasing

experiments), excluding the possible occurrence of a wide variety of T(L) due to

the large spectral width of the incident light. As expected, the transport mean free

path is shorter for the HIPE presenting the smaller pore sizes. Also, the latter

being the denser sample, it exhibits the shorter absorption length. The stationary

solution of the diffusion equation including absorption fits particularly well the

experimental data, providing values for the transport mean free path such that k*lt

>> 1. Although these values are inherent to diffusive light transport, the plots

shown in Fig. 4.3 exhibit a quadratic dependence (1/T ∝ L2) (black dash lines in

Fig. 4.3) rather than a linear relationship, expected from the classical diffusion

(equation 3.11) in the absence of absorption. At first, E. Abrahams et al. and later,

Wiersma et al. used the scaling theory of localization and predicted that this type

of quadratic dependence may appear near the localization transition. This

observation lifts the issue of whether the quadratic dependence 1/T ∝ L2 provides

evidence that the described systems are near the localization transition or simply

reflects the diffusive behavior in moderately absorbing samples. In order to solve

this issue, we performed dynamic measurements of pulse transmission through

80

the samples.

Fig 4.5: Wavelength dependent transport mean free path (a) and absorption length (b) of 60- SiO2(HIPE).

II.2.2 Time of flight experiments:

The experimental setup used to perform time resolved measurements is

described in chapter III (Fig. 3.6). Using this experimental setup, we have

performed time of flight experiments on various samples, with thickness ranging

from 1 to 10 mm in the case of 35-SiO2(HIPE) and from 1 to 4 mm for 60-

SiO2(HIPE). Figure 4.6 shows typical results for three 35-SiO2(HIPE) samples of

thicknesses 2.26, 4.05, 5.84 mm. The insets exhibits a part of the corresponding

measured streak plots. These plots are bi-dimensional with the horizontal and

vertical axis being wavelength and time delay between excitation and detection,

respectively. The top left plot displays the pulse characteristics with a spectral and

temporal width of 1.4 nm around 515 nm and 80ps, respectively. Clearly, the

samples exhibit a strongly multi- diffusive character, with photons being

significantly delayed in the samples in all cases. As the thickness of the sample

increases, the mean exit time of the photons also increases, and the pulse is

delayed more and more in time. The insets from Fig 4.6 clearly indicate a

broadening of the spectral width with respect to pulse profile shown on the top

left of the Fig 4.6.a. This broadening is of course not related to the mixing of

81

frequencies originating from the source but merely results from the multiple

scattering of light within the sample, leading to divergent outgoing beams focused

by the lens at slightly different positions on the entrance slit of the spectrograph.

Furthermore, there is a huge strengthening of the multi-diffusive process while

densifying the sample. The dynamic measurements of 60-SiO2 (HIPEs) for three

different thicknesses are shown in Fig 4.7 a, b, c, with thicknesses of 1, 2.71, 3.49

mm, respectively. The 60-SiO2(HIPE) with a thickness L = 3.49 mm (Fig 4.7 c)

shows a time profile more extended than to the one exhibited by the 35- SiO2

(HIPE) with a nearly similar thickness L = 4.05 mm ( fig 4.6 b), indicating that

the time delay (i. e. the multiple scattering path) is more important in the denser

sample.

We have chosen time windows of 2ns, 5ns, 10ns or 20ns, depending on the

samples characteristics. For all time windows, we have a fixed number of data

points equal to 240. If the time window is too short with respect to the typical

time spent by the photons in the sample, we loose the information pertaining to

the tail of the time profile. On the contrary, if the time window is too long, we

loose the temporal resolution on the measurement. For example, Fig 4.8. a and b

show the same sample measured on two different time scales (2 ns and 5 ns).

From Fig 4.8 a, the relevant part of the decay profile is clearly longer than 2 ns.

We thus loose the long time behavior of the multi-diffusive process. By choosing

a time window of 5 ns, we evidence the long time behavior while keeping enough

data points to have a good resolution (Fig 4.8 b). All time profiles have been fitted

by the asymptotic form of the classical diffusion equation mentioned in Eq 3.14

(blue dashed-dotted lines). Clearly, substantial increases in transmission relative

to that predicted by the diffusion model are observed at long times. Measurements

in the time domain make it possible to unravel the effects of absorption.

Absorption in homogeneously absorbing samples simply introduces a

multiplicative exponential factor in time. All photon paths emerging from the

sample at a given delay time t have the same length and have suffered the same

diminution due to absorption. Because the weight of the path distribution is not

changed by the absorption at a given t, and since all partial waves arriving at a

82

fixed time are equally suppressed by the absorption, weak localization is not

Fig 4.6: Time of flight experiments (red circles with black connecting line) performed on 35-SiO2

(HIPE). Figures a, b, c correspond to samples of 2.26, 4.05, 5.84 mm thicknesses, respectively.

The pulse temporal profile is shown in the top figure (a, solid black line). The fits corresponding

to the asymptotic form of the time dependent diffusion equation (blue dashed) and to the

asymptotic form of T(t) near the localization transition (green dashed lines) are also shown. The

insets show the streak plots from which the profiles are built (pulse streak plot on the top left).

83

Fig 4.7: Time of flight experiments (red circles with black connecting line) performed on 60-SiO2

(HIPE). Figures a, b, c correspond to samples of 1, 3.71, 3.49 mm thickness, respectively. The fits

corresponding to the asymptotic form of the time dependent diffusion equation (blue dashed) and

the other fit corresponding to the asymptotic form of T(t) near the localization transition (green

dashed lines) are also shown. The insets show parts of the streak plots from which the profiles are

built.

84

Fig 4.8: Time of flight experiments (red circles with black connecting line) performed on 60-Si

(HIPE). Figures a, b correspond to samples of 2.05 mm recovered with time windows of 2 ns and

5 ns respectively. The fits corresponding to the asymptotic form of the time dependent diffusion

equation (blue dashed) and the other fit corresponding to the asymptotic form of T(t) near the

localization transition (green dashed lines) are also shown.

affected by absorption in the time domain. The influence of a kind of pre-

localization regime can be seen as a reduction of the decay rate with increasing

time delay. As this is precisely what is seen in Fig 4.6 and Fig 4.7, we have fitted

the experimental results with the asymptotic form of T(t) near the localization

transition, mentioned in Eq. 3.18 of chapter III, featuring a time dependent

diffusion constant D(t) = D0(τ/t)1/3, where τ is the elastic scattering time. These

asymptotic forms (green-dashed lines) provide better fits of the recorded data then

85

Scholar no. 35-SiO2 (HIPE) 60-SiO2 (HIIPE)

L D0 L D0

Thickness (in mm) (in m2/s) Thickness (in mm) (in m2/s)

1. 2.26 2858 1 360

2. 3.21 3780 1.67 600

3. 4.05 4224 1.89 650

4. 5.84 4350 2.05 790

5. 6.25 6520 2.63 760

6. 6.27 6577 2.71 820

7. 7.91 8050 3.49 1110

8. 9.45 9730

9. 10.4 9930 Table 4.2: Diffusion constant versus thickness of 35-SiO2 (HIPE) and 60-SiO2 (HIIPE).

the asymptotic blue-dashed forms. The values of the diffusion coefficients

extracted from the asymptotic forms (from Eq 3.18) are given in table 4.2 for both

SiO2 (HIPE)s. Obtained diffusion constants versus thickness are plotted in fig 4.9.

These plots show that the diffusion constants of 35-SiO2(HIPE) and 60-

SiO2(HIPE) are linearly dependent functions of the thickness. Other materials, for

example biological membranes, have been reported to exhibit size-dependent

diffusion constants (65, 66). The obtained values of both diffusion coefficients

and transport mean free paths, in this study, are nearly two orders of magnitude

larger than those measured by Storzer et al. in very dissimilar structures (67). It is

very remarkable that our very low refractive index n ~ 1.1 SiO2(HIPE)s exhibit

time transmission profiles with clear deviations from diffusive regime. Taken

together, the quadratic dependence 1/T ∝ L2 observed in Fig. 4.3 and the long

time departure from a single exponential decay observed in our time of flight

experiments, clearly indicate a non-standard diffusive transport regime of our

samples. Since the value of the diffusion constant and the transport mean free path

are far from the localization criteria, we cannot univocally certify that the non-

86

classical diffusion regime that we observe is a true pre-localization regime. In all

respect, the complexity certainly originates from the hierarchical porosity of our

material.

Fig4.9 Diffusion constant versus thickness behavior for the 35-Si(HIPE) (black star) and 60-

Si(HIPE) (blue star) fitted by using linear fit (in red solid line).

III Random lasing:

In order to perform random lasing experiments in our highly disordered

systems, we have infiltrated samples with Rhodamine 6G. The dye infiltration

method is described in chapter III. We have performed random lasing experiments

on the two type of samples: 35-SiO2 (HIPE) and 60-SiO2(HIPE). After optical and

structural characterizations, we know that 60-SiO2 (HIPE) has smaller pore

diameters and lower tansport parameters (lt and D0) than the 35-SiO2 (HIPE).

Therefore we expect to have lower lasing threshold in the former sample. TGA

analysis and random laser properties are discussed in this section in detail.

III.1 Thermogravitometric analysis:

From TGA measurements, we can obtain the percentage of weight loss

within the structure. From the weight loss, we can calculate the number of dye

87

molecules per unit volume. The data are given in table 4.3. Once we know the

amount of dye molecules within the structure, we can normalize the random

lasing data for each material. TGA analysis reveals that 60-SiO2 (HIPE)s has less

weight loss than 35-SiO2 (HIPE) (table 4.3); these structures thus contain a

smaller amount of dye molecules. By taking into account the bulk density of the

structure (which is higher for the denser sample), we have however obtained a

number of molecules per unit volume larger for 60-SiO2 (HIPE) (given in table

4.3).

35-SiO2 (HIPE) 60-SiO2 (HIPE) Weight loss No of molecules/volume Weight loss No of molecules/volume

(in %) mol/cm3 (in %) mol/cm3

7.9 0.15*10-4 6 0.31*10-4 Table 4.3: TGA data of two samples 35-SiO2 (HIPE) and 60-SiO2 (HIPE).

III.2 Results and Discussion for R.L.:

The experimental setup is described in chapter III (Fig 3.14). We have

performed random lasing experiments on two types of samples: 35-SiO2 (HIPE)

and 60-SiO2 (HIPE) with, for example, 4.66 and 4.74mm thicknesses. Results are

shown in Fig 4.10 and 4.11. the emission spectra of 35-SiO2 (HIPE) shown in Fig

4.10.a clearly show that, with increasing the input intensity, the output intensity

also increases. It is clear that the line-width narrows as a function of increasing

pump power. For large enough input power, narrow spikes appears on top of the

emission spectra (in Fig 4.10.b). At three points, we have calculated the Full

Width at Half Maxima (FWHM) (bottom, middle and top which are 12.11, 5, 0.6

nm, respectively). On top of the emission profile (in Fig 4.10.b), the FWHM

reduces to less than a nanometer, featuring random laser spikes in our material.

The characteristics output versus input pump energy (Fig 4.10c) looks like a

conventional laser characteristics (see chapter III in Fig 3.9). Fitting these

experimental results, using linear fits, we are able to obtain lasing thresholds as

88

Fig 4.10: Random lasing performed on 35-SiO2(HIPE) @4.66 mm thickness. Emission spectra are

shown in (a). Narrow spikes on the top of the emission profile are zoomed in (b). Input/output

power dependence is shown in (c); black stars are the experimental data points and red solid lines

are linear fits.

the cross-sections (in red solid lines) of horizontal and vertical lines from Fig

4.10c. These linear fits match well with the experimental data, with an accuracy in

the determination of the parameters larger then 98% for the horizontal (Horizontal

regression coefficients; H.R.C.) and vertical regression coefficients; V.R.C.) (see

table 4.4).

89

Fig 4.11: Random lasing performed on 60-SiO2(HIPE) @4.74 mm . Emission spectra are shown

in (a). Narrow spikes are zoomed in (b). Input/output power dependence is shown in (c); Black

stars are the experimental data points and red solid lines are horizontal and vertical linear fit.

In a second step, repeating the measurements on the same spot of the sample, we

have replicated the experimental data. Our results are thus fully reproducible and

further indicate that the dyes are not bleaching too fast. Off-course illuminating

the sample with a high power for more than 2-3 minutes leads to a bleaching of

the dyes in our materials. We have observed that the HIPEs themselves are not

damaged by continuous exposure to the high intensity pump beam: they are hard

enough to sustain the large excitation. We have also performed these experiments

while changing the spot position on the same sample and observed similar results.

The random lasing thresholds determined for all our experiments on this sample

are given in table 4.4. Similar experiments have been performed on 60-

SiO2/TiO2(HIPE) sample. Results are shown in figure 4.11. These samples also

90

show random lasing characteristics (i. e. narrowing of the emission lines as a

function of power (Fig. 4.11 a) and threshold behavior (Fig. 4.11 c)) and exhibit

very sharp peaks on top of the emission profiles (see the zooming area Fig 4.11

b).

Repeating the similar measurements as described above at the same spot position,

we are able to reproduce the results. The lasing characteristics are collected in

table 4.4. By changing the spot position, we repeated the measurements and

observed almost similar lasing thresholds in all cases. We have compared the

results of the 35-SiO2 (HIPE) and the 60-SiO2 (HIPE) on the basis of lasing

performances, shown in table 4.4. Clearly, the threshold values are larger for the

60-SiO2 (HIPE)s than for the 35-SiO2 (HIPE)s. These observations are

counterintuitive with the facts that the denser 60-SiO2 (HIPE)s have i) smaller

pore size distributions and ii) more dye molecules per unit volume than 35-SiO2

(HIPE)s. The lasing threshold is higher in the denser sample (average value of

141 µJ for the 60-SiO2(HIPE) while it is 90 µJ for the 35-SiO2(HIPE)). In three

35-SiO2(HIPE) @ 4.66mm 60-SiO2 (HIIPE)@ 4.74mm

Threshold H. R.C. V. R.C. Threshold H. R.C. V. R.C.

(in µJ) (in %) (in µJ) (in %)

1. 77.5 99.6 99.7 139 99.8 99.4

2. 85 99.5 99.7 84 99.5 98.8

3. 100 99.1 99.5 202 98.8 99.5

4. 100 98.8 99.5

Av.V. 90.62 141.6 Table 4.4. Random lasing threshold for 35-SiO2(HIPE) @ 4.66mm and 60-SiO2 (HIIPE)@

4.74mm. The values of Horizontal and vertical regression coefficients (H.R.C. and V.R.C.) for fits

are given.

dimensional systems this unexpected results may depend upon various issues.(i)

The multiple scattering of the pump light might restrict the excitation to the

proximity of a sample surface. The emitted photons from this sample surfaces

91

might readily escape through the sample surface, leading to a high lasing

threshold. (ii) We have observed that, for the denser sample, the absorption length

is smaller. Due to absorption, local pumping in an absorbing medium might create

a spatial “trapping” of the lasing modes. (iii) It is also possible that due to strong

scattering/localization, the pump beam itself gets trap within the system

producing a delayed emission from another mode later in time. Therefore, we

may have a larger lasing threshold for the highly scattering sample (in 60-

SiO2(HIPE)). Finally, in 3D systems, a large number of modes are involved in the

lasing action leading to a difficult observation of intense narrow lasing spikes.

IV. Conclusion:

Two types of samples (60-SiO2 (HIPE) and 35-SiO2 (HIPE)) were

investigated structurally and optically. Structural information shows that by

increasing the oil volumic fraction, we were able to decrease the pore diameters

and the porosity of the material. We found that 60-SiO2(HIPE) is denser than 35-

SiO2(HIPE). Static and Dynamic measurements were performed for more than 10

thicknesses. Both types of measurements provide us with the material transport

parameters. These slabs have lateral dimensions of a few cm2 (Fig. 4.1a) and are

thus really three-dimensional system. According to the expectations, the denser

samples exhibit the smaller transport and absorption mean free paths as well as

the smaller diffusion coefficients. Unexpectedly, both types of samples exhibit a

non-standard light diffusion behavior, clearly manifested by the observation of a

quadratic dependence 1/T ∝ L2 and by the reduction of the decay rate with

increasing time delay in the time transmission profiles. Such features cannot be

totally explained by absorption, as this would only lead to an additional

exponential decrease in the time of flight measurments. Such observations

performed while the Ioffe-Regel criterion is not fulfilled point to a peculiar

behavior being mainly due to the extremely disordered aspect and hierarchical

porosity of the structures.

Random lasing experiments were performed on the two types of samples

with almost similar thicknesses. Typical laser characteristics, i.e. input/output

92

power dependences, have been noticed in our materials. The narrowing of the

line-width of the Rh6G emission spectra and narrow spikes developing on the top

with increasing pump power have been observed. These features clearly point to

the large potential of our structures to be used as random lasers. The denser

sample shows a larger lasing threshold pointing to the fact that the pump beam

may be trapped in a mode within the material prior the emission can be released

in another mode later in time. More fundamental studies are however needed to

clearly unravel and allow us to understand the occurrence of the lasing threshold

with respect to the material hierarchical structure. Also, the observed increase of

the diffusion constant with the thickness of the sample has to be elucidated by

further investigation.

93

Chapter V SiO2/TiO2 (HIPE) for multiple scattering/localization and random lasing

94

95

I. Introduction:

Titanium dioxide is a semiconductor (with band gap at 3.27 eV) which

crystallizes in three polymorphic forms: rutile, anatase and brookite (68). Rutile is

the only stable form, whereas anatase and brookite are metastable phases and

transform to rutile phase, upon annealing. Nanosized titanium dioxide based

materials have been in the focus of researchers because they exhibit modified

physico-chemical properties in comparison with their bulks. Titania nanocrystals

have received great attention in recent years for their extensive applications in

conventional catalyst support, optics, cosmetics, white paint and solar cells (69,

70).

Titania is a common constituent of ceramics and glasses. Silica, with a few

percent of TiO2 (71), is used for length standards and astronomical mirror blanks

(72). Titania-doped silica materials played a crucial role in the development of

optical fibers (73) due to higher refractive index contrast between SiO2/TiO2

ordered composites. Also the high refractive index material leads to higher

multiple scattering in the case of disordered systems. Inspired from the above

specifications, we have synthesized SiO2/TiO2 hybrid, macro-cellular foams,

poly-HIPEs to enhance multiple scattering. Syntheses procedures of these

composites have been discussed in chapter II. Structural information on these

materials was obtained on various length scales using SEM, mercury porosimetry,

TEM with TED and XRD. Results are discussed in the current chapter. The

‘anatase’ and ‘rutile’ forms of titania are the most abundant. These forms have a

slightly different refractive index (2.4 for anatase and 2.6 for rutile). To know

which form is present in our composite, we have performed XRD and TEM-TED

measurements using the tools described in chapter II. In order to know the

material transport properties, we have performed transmission versus length and

time of flight measurements. Finally, in order to test these materials as potential

random lasers, we have infiltrated the samples with Rhodamine 6G laser dyes.

The infiltration method has been given in chapter II. After infiltration, in order to

determine the amount of dye molecules absorbed, we have performed

Thermogravitometric analyses (TGA). Results and discussion on random lasing

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performances are given in detail in this chapter as well.

II Results and discussion; All characterizations:

Two types of materials (85/15-SiO2/TiO2(HIPE) and 90/10-

SiO2/TiO2(HIPE)) have been synthesized and characterized both structurally and

optically. The results are reported in this section. The experimental details of the

setups are described in chapter II and III.

II.1 Structural characterizations:

Structural characterizations were performed on three different length

scales. The macroscopic length scale has been characterized by SEM and mercury

porosimetry. The mesoscopic length scale has been characterized by TEM-TED,

EDXS. The microscopic characterization has been performed by XRD. All the

three types of characterization techniques are given in this section.

II.1.1 Macroscopic length scale via SEM:

SEM images of 90/10-SiO2/TiO2(HIPE) and 85/15-SiO2/TiO2 (HIPE) are

shown in Fig 5.1. An inorganic monolith-type material of 85/15-SiO2/TiO2(HIPE)

is shown in Fig. 5.1.a. Fig 5.2 shows the SEM image analysis performed on these

two samples. The pore sizes of 90/10-SiO2/TiO2(HIPE) and 85/15-

SiO2/TiO2(HIPE) are distributed between 2 to 44 μm and between 1.17 to

2.22μm, respectively. Fig 5.1 clearly illustrates that the 90/10-SiO2/TiO2(HIPE) is

bearing larger pore sizes than those of the 85/15-SiO2/TiO2(HIPE). By increasing

titania by a small weight percentage (from 10 % to 15 %) we are able both to

reduce the pore diameter and to increase their mono-dispersity. By adding titania,

we intend to increase the refractive index contrast between pores and their

surroundings. We have observed that this addition of titania also reduces the pore

diameters due to higher shrinkage during the polycondensation, and strong

sintering when the thermal tretament is applied, a process based on atomic

diffusion. In most sintering processes, the powdered material is mold in a

particular shape and then heated to a temperature below its melting point. The

atoms in the powder particles diffuse across the boundaries and thus, fusing the

97

particles together and creating a single solid piece. Because the sintering

temperature should be lower than the melting point of the material, sintering is

often chosen as the shaping process for materials. After this sintering, we have

observed shrinkage and reduced pore diameter caused by titania due to fusion of

many atoms in the particle under the high temperature thermal treatment. Here, it

is very important to notice that the 85/15- SiO2/TiO2(HIPE) sample is highly

mono-dispersed. The observed narrow distribution of pore sizes and the random

positioning of these pores makes, our material an excellent candidate for light

multi-diffusion/localization.

II.1.2 Macroscopic and mesoscopic length scale via Mercury porosimetry:

In order to provide foams skeletal, bulk densities and to quantify the mesoscale

void windows distributions, we have performed mercury intrusion porosimetry

measurements. Overall, if we increase the amount of titania, due to the shrinkage

caused by titania and sintering effect, the pore diameters will reduce. By

increasing the amount of titania, we have reduced the pores diameters and

increased the number of pores. Hence the number of cell walls per unit volume is

increased causing an increase of the bulk as well as the skeleton densities (given

FIG. 5.1: SEM images of 90/10-SiO2/TiO2(HIPE) (b) and 85/15-SiO2/TiO2(HIPE) samples (c) are

shown. (a) shows a 85/15-SiO2/TiO2(HIPE) monolith sample.

98

FIG. 5.2: Normalized pore size distribution for the 90/10-SiO2/TiO2(HIPE) (solid black line) and

85/15-SiO2/TiO2(HIPE) (dotted red line).

Materials Porosity Skeleton Bulk

(%) density density (g/cm3) (g/cm3)

90/10-SiO2/TiO2 (HIPE) 90.2 1.11 0.1086

85/15- SiO2/TiO2 (HIPE) 71.6 1.5 0.43

TABLE 5.1: Mercury intrusion porosimetry data of two samples (90/10-SiO2/TiO2 (HIPE) and 85/15- SiO2/TiO2 (HIPE)).

FIG. 5.3: Distribution of cell window sizes for the of 85/15-SiO2/TiO2(HIPE) (a) and the 90/10-

SiO2/TiO2(HIPE) (b).

99

in Table 5.1).The skeleton densities are smaller than the density of silica and

titania because the foam walls are indeed bearing a large degree of mesoporosity.

From this technique, we can measure the exact diameters of the cell windows, the

distribution of which is shown in Fig 5.3. In the case of the 85/15- SiO2/TiO2

(HIPE), the pore size distribution is very monodisperse around an average value

of 2 µm (Fig 5.2). From fig 5.3 the mean cell window diameter is close to 0.5 µm

for 85/15- SiO2/TiO2 (HIPE) and around 1.6 µm for 90/10-SiO2/TiO2 (HIPE).

II.1.3 Mesoscopic length scale via TEM-TED, HR-TEM and EDXS:

We have performed HR-TEM measurements on three types of samples: 90/10-

SiO2/TiO2 (HIPE), 85/15-SiO2/TiO2(HIPE) and 75/25-SiO2/TiO2(HIPE)

composites. In the case of the 90/10-SiO2/TiO2 (HIPE), due to the small amount

of titania present in the structure, results were not significant. A TEM image of

85/15-SiO2/TiO2(HIPE) samples is shown in Figure 5.4 a. On one hand, if the

material is amorphous, a light gray color will appear in the shown TEM image.

On the other hand, if the material is crystalline, it will appear as dark black color

Fig 5.4: Transmission electron micrograph of 85/15-SiO2/TiO2(HIPE) (a) gray color shown in

circle is SiO2 material and black color shown in another circle is TiO2. A TED pattern of the

85/15-SiO2/TiO2(HIPE) is shown in b. Inset in (b) shows the model representation of diffraction

pattern for amorphous material.

in the TEM image. In this composite, SiO2 is amorphous whereas TiO2 is in a

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crystalline phase. A TED image of the 85/15-SiO2/TiO2(HIPE) is shown in Fig.

5.4.b. In this sample the amorphous state of silica is dominating on the crystalline

form of titania, only diffused rings with a centered dot in the diffraction pattern

are observed. A comparison with a numerical diffraction pattern calculated for an

amorphous material is shown in inset of Fig 5.4b. The TEM image of the 85/15-

SiO2/TiO2(HIPE) indicates that some crystalline form of TiO2 is also present

Fig 5.5: Transmission electron micrograph of 75/25-SiO2/TiO2(HIPE) (a) gray color shows SiO2

material and black color is TiO2 material. The TEM image of one TiO2 particle in the silica matrix

is shown in (b). A zoom on the TiO2 particle shows clear crystalline form (c). (d) The TED pattern

of the 75/25-SiO2/TiO2 (HIPE) reveals a tetragonal system.

(black spots in Fig. 5.4. a feature of a crystalline phase). To obtain a more

accurate information about which of the allotropic phase of titania is present in

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our sample, we have also performed experiments on the 75/25-SiO2/TiO2(HIPE).

The TEM and TED images of this structure are shown in fig 5.5. Fig 5.5 (a)

confirms the presence of both silica and titania (indicated by gray and black

colors, respectively). On zooming down to the nanometer scale, we found that

TiO2 particles are dispersed in silica matrix (Fig 5.5 b) and the particle size ranges

between 10 to 15 nm in size. A further magnification allows us to see the

crystalline structure (fig 5.5 c) of the titanium dioxide nanoparticle. In order to

determine the allotropic form of this nanoparticle, we have performed TED

measurements (Fig 5.5 d). The obtained diffraction pattern demonstrates that TiO2

crystallizes in the tetragonal system, indicating the presence of the Anatase

allotropic form of Titania (68).

To obtain the atomic weight fraction of Ti and Si, we have performed elemental

analysis using EDXS. The EDXS results are given in table 5.2. The EDXS

analysis confirms that 85/15-SiO2/TiO2(HIPE) has as smaller amount of Ti (3.22

and 4.41) than 75/25-SiO2/TiO2(HIPE) (table 5.2).

Materials Atomic weight % of Si Atomic weight % of Ti

75/25-SiO2/TiO2 (HIPE) 95.59 4.41

85/15- SiO2/TiO2 (HIPE) 96.78 3.22

Table 5.2: EDXS elemental analysis data of two samples (75/25-SiO2/TiO2 (HIPE) and 85/15- SiO2/TiO2 (HIPE)).

II.1.4 Microscopic length scale via XRD:

Titania is known for its allotropic phase transformation (from brookite to

anatase form then to rutile form) upon thermal treatment. At 800°C, various

scientific groups have observed the rutile form (68). From TEM with TED

measurements, it is clear that SiO2/TiO2(HIPE)s is present in the anatase form of

titania, even though we have used a high temperature (800°C) to calcine our

HIPEs. To clearly confirm this allotropic form of titania, we have performed X-

ray diffraction (XRD) on these hybrid materials. Results are shown in Fig 5.6.

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From the available literature, we know that the anatase form of titania shows a

very sharp peak at 2θ = 25° (68) but, due to the small amount of titania present in

the 90/10-SiO2/TiO2(HIPE) and 85/15-SiO2/TiO2(HIPE), we have rather observed

a broad hump around 2θ =25°.

Fig 5.6: XRD of three samples 90/10-SiO2/TiO2(HIPE) in black, 85/15-SiO2/TiO2(HIPE) in red,

75/25-SiO2/TiO2(HIPE) in blue, black circle showing the peak at 25°.

By increasing the titania content in the composite (75/25-

SiO2/TiO2(HIPE)), we have observed a narrow peak around 2θ = 25°

superimposed to the broad bump. In fig. 5.6 the sharp peak superimposed to the

broad bump (see blue curve) shows the bi-phasic nature of the sample, consisting

of an amorphous phase and a crystalline phase: sharp peak (evidenced in the black

circle). Therefore, from both XRD and TEM-TED measurements, it is clear that

we have obtained the anatase form of titania embedded within an amorphous

network. The surrounding amorphous network is certainly locking the anatase

allotropic change toward the rutile one, as rutile, being the stable form, should be

present at 800°C.

II.2 Optical Characterizations:

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The Two types of materials (90/10-SiO2/TiO2(HIPE) and 85/15-

SiO2/TiO2(HIPE)) were characterized by transmission versus length

measurements and time of flight experiments. The results are reported in this

section. The experimental details of the setups are described in chapter III. The

obtained experimental data were analyzed according to the theories mentioned in

chapter III.

II.2.1 Transmission versus length measurements:

White light transmission through samples of various versus lengths (T(L)) have

been performed on the two types of samples with more than 10-20 length

(thicknesses) ranging between 1 to 5 mm. Figs 5.7 (a) and (b) exhibit the

conductance versus thickness behavior for the two types of samples (90/10-

SiO2/TiO2(HIPE) and 85/15-SiO2/TiO2(HIPE)) at two different wavelengths (blue

stars: 500nm and red stars: 700 nm). From Fig 5.7, it is clear that our

experimental data do not follow a linear relationship between 1/T and L. The

samples are not following the Ohm’s law (it should be linear for diffusive sample

only if there is no absorption, see Eq 3.11). A quadratic dependence (1/T ∝ L2)

(black dotted lines in Fig. 5.7) better fits our experimental data. The experimental

results have been also fitted by the stationary solution of the diffusion equation

(see eq 3.9) including absorption (blue and red solid lines in Fig. 5.7). The insets

of Fig 5.7 exhibits the residuals of the fits as a function of the thickness. By using

this fitting procedure, we are able to obtain the transport mean free path ‘lt’ and

the absorption length ‘la’ for the full range of white light illumination (from 500 to

800nm). The obtained values of ‘lt’ and ‘la' are plotted in Figs 5.8 and 5.9. The

transport mean free path at 515 nm for the 90/10-SiO2/TiO2(HIPE) and 85/15-

SiO2/TiO2(HIPE) are 11.81 μm and 11.19 μm, respectively. Their absorption

lengths at 515 nm for the 90/10-SiO2/TiO2(HIPE) and the 85/15-SiO2/TiO2(HIPE)

are 3.33 and 2.52mm respectively. From the SEM analysis of these samples we

expect to have a lower lt and la for the 85/15- SiO2/TiO2(HIPE) than for the 90/10-

SiO2/TiO2(HIPE), since the 85/15-SiO2/TiO2(HIPE) has a distribution of more

monodisperse and smaller pore sizes (see Fig 5.2). The absorption lengths of these

104

Fig 5.7: Inverse transmittance versus thickness behavior for 85/15-SiO2/TiO2 (HIPE) (a) and

90/10-SiO2/TiO2 (HIPE) (b) at λ=500 nm (blue stars) and λ=700 nm (red stars) fitted by the

stationary solution of the diffusion equation, (fits are blue and red solid line, respectively) as well

as by the 1/T∝ L2 law (fits are black dotted lines). Insets of (a) and (b) show the residuals of the

fits.

105

Fig 5.8: Wavelength-dependent transport mean free path lt (a) and absorption length la (b) of a

90/10-SiO2/TiO2(HIPE).

Fig 5.9: Wavelength-dependent transport mean free path lt (a) and absorption length la (b) of a

85/15-SiO2/TiO2(HIPE).

samples are in good agreement with their bulk densities (denser sample has lower

la). However, lt is not significantly different for both samples. A common behavior

for the transport mean free path is to vary with frequency, which we observe in

Figs. 5.8 (a) and 5.9 (a) and contrarily to what we reported for 35-SiO2(HIPE) and

60-SiO2(HIPE) in chapter IV. By increasing the wavelength, lt increases in both

samples. The experimental data in the case of 85/15-SiO2/TiO2(HIPE) are very

106

much scattered (Fig 5.7a). This may be attributed to randomly positioned TiO2

nano-particles, introducing some additional multiple scattering at random

positions from sample to sample or place to place in the same sample. The

stationary solution of the diffusion equation including absorption fits particularly

well the experimental data, providing the values of the transport mean free path

such that k*lt >> 1. These values are inherent to diffusive light transport.

However, the plots shown in Fig. 5.7 are also nicely fitted by a quadratic

dependence (1/T ∝ L2) (black dotted lines in Fig. 5.7), which might provide some

indication of light pre-localization.

II.2.2 Time of flight experiments:

The experimental setup used to perform time resolved measurements is

described in chapter III (Fig. 3.6). Using this experimental setup, we have

performed time of flight experiments on various samples with thicknesses ranging

between 1 to 5 mm for the 90/10-SiO2/TiO2(HIPE) and 85/15-SiO2/TiO2(HIPE).

Fig 5.10 shows typical results for samples 85/15-SiO2/TiO2(HIPE) and 90/10-

SiO2/TiO2(HIPE) at thicknesses 2.5 and 3.08 mm, respectively. The inset exhibits a

part of the corresponding measured streak plots. The samples exhibit a strongly

multi-diffusive character, with photons being significantly delayed in the samples

in all cases. From Fig 5.10 (a) and (b), it is clear that the time profile is more

extended in the 85/15-SiO2/TiO2(HIPE) with respect to the 90/10-SiO2/TiO2(HIPE)

((a) has smaller thaickness than (b)). This suggests that the delay develops more in

the denser sample as it is expected from longer paths performed by light in the

sample due to stronger multiple scattering. All traces have been fitted by the

asymptotic form of the diffusion equation described by Eq 3.14 (blue dashed-dotted

lines). Clearly, substantial increases in transmission relative to that predicted by the

diffusion model are observed at long times. Measurements in the time domain

make it possible to unravel the effects of absorption. The influence of localization

can be seen in a reduction of the decay rate with increasing time delay. As this is

precisely what is seen in Fig 5.10.b we have fitted the experimental results with the

asymptotic form of T(t) near the localization transition, described by Eq. 3.18,

107

featuring a time dependent diffusion constant D(t) = D0 (τ/t)1/3, where τ is the elastic

scattering time. These asymptotic forms (green dashed lines) provide slightly better

Fig 5.10: Time of flight experiments (red circles with black connecting line) performed on (a)

85/15-SiO2/TiO2(HIPE) and (b) 90/10-SiO2/TiO2(HIPE) at thicknesses 2.5 and 3.08 mm,

respectively. The fits corresponding to the asymptotic form of the time dependent diffusion

equation (blue dashed) and to the asymptotic form of T(t) near the localization transition (green

dashed lines) are also shown. The insets show parts of the streak plots from which the profiles are

built.

fits of the recorded data. Basically these theories were not developed for poly-

HIPEs. Therefore such kind of complex material is difficult to characterize using

the mentioned theories. The values of the diffusion coefficients extracted from the

Scholar no. 90/10- SiO2/TiO2 (HIPE) 85/15- SiO2/TiO2 (HIPE)

L D0 L D0

Thickness (in mm) (in m2/s) Thickness (in mm) (in m2/s)

1. 3.08 2000 1.5 1910

2. 3.94 1304 2.5 1030

3. ------ ------- 2.77 1010 Table 5.3: Thickness and diffusion constants of 90/10-SiO2 /TiO2(HIPE) and 85/15-SiO2/TiO2

(HIIPE).

108

asymptotic forms are given in table 5.3 for both SiO2/TiO2(HIPE)s. From these

values of diffusion constants, it is clear that the more we add titania in the

SiO2/TiO2(HIPE), the more we are able to reduce D0. This drop in D0 originates

from both a better monodispersity of the pore sizes and a larger refractive index

contrast in the case of 85/15-SiO2/TiO2(HIPE). Taken together, the quadratic

dependence 1/T ∝ L2 observed in Fig. 5.7, and the long time departure from a

single exponential decay observed in our time of flight experiments clearly indicate

that our samples follows a non-standard diffusive transport regime while not clearly

attributable to a pre-localization regime.

III Random lasing:

We have performed random lasing on both types of samples: 85/15-

SiO2/TiO2(HIPE) and 90/10-SiO2/TiO2(HIPE). In order to measure the amount of

dye molecules within the structure, we have performed TGA. The random lasing

properties of our samples and TGA results are discussed in this section in detail.

III.1 Thermogravitometric analysis:

From TGA measurements we can obtain the percentage of weight loss

within the structure as a function of temperature. From the weight loss, we can

calculate the number of molecules per unit volume. The data are given in table

5.4. The 85/15-SiO2 (HIPE) has less weight loss. A smaller amount of dye

90/10- SiO2/TiO2 (HIPE) 85/15- SiO2/TiO2 (HIPE)

Weight loss (in %) No of molecules Weight loss (in %) No of molecules

mol/cm-3 mol/ cm-3

12.8 0.33*10-4 8.9 0.88*10-4

Table 5.4: TGA data of 90/10-SiO2 /TiO2(HIPE) and 85/15-SiO2/TiO2 (HIIPE).

molecules is thus present per unit volume in this HIPE with respect to the 90/10-

SiO2 (HIPE). Taking into account the bulk density of the structure, which is larger

109

for the denser sample, we have more molecules per unit volume in this sample.

III.2 Results and Discussion for R.L.:

In order to test the potentialities of random lasing in our highly disordered

systems, we have infiltrated them with Rhodamine 6G dyes by the method

discussed in chapter II. The experimental setup is described in chapter III. Owing

to the mentioned experimental geometry, we have performed random lasing on

two types of samples 85/15-SiO2/TiO2(HIPE) and 90/10-SiO2/TiO2(HIPE) at two

different thicknesses (at 1.4 and 3.5 mm). Results are shown in Figs 5.11 and

5.12. Emission spectra of 90/10-SiO2/TiO2(HIPE) shown in Fig 5.11.a clearly

show that with increasing input intensity, the output intensity also increases. Also,

it is clear that the line-width gets significantly narrower with increasing pump

power. A magnification of a part of the emission spectra is shown in Fig 5.11(b).

The overall narrowing of the spectra occurs together with the narrow spikes

observed on the top. These spikes occur at random frequencies. At three points we

have calculated the Full Width at Half Maxima (FWHM) (bottom, middle and top

which are 10.9, 6.15, 0.42 nm, respectively). The top spikes exhibited in the

emission profile (Fig 5.11.b) have a FWHM that reduce to less than a nanometer,

featuring a random laser spike originating from our material. The characteristic

output versus input pump energy (Fig 5.11.c) looks like a conventional laser

characteristic. Fitting these experimental results, using linear fits, we are able to

obtain lasing thresholds at the cross-sections (crossing of the red solid lines) of

horizontal and vertical lines from Fig 5.11.c. This linear fit matches very well

with the experimental data. The majority of the plots are giving more than 95%

accurate values of regression coefficients for horizontal and vertical (Horizontal

regression coefficients (H.R.C.) and vertical regression coefficients (V.R.C.), (see

table5.5). In a second step, repeating the measurements on the same spot of the

sample, we have replicated the experimental data. Our results are thus fully

reproducible and further indicate that the dyes are not bleaching too fast. We have

also performed these experiments while changing the spot position on the same

sample and observed similar results. The random lasing thresholds determined for

110

all our experiments on this sample are given in table 5.5. Similar experiments

have been performed on a 85/15-SiO2/TiO2(HIPE) sample. Results are shown in

Fig 5.11: Random lasing performed on 90/10-SiO2/TiO2(HIPE) @1.43 mm thickness. a) Emission

intensity versus wavelength curves are shown. b) Narrow spikes appearing on the top of the

emission profile are zoomed. (c) Input/output power dependence curve is shown. The black stars

are the experimental data points and the red solid lines are linear fits to the data.

111

Fig 5.12: Random lasing performed on 85/15-SiO2/TiO2(HIPE) @1.44 mm . a) Emission intensity

versus wavelength curves are shown. b) Narrow spikes appearing on the top of the emission

profile are zoomed. (c) Input/output power dependence is shown. The black stars are the

experimental data points and the red solid lines are horizontal and vertical linear fits to the data.

figure 5.12. This sample also shows random lasing characteristics (fig 5.12.c) and

exhibit very sharp peaks on top of the emission profiles (see inset of Fig 5.12 b).

Repeating the measurements as described above at the same spot position, we are

able to reproduce the results. By changing the spot position, we repeated the

measurements and observed almost similar lasing thresholds in all cases. All

threshold values are collected in table 5.5. Since the average pore diameters in the

85/15-SiO2/TiO2(HIPE) are smaller than the one of the 90/10-SiO2/TiO2(HIPE),

we expect the lasing threshold to decrease in the denser sample. Also the high

refractive index contrast of titania should help to reduce the lasing threshold in

112

these denser materials. From the results in table 5.5, it is clear that the lasing

threshold is lower in the denser sample (average value: 235 µJ in 85/15-

SiO2/TiO2(HIPE) and 347 µJ in 90/10-SiO2/TiO2(HIPE)). This experiment clearly

confirms that the lowering of the transport parameters, observed in the T(L) and

time of flight experiments, is due to stronger scattering/localization, leading to a

reduction of the lasing threshold in the denser sample. We have performed similar

measurements on 85/15-SiO2/TiO2(HIPE) and 90/10-SiO2/TiO2(HIPE) with a 3.5

mm thickness. The results are given in table 5.6. By increasing the thickness, we

aim to decrease lasing threshold. But due to lack of time, we have measured only

two sample thicknesses, which is not sufficient to conclude on the performance of

random lasers as a function of thickness. From Fig 5.11.c and 5.12.c, it is clear

that 85/15-SiO2 /TiO2(HIPE) has a lower lasing threshold than the 90/10-SiO2

/TiO2(HIPE). For all 85/15-SiO2 /TiO2(HIPE) samples, we have observed a very

sharp peak centered around 573.5 nm superimposed to the emission spectra of

Rhodamine 6 G (Fig 5.13). the origin of this peaks, occurring systematically at the

same wavelength is not clear and cannot attribute to a random lasing effect.

90/10-SiO2 /TiO2(HIPE) @ 1.43 mm 85/15-SiO2 /TiO2 (HIIPE)@ 1.4mm

Threshold H. R.C. V. R.C. Threshold H. R.C. V. R.C.

(in µJ) (in %) (in µJ) (in %)

1. 338 92.1 99.9 202 94.5 99.4

2. 300 98.5 99.12 224 95.5 99.7

3. 390 98.1 99.6 265 96.6 99.6

4. 360 99.8 98.6 250 98.8 99.8

Av.V. 347 235.5 Table 5.5: Random lasing threshold for 90/10-SiO2 /TiO2 (HIPE) @ 1.43 mm and 85/15-SiO2

/TiO2 (HIPE) (HIIPE)@ 1.4 mm have been given. The value of H.R.C. and V.R.C. (Horizontal and

vertical regression coefficient) for horizontal and vertical fit have been given.

113

Fig 5.13: Emission intensity versus wavelength curves are shown for a 85/15-SiO2/TiO2(HIPE)

@3.5mm. Very sharp spikes at 573.52 nm have been observed.

90/10-SiO2 /TiO2(HIPE) @ 3.5 mm 85/15-SiO2 /TiO2 (HIIPE)@ 3.5mm

Threshold H. R.C. V. R.C. Threshold H. R.C. V. R.C.

(in µJ) (in %) (in µJ) (in %)

1. 340 98.1 99.6 115 98.5 99.6

2. 350 98.5 99.5 100 97.5 99.8

3. 400 98.9 98.7 121 96.6 99.8

4. 350 96.8 98.2

Av. V. 360 112 Table 5.6: Random lasing thresholds for 90/10-SiO2 /TiO2 (HIPE) @ 3.5mm and 85/15-SiO2

/TiO2 (HIPE)@ 3.5mm. The value of H.R.C. and V.R.C. (Horizontal and vertical regression

coefficient) for horizontal and vertical fits are also given.

114

IV Conclusion:

SiO2/TiO2 composites have been investigated structurally and optically

using various techniques. SEM analysis of two types of samples (85/15-

SiO2/TiO2(HIPE) and 90/10-SiO2/TiO2(HIPE)) shows that by increasing the

amount of titania, we are able to reduce the pore diameters. From TEM-TED and

XRD, we know that these composites combine an amorphous state of silica and a

crystalline phase of titania. T(L) measurement have been performed on different

thicknesses varying from L = 1 mm to 5mm. Dynamic measurements were also

performed for all the thicknesses. Both types of measurements provide us with the

material transport parameters. These slabs have lateral dimensions of a few cm2

and are thus really three-dimensional systems. According to the expectations, the

denser sample exhibits the smaller transport and absorption mean free paths as

well as the smaller diffusion coefficients. Unexpectedly, both types of samples

exhibit a non-standard light diffusion behavior, clearly manifested by the

observation of a quadratic dependence 1/T ∝ L2 and by the reduction of the decay

rate with increasing time delay in the time transmission profiles.

Random lasing was performed on the two types of samples with two

thicknesses. Typical laser characteristics, input/output power dependences, have

been noticed in our materials. As expected, the denser sample shows a lower

lasing threshold. The narrowing of the line width with increasing pump power has

been observed. An overall narrowing of the emission spectrum together with the

narrow spikes on the top, have been observed. The titania nano-particles embaded

in the silica matrix are 10 to 15 nm in size. These dimensions are not likely to

affect very much the light transport properties of the materials. Nevertheless, this

titania addition induced more monodisperse pore diameters distributions

responsible, with the larger dielectric contrast, to the observed behaviour of the

transport paramters.

115

Chapter VI Conclusions and perspectives

116

117

In this thesis, our aim was to probe new materials potentially able to

multidiffuse/localize light and act as random lasers. In this context, disordered,

porous, white, hierarchical materials have been synthesized by using a sol-gel

process combined with the physical chemistry of complex fluids (emulsion,

lyotrope mesophase). The whole synthesis process is known as integrative

chemistry and is a potential technique to control the morphology of the materials

at macro and mesoscopic length scales. The obtained self-standing slabs have

lateral dimensions of a few cm2 and a thickness ranging from 0.5 mm to several

mm. They are thus real three-dimensional systems. Due to the lack of materials

having a large refractive index in the visible range of the spectrum

electromagnetic, it is a very challenging task to obtain light localization in 3D

systems. In spite of this fact, we attempted to synthesized materials exhibiting this

behaviour. To determine the structure of our materials at the macro, meso, and

micro length scales, we have characterized them by SEM, mercury porosimetry,

TEM, TED, EDXS, and XRD. To determine the light transport parameters, we

have characterized these materials optically via transmission versus length

measurements and time of flight measurements. The investigation of the light

diffusing properties of these new materials is reported here for the first time.

In a first step, owing to the above mentioned technique, two types of

samples: 35-SiO2 (HIPE) and 60-SiO2 (HIPE) were synthesized by varying the

oil-volumic fraction of the emulsion. The structural characterizations (SEM) have

been performed on these samples. They revealed that we are able to reduce the

pore diameters distributions from 10 − 40μm to 1 − 3.5μm in the cases of 35-SiO2

(HIPE) and 60-SiO2 (HIPE), respectively, by increasing the oil-volumic fraction.

The mercury porosimetry measurements performed on these samples illustrate

that the 60-SiO2 (HIPE) sample has a larger bulk density than the 35-SiO2 (HIPE).

Therefore, 60-SiO2 (HIPE) is a denser sample than 35-SiO2 (HIPE).

Optical characterizations (T(L) and time of flight measurements) were

then performed. These complementary measurements provide us with the material

transport parameters: transport and absorption mean free paths, diffusion constant.

118

By using well established theories, we have analyzed our results and obtain the

transport parameters. The obtained T(L) data have been fitted with the stationary

solution of the classical diffusion equation. We observed that the inverse

transmittance has a quadratic dependence on thickness. This quadratic

dependence may be attributed either to absorption phenomenon or multiple

scattering inhibition close to the localization regime. According to the

expectations from the classical light diffusion theory, the denser samples must

exhibit the smaller transport and absorption mean free paths. We observed this

typical trend in our SiO2 (HIPE) materials. The obtained values of ‘lt’ is 86 µm for

35-SiO2 (HIPE) and is 19µm for 60-SiO2 (HIPE).

Time of flight experiments in the time domain must allow us to unravel

the effects of either absorption or scattering inhibition. Absorption in

homogeneously absorbing samples simply introduces a multiplicative exponential

factor in time. The influence of a pre-localization regime can be seen as a

reduction of the decay rate with increasing time delay, which would lead to a non-

exponential time tail at longer time scales. Times of flight measurements have

been performed: we observed a non-exponential decay tail. By using both the

diffusion and localization theories, we have fitted our results and observed that the

localization theory provides a better fit function with the experimental data.

However, due to the weak scattering strength measured in T(L) experiments, k lt

>> 1, we cannot simply ascertain that observe a pre-localization regime.

Furthermore, these theories are not fully appropriate for the analysis of our

complex materials. From the fitting results, we have obtained the values of the

diffusion constant and observed that it is a function of thickness (by increasing the

thickness, D0 is increasing), an unusual property of classically diffusing materials.

Therefore, there is a strong need nowadays to develop an appropriate theory for

our materials.

In a second step, we have synthesized 85/15-SiO2/TiO2(HIPE) and 90/10-

SiO2/TiO2(HIPE) samples by addition of a small amount of TiO2 in the SiO2

materials, to enhance the refractive index contrast. These materials have been

structurally characterized by various techniques such as SEM, mercury

119

porosimetry, TEM, TED, EDXS, XRD. Results obtained from TEM-TED and

XRD reveladed that these composites combine an amourphous state of silica and

a crystalline phase of titania. The SEM observations illustrate that the 85/15-

SiO2/TiO2(HIPE) has a very narrow pore size distribution as compared to the one

of the 90/10-SiO2/TiO2(HIPE): pore size ranging from 1.17 to 2.22 μm and from 2

to 44 μm, respectively. From the mercury porosimetry experiments, 85/15-

SiO2/TiO2(HIPE) has a higher bulk density. Therefore, it is a denser sample, than

the 90/10-SiO2/TiO2(HIPE).

T(L) measurements performed on different thicknesses exhibit a similar

quadratic dependence of inverse transmittance versus thicknesses as the SiO2

(HIPE)s. By applying diffusion theory, we have obtained the values of ‘lt’ for the

90/10-SiO2/TiO2 (HIPE) and 85/15-SiO2/TiO2 (HIPE). They are 11.81 μm and

11.19 μm, respectively. lt is not significantly different for both samples. This small

values of ‘lt’ in the case of the 90/10-SiO2/TiO2(HIPE) sample might originate

from the narrow cell windows size distribution centered around 1 μm.

Dynamic measurements were also performed and revealed that the denser sample

(85/15-SiO2/TiO2 (HIPE)) has a lower diffusion constant than that of the 90/10-

SiO2/TiO2 (HIPE). In these composites materials, we have observed that the long-

time departure from the single exponential decay is stronger than pure SiO2-

(HIPEs). Since we have not performed our measurements on many samples, we

are not able to establish a relation between the diffusion constant and the

thickness of these composites.

All types of samples investigated in our studies exhibit a non-standard

light diffusion behavior, both in the T(L) and in the time of flight measurements.

Such features cannot be explained by absorption, as this would only lead to an

additional exponential decrease in the time decay profiles. These features thus

constitute somewhat direct evidence for either the slowing down of photon

diffusion due to the approach to the Anderson localization transition or some

peculiar behavior due to the hierarchical porosity of our disordered structures.

Such observations performed while the Ioffe-Regel criterion is not fulfilled point

to observation being mainly due to the extremely disordered aspect and

120

hierarchical porosity of the structures.

In order to strengthen our observations and investigations, more evidence

is nowadays required, Speckle pattern analyses, measurements in the frequency

domain, and coherent back scattering experiments might help in fully elucidating

the observed behaviour. Also, the observed increase of the diffusion constant with

the thickness of the sample has to be elucidated by further investigation.

The disordered systems synthesized and characterize here above can act as

“random lasers”. Therefore, we have investigated their random lasing

performances by infiltrating the four types of aforementioned samples with

Rhodamine 6G laser dyes. Typical laser characteristics, i.e. input/output power

dependences, with lasing threshold, have been noticed in all materials. For each

sample, the narrowing of the line-width of the Rh6G emission spectra with

increasing pump power has been observed. For each sample, overall narrowing of

the emission spectrum with narrow spikes developing on top of the spectrum has

been observed. These features clearly point to the large potential of our structures

to be used as random lasers.

On the one hand, the denser (60-SiO2 (HIPE)) sample shows a larger

lasing threshold than the (35-SiO2(HIPE)) pointing to the potential fact that the

pump beam may be trapped in a mode within the material prior that the emission

can be released in another mode later in time.

On the other hand, as expected, the denser (85/15-SiO2/TiO2 (HIPE) as

compared to the 90/10-SiO2/TiO2 (HIPE)) sample shows a lower lasing threshold

in the case of SiO2/TiO2 (HIPE) composites. The 85/15-SiO2/TiO2 (HIPE) also

shows a very sharp shoulder peak which cannot be ascribe at the moment.

As perspectives, we can briefly mention:

1. More experimental proofs are needed to justify that the observed regime is

a “light pre-localization regime”. Therefore, speckle pattern analysis and

measurements in the frequency domain are suggested for our materials.

2. In order to fully analyze this new type of diffusing materials, it is required

121

to develop the appropriate theories for such complex materials.

3. To obtain the clear trend of random lasing threshold with thickness.

Experiments performed for more thicknesses are needed.

4. To avoid the dye bleaching problems within the materials during random

lasing experiments, quantum dots can be infiltrated and observed.

122

123

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