Jaque et al. Vol. 20, No. 10 /October 2003 /J. Opt. Soc. Am. B 2075

Diode-pumped laser action at 1.34 mm from theNd31:Ca3Ga2Ge3O12 garnet crystal:

influence of Nd31 multicenter distribution

Daniel Jaque

Departamento de Fisica de Materiales, Facultad de Ciencias, Universidad Autonoma de Madrid,28049 Madrid, Spain

Alain Brenier

Laboratoire de Physico-Chimie des Materiaux Luminescents, Unite Mixte de Recherche, Centre National de laRecherche No. 5620, Universite Claude Bernard-Lyon I, 10 rue Ampere, 69622 Villeurbanne Cedex, France

Carmen de las Heras

Departamento de Fisica de Materiales, Facultad de Ciencias, Universidad Autonoma de Madrid,28049 Madrid, Spain

Georges Boulon

Laboratoire de Physico-Chimie des Materiaux Luminescents, Unite Mixte de Recherche, Centre National de laRecherche No. 5620, Universite Claude Bernard-Lyon I, 10 rue Ampere, 69622 Villeurbanne Cedex, France

Jose Garcıa Sole

Departamento de Fisica de Materiales, Facultad de Ciencias, Universidad Autonoma de Madrid,28049 Madrid, Spain

Received January 27, 2003; revised manuscript received May 29, 2003

Diode-pumped laser action at 1.34 mm from the Nd31:Ca3Ga2Ge3O12 system is demonstrated and the physicalparameters of relevance in laser dynamics reported. The pump-to-infrared conversion efficiency has been in-vestigated as a function of both Nd31 concentration and output mirror transmittance. From the analysis oflaser curves it has been demonstrated that the low laser efficiencies arise from the inhomogeneous line broad-ening of emission bands induced by multicenter distribution. This analysis has also been employed to deter-mine the ratio between inhomogeneous and homogeneous line broadening (Dn inh /Dnh ' 2.5), the result beingin good agreement with that obtained from spectroscopy. Other mechanisms that could affect the extractionefficiency, such as excited-state absorption and energy-transfer upconversion, have also been evaluated, theresults indicating that their influence in laser dynamics is negligible. Finally, we also report on the influenceof multicenter distribution on the spectral shape of the 1.34-mm output laser radiation. © 2003 Optical So-ciety of America

OCIS codes: 140.3530, 140.3480, 140.3380.

1. INTRODUCTIONThere is presently great interest in the development ofsolid-state materials that show efficient laser operation at;1.3 mm. In addition to the very wellknown practicalapplications of this radiation (remote sensing,1 guided op-tical communications,2 and soft-human-tissue applica-tions), the interest in these laser sources has increasedbecause of the recent development of red-green-blue laserdevices based on diode-pumped, 1.3-mm lasers.3

The 4F3/2 → 4I13/2 laser channel of Nd31 ions provides away of realizing solid-state infrared lasers emitting in the1.3–1.45-mm range. In addition, such lasers can be effi-ciently diode pumped, leading to compact, miniaturized,even microchip laser systems.4–7

0740-3224/2003/102075-09$15.00 ©

Nd:YAG has been extensively used in the past for diodepumping.4 However, it has some disadvantages: nar-row absorption bands (which complicate diode pumping)and a relatively expensive growth process due to its highmelting point (1960 °C).8

Nd31-doped laser crystals exhibiting broad absorptionbands, such as Nd31:YVO4 (Nd:YVO)4,5 andNd31:Ca3Ga2Ge3O12 (Nd:CGG),9,10 have been proposedas alternatives to Nd:YAG. In particular, much attentionhas been paid to the Nd:CGG laser system because of itsgood spectroscopic properties for infrared laseroscillation.11 Nd:CGG laser crystals show broad absorp-tion and emission bands that are due to the presence ofseveral nonequivalent sites,12,13 so that stabilization of

2003 Optical Society of America

2076 J. Opt. Soc. Am. B/Vol. 20, No. 10 /October 2003 Jaque et al.

pump wavelength is not critical. In addition, it can begrown by using common silicon carbide ovens (meltingpoint is 1400 °C). Finally, quantum efficiency of its meta-stable state is as high as 0.7–0.9, resulting in low pump-induced crystal heating.10,11 Although cw laser oscilla-tion around 1 mm (4F3/2 → 4I11/2 laser channel) hasalready been studied,9–11 the potential application of thiscrystal in diode-pumped laser sources operating at 1.3 mmremains to be investigated.

In this paper, we report on diode-pumped, cw laser os-cillation at 1.3 mm from the Nd:CGG system. In addi-tion, the spectroscopic parameters of relevance in the la-ser dynamics of the 4F3/2 → 4I13/2 channel are reported.Laser slope efficiencies have been found to be lower thanexpected and also lower than those obtained from otherNd31-doped laser systems operating under the same ex-perimental conditions (such as Nd:YAG). The possiblemechanisms leading to these low laser efficiencies (crystallosses, inhomogeneous broadening, and excited-state ab-sorption processes) are discussed and their correspondingweight in the reduced extraction efficiency determined.Finally, the influence of inhomogeneous broadening ofemission bands on the spectral distribution of output la-ser radiation has been studied.

2. EXPERIMENTALThe Nd:CGG crystals employed in this work were grownfrom the melt by the Czochralski technique. Nd31 con-centration in the melt was varied from 0.1 up to 8 at.%(0.1, 0.5, 1, 2, and 8 at.%). For the sake of comparison wehave also carried out laser experiments on a Nd:YAGcrystal with a Nd31 concentration of 1.1 at.%. All thecrystals were cut to 3 mm 3 3 mm 3 4 mm elements andpolished to laser quality. Laser action was achievedalong the longest dimension in all cases.

Room-temperature fluorescence spectra were recordedexciting the samples by a fiber-coupled laser diode tunedto 808 nm. The emitted light was dispersed by a 0.5 MSpex (0.01 nm resolution) monochromator and detectedby a calibrated germanium detector.

Excited-state absorption (ESA) measurements around1.3 mm were performed by using two-beam spectroscopy,which consists of two collinear laser beams propagatingsimultaneously along the crystal. The pump beam (l' 750 nm) populates the 4F7/2 excited state of Nd31 ionsfrom which the 4F3/2 metastable level is populated. Thebeam was produced by an optical-parametric oscillatorpumped by a frequency-tripled Continuum ® Nd:YAG la-ser. The second beam (probe beam) in the 1300–1400-nmrange was generated by a dye laser (Laser Analytical Sys-tems) through a hydrogen cell Raman shifter. The probebeam (8 ns) was 0.5-ms delayed from the pump beam andoverlapped it inside the sample. To obtain the ESA spec-trum we recorded the excited-state laser excitation spec-trum of the 600-nm fluorescence (4G7/2 → 4I11/2 transi-tion) in the 1300–1400-nm range. The excited-statelaser excitation spectra are the image of the ESA spectra.They are obtained in arbitrary units, and we have con-verted them to cross section units (cm2) with the help ofthe Judd–Ofelt formalism.

The experimental setup used for laser experimentsis shown in Fig. 1. We used a quasi-hemispherical cav-ity consisting of a flat, dichroic input mirror (IM;R . 99.9% from 1300 to 1400 nm and T 5 90% for pumpradiation). The output coupler (OC) had a 10-cm radiusof curvature. Four different output coupler transmit-tances (0.3, 1, 3, and 5.5%) were used. End pumping wasperformed by a 0.6-W fiber-coupled laser diode with a corediameter of 0.2 mm and a beam divergence of 16°. Thefiber output was first collimated (C) and then focused by asingle 5-mm focal-length lens (L) into the crystal. Thepump spot diameter was estimated to be 150 mm (M2

5 31). Cavity length was 9.5 cm, leading to a laserbeam waist wL of 90 mm. Pump power was changed byadjusting the diode current. A calibrated silicon detectorwas used for measuring the output laser power. For ana-lyzing the spectral distribution of the output laser radia-tion the same equipment as for fluorescence experimentswas used. In these experiments, the etalon effect be-tween crystal faces and cavity mirrors (which modifiesthe spectral shape of laser radiation) was avoided by us-ing an antireflection-coated sample (2 at.% concentratedsample). The antireflection coatings were deposited bythermal evaporation of MgF2 layers in an Edward Auto306 coating system.

3. RESULTS AND ANALYSISA. Laser Experiments: Pump Thresholds and LaserSlope EfficienciesFigure 2 shows the 1.3-mm laser curves as a function ofoutput mirror transmittance for all the samples studiedin this work (including Nd:YAG). The output beam wasfound always to follow a TEM00 Gaussian distribution.No laser action was achieved from the 0.1-at.% and the8-at.%-concentrated samples. Maximum output powerwas obtained from the 2-at.%-doped sample for all theoutput mirrors employed. These results are in accor-dance with previous experimental and theoretical studieson laser oscillation at 1 mm from the Nd:CGG system inwhich it was stated that optimum Nd31 content is ;2–3at.%.11

From laser curves it is possible to determine the opticallosses (L) and the product snettF ( snet is the net emissioncross section and tF is the 4F3/2 metastable state fluores-cence lifetime) by the Findlay–Clay method.14 Since thefaces of the Nd:CGG and Nd:YAG crystals used in the la-ser experiments were uncoated, the output mirror trans-mittances must be corrected taking into account the sur-face reflectivity r of the crystal and the reflectance R ofthe mirrors. The effective transmittance T8 is given by

T8 5 1 2~r1/2 1 R1/2!2

@1 1 ~rR !1/2#2. (1)

Fig. 1. Experimental setup used for laser measurements: LD,laser diode; C, collimating lens; L, focusing lens; IM, input mir-ror; OC, output coupler.

Jaque et al. Vol. 20, No. 10 /October 2003 /J. Opt. Soc. Am. B 2077

Then the absorbed pump power at threshold is given by15

Pth 5hnpp~wc

2 1 wp2!~T8 1 L !

4hpsnettF, (2)

where np is the pump frequency; wp and wc are the pumpand laser beam radii along the length of the crystal, re-spectively; snet 5 sem 2 sESA is the net emission crosssection ( sem and sESA are the stimulated emission andthe ESA cross sections at laser wavelength, respectively);tF is the fluorescence lifetime, hp is the fraction of ab-sorbed pump photons that contribute to the population ofthe 4F3/2 metastable state (hp ' 1); and T8 is the effec-

Fig. 2. Laser power versus absorbed pump power for differentoutput mirror transmittances and Nd31 concentrations. Thedata obtained from the Nd:YAG system are also shown.

Fig. 3. (a) Pump powers at threshold and (b) laser slope efficien-cies, both as a function of output mirror transmittance for differ-ent Nd31 concentration. The corresponding data for theNd:YAG crystal are also displayed.

tive output coupling of the cavity as defined in Eq. (1).Figure 3(a) shows the dependence of the absorbed pumppower at threshold (Pth) on the effective transmittance(T8) for different Nd31 concentrations (Nd:YAG data arealso included in this figure). The best linear fit to eachdependence is also shown (dotted curves). From thesefits, the net emission cross section ( snet) and the internalloss factor (L) can be estimated according to expression(2). Results are listed in Table 1 together with the valuesof the fluorescence lifetime, pump power at threshold, andlaser slope efficiency for all the Nd31 concentrations andoutput mirror transmittances. The values obtained fromthe Nd:YAG crystal are also listed for the sake of compari-son. In Nd:CGG crystals the internal loss factor hasbeen found to be almost independent of neodymium con-centration in the 0.5–2-at.% range, being L ' 1% cm21

and similar to that reported for other Nd31-doped lasermaterials, including Nd:YAG.16 The pump power atthreshold increases with the Nd31 content, mainly as aresult of reduction in the fluorescence lifetime caused byconcentration-induced fluorescence quenching.11

Figure 3(b) shows the laser slope efficiencies as a func-tion of output coupler effective transmittance for eachNd31 concentration. Results obtained for Nd:YAG arealso shown. Compared with the case of pump thresholds,the laser slope efficiencies have been found to follow avery different trend. The laser slope efficiencies obtainedin Nd:CGG crystals were always lower than those corre-sponding to Nd:YAG, although both crystals showed simi-lar optical losses (see Table 1). This effect has been ob-served for all the Nd31 concentrations in which laseraction was achieved. Differences become more signifi-cant as the output mirror transmittance is increased.This indicates that the intracavity laser power, which de-pends on the output mirror transmittance, plays an im-portant role in the mechanism causing the slope efficiencyreduction.

In the case of uncoated crystals, as here, the laser slopeefficiency is given by17,18

hL 5 hP

hnL

hnP

T8

T8 1 LhChESAhe , (3)

where the variables are defined as follows:

1. nL and nP are the laser and pump frequencies, re-spectively (hnL /hnP ' 0.61);

2. T8 is the effective output coupler transmittance;3. L is the round trip optical losses (determined by the

Findlay–Clay method);4. hP ' 1 has been defined in expression (2);5. hC is the geometrical coupling efficiency between

the pump and laser modes; this is a function of the ratiobetween the cavity and pump beam waists (a 5 wC /wL' 1 in our experimental conditions); it also depends onthe so-called saturation parameter S which can be writ-ten as S 5 2P/ISpwC

2, where P stands for the intracav-ity circulating power (P 5 Pout /T) and IS 5 hnL /snettFis the saturation intensity;

2078 J. Opt. Soc. Am. B/Vol. 20, No. 10 /October 2003 Jaque et al.

Table 1. Laser Parameters of Nd:CGG and Nd:YAG Crystals Used in This Work

MaterialT a,

(percent) P thb (mW) h l

csnet

d tFe

(cm2 s) Lf (cm21) tFe (ms) Sg he

h

Nd:CGG(0.1 at.%)

0.3 .300 — — — 241 — —1 .300 — — —3 .300 — — —5.5 .300 — — —

Nd:CGG(0.5 at.%)

0.3 67 0.045 1.9 3 10223 0.012 247 8.5 0.761 96 0.17 3.1 0.723 180 0.20 0.8 0.515.5 .300 — — —

Nd:CGG(1 at.%)

0.3 75 0.043 1.6 3 10223 0.011 221 11 0.781 105 0.18 4.1 0.743 187 0.20 1.1 0.565.5 280 0.094 0.2 0.39

Nd:CGG(2 at.%)

0.3 73 0.045 1.1 3 10223 0.008 200 10 0.751 104 0.17 3 0.713 243 0.19 0.8 0.545.5 370 0.094 0.14 0.4

Nd:CGG(8 at.%)

0.3 .300 — — — 36 — —1 .300 — — —3 .300 — — —5.5 .300 — — —

Nd:YAG 0.3 53 0.06 2.0 3 10223 0.010 230 34 11 80 0.24 12 13 130 0.34 5 15.5 210 0.28 2 1

a Output mirror transmittance.b Pump power at threshold.c Laser slope efficiency.d Net emission cross section.e Fluorescence lifetime of metastable state.f Optical loss factor.g Saturation parameter.h Power extraction efficiency term.

6. hESA stands for the reduction caused by the presenceof ESA processes at pump or laser wavelengths; and

7. he is a power extraction efficiency term which de-pends on the saturation parameter S and on the ratioDn inh /Dnh , where Dn inh and Dnh are the inhomogeneousand homogeneous line widths of emission bands, respec-tively.

Among all the terms listed above only the geometricalcoupling efficiency hC can be considered as independent ofthe laser material employed, as it depends only on theparticular characteristics of the experimental setup (onthe pump and laser beam waists).18 Although its influ-ence on the pump-to-laser conversion efficiencies cannotbe neglected, it does affect in a similar way both Nd:YAGand Nd:CGG systems, and therefore, it does not contrib-ute to the large differences observed in the laser slope ef-ficiencies. To gain a fuller understanding of the mecha-nism causing the low extraction efficiencies [see Fig. 3(b)]shown by Nd:CGG, the reduction terms hESA and he mustbe evaluated.

At this point it is important to mention that the exis-tence of energy transfer upconversion (ETU) processes inthe Nd:CGG system can also influence its laserperformance.19,20 ETU is an energy transfer process inwhich two nearby excited ions initially excited in the

metastable state interact with each other, and, because oftheir interaction, one ion decays to the ground state andthe second one transits to a higher level. In Fig. 4 theETU process and the ESA of both pump and laser radia-tion are displayed over the energy level diagram of Nd31

Fig. 4. Energy level diagram of Nd31 ions in CGG. Energytransfer upconversion (1), excited state absorption of laser radia-tion (2), and excited state absorption of pump radiation (3) pro-cesses are indicated.

Jaque et al. Vol. 20, No. 10 /October 2003 /J. Opt. Soc. Am. B 2079

in CGG so that the differences between them are clearlyobservable. In some Nd31-doped crystals, ETU can limitthe fluorescence excitation efficiency by reducing the ef-fective fluorescence lifetime of the 4F3/2 level.19 To checkfor the possible influence of ETU in the laser performanceof the Nd:CGG system we have measured the 4F3/2 fluo-rescence lifetime under 808-nm excitation for differentpump densities varying from 0 up to 8 kW/cm2 (two timesthe maximum pump density achieved during the laser ex-periments). In the range of pump densities studied, the4F3/2 fluorescence lifetime was found to be independent ofexcitation density (for all the concentrations studied inthis work). Thus, we conclude that ETU does not signifi-cantly perturb the laser performance of this system.

B. Effect of Excited-State Absorption on Laser SlopeEfficiencyThe effect of ESA on the laser slope efficiency of Nd31

doped lasers has been extensively studied.19 When ESAtakes place at the laser wavelength it causes a reductionin the net emission cross section, leading to an increase inthe pump power at threshold, but it has no effect on thelaser slope efficiency. On the other hand, when ESAtakes place at both pump and laser wavelengths its effecton the laser slope efficiency cannot be neglected. The re-duction in laser slope efficiency due to the presence ofESA, hESA , can be written as19

hESA 5sem 2 sESA

L

sem 1 sESAL

F 1

2

exp~2s0pN0d !S 1 2

T8

22 L D 22r2s0

P/~ sem2sESAL !

1 2 exp~2s0pN0d !

3~ s0

P 1 sESAP !~T8 1 2L !

2~ sem 2 sESAL !

G (4)

where sem and sESAL are the stimulated emission and ESA

cross sections at laser wavelength, respectively; d is thecrystal length; s0

P and sESAP are the ground state and ESA

cross sections at the pump wavelength, respectively; andr is a dimensionless parameter that measures the relativemagnitude of the ESA and of the stimulated emissioncross sections and is given by19

rESA 5sESA

P

sem 2 sESAL

. (5)

The evaluation of hESA from Eq. (4) is rather compli-cated. However, the problem is usually solved by nu-merical methods that show that the value of hESA dependsmainly on the particular value of rESA in such a way thathESA decreases as rESA increases.19 It has been shownthat for small values of rESA (rESA , 0.5), the ESA pro-cesses have a negligible effect on laser slope efficiency(hESA ' 1).19

In this section we have determined all the emissioncross sections appearing in expression (5), so that the in-fluence of ESA in the laser slope efficiency can be evalu-ated. The stimulated emission cross section sem can beobtained from the RT emission spectra21:

sem~l! 5l5bI~l!

8pn2ctRE lI~l!dl

, (6)

where I(l) is the emission intensity as a function of wave-length, b is the branching ratio corresponding to the4F3/2 → 4I13/2 transition (b ' 0.1),10,11 tR is the radiativelifetime of the 4F3/2 metastable state (1/tR ' 3.93 103 s21),11 and n is the refractive index. Figure 5(a)shows the spectral dependence of sem obtained for the2-at.%-doped sample (hereafter we will focus our atten-tion on this concentration since it leads to the optimumpump-to-infrared conversion efficiency). The peak crosssection is sem 5 1.5 3 10220 cm2 at 1332.5 nm. At thispoint it is important to note that the emission cross sec-tion obtained for Nd:CGG is lower than that reportedfor Nd:YAG ( sem 5 9 3 10220 cm2),22 this fact explain-ing the higher pump powers at threshold obtained forNd:CGG crystals [see Fig. 3(a)].

The spectral dependence of the ESA cross section forthe 4F3/2 → 4I13/2 laser channel has been also measured.This ESA spectrum was obtained from the excitationspectra corresponding to the 4G1/2 → 4I11/2 visible lumi-nescence at 600 nm. The excitation spectrum obtained inthis way reproduces the wavelength dependence of theexcited-state cross section. Calibrating the sESA spec-trum in terms of cross section units can be accomplishedby using the Judd–Ofelt formalism, together with thepreviously reported Judd–Ofelt parameters of Nd31 ionsin CGG.23 This calibration method has been widely used

Fig. 5. Spectral dependence of the stimulated emission (a) andexcited state absorption (b) cross sections obtained for the 2-at.%-doped sample. Vertical dotted line indicates laser wavelength.

2080 J. Opt. Soc. Am. B/Vol. 20, No. 10 /October 2003 Jaque et al.

for Nd31 ions in other materials.19 Figure 5(b) shows theESA cross section around 1.3 mm. At the laser wave-length (where the emission cross section peaks) we haveobtained sESA

L (1332.5 nm) 5 0.2 3 10220 cm2, whichleads to snet 5 sem 2 sESA 5 1.3 3 10220 cm2. The netemission cross section snet estimated from laser experi-ments is 7 3 10220 cm2 (see Table 1). Thus both valueslie within the same order, and the discrepancy betweenthem could be attributed to experimental uncertainties.

As was mentioned before, the evaluation of the influ-ence of ESA in the laser slope efficiency requires the ESAcross section at pump wavelength. Unfortunately, thestrong ground-state absorption does not allow for an ex-perimental measurement of ESA in this spectral range.In Nd31-doped crystals it is possible to calculate the ESAspectra around 800 nm by using the Judd–Ofelttheory.19,23 From the analysis of the Nd31 energy leveldiagram, ESA at pump wavelength (806 nm) can takeplace through the 4F3/2 → 2D5/2 and 4G7/2 → 2L17/2transitions.19 Nevertheless, the contribution to laser dy-namics of the latter is usually neglected because of thesmall population of the 4G7/2 state. As a consequence,we will focus our attention on the 4F3/2 → 2D5/2 transi-tion. We have built the ESA spectra corresponding tothis transition by using the expression19

sESAJ→J8~l! 5 lSed~J

→ J8!(i, j

f i

2J8 1 1

1

p

Dl/2

~l 2 l ij!2 1 ~Dl/2!2

,

(7)

where J 5 3/2 and J8 5 5/2 corresponds to initial (4F3/2)and final (2D5/2) states, respectively; fi is the Boltzmannfactor of the initial Stark level; Dl is the linewidth of theESA lines assumed with a linewidth equal to that of theground-state absorption band (Dl ' 2.5 nm); l ij are thewavelength positions of the ESA lines; l is the averagewavelength (810 nm); and Sed(J → J8) is the electric-dipole-absorption line strength, which can be calculatedfrom the Judd–Ofelt parameters.11,23 Figure 6 shows the

Fig. 6. Calculated excited state absorption cross section in thepump wavelength range obtained for the 2-at.%-doped sample(dashed curve). The ground state absorption cross section isalso displayed (solid curve). The vertical dotted line indicatesthe pump wavelength.

resulting ESA cross section together with the ground-state absorption cross section. The vertical dashed lineindicates the most efficient pump wavelength. For thiswavelength we have obtained sESA

P 5 4 3 10223 cm2.At this point the ratio rESA 5 sESA

P /sem 2 sESAL can be

calculated as rESA 5 0.002. For this low rESA value, Eq.(4) gives hESA 5 1. In other words, the presence ofexcited-state processes at pump and laser wavelength hasno significant effect on the laser slope efficiency.

C. Effect of Inhomogeneous Broadening on Laser SlopeEfficiencyThe influence of inhomogeneous line broadening on laserdynamics was first studied by Krausz et al.17 In thatwork it was concluded that inhomogeneous line broaden-ing causes a decrease in the laser slope efficiency, but itdoes not affect the laser threshold given by expression (2).According to formula (3), the influence of inhomogeneousline broadening on the laser slope efficiency is describedby the power extraction efficiency term he which is givenby16,17

he 5 b inh21Ap exp~b inh

22 !@1 2 erf~b inh21 !#, (8)

with

b inh 5Dn inh

Dnh$ln@2~1 1 S !#%1/2, (9)

where Dn inh , Dnh and S have been previously defined inSubsection 3.A. Since he depends on the parameter b inhand thus on the saturation parameter S and the ratioDn inh /Dnh , this can be drawn as a function of S for differ-ent Dn inh /Dnh values. These curves are shown in Fig. 7(dotted curves). For all the Dn inh /Dnh ratios, he in-creases with S. This means that for inhomogeneously,broadened laser media, the portion of active ions partici-pating in the laser emission is increased with the circu-lating power in the cavity (S). As a consequence the de-crease in laser slope efficiency caused by inhomogeneousbroadening is enhanced as the output mirror transmit-tance is increased. As we shall see this also influencesthe effective width and spectral shape of the laser line.

Fig. 7. Laser slope efficiencies (obtained for the 2-at.%-dopedsample) as a function of the saturation parameter S. Solidcircles are experimental data and dotted curves are the theoret-ical predictions assuming different Dn inh /Dnh ratios (indicated inthe figure).

Jaque et al. Vol. 20, No. 10 /October 2003 /J. Opt. Soc. Am. B 2081

For the Nd:YAG crystal (homogeneous line broaden-ing), he ' 1, so that the laser slope efficiency is given byhL

YAG 5 0.6(T8/T8 1 LYAG)hcYAG . On the other hand the

effect of inhomogeneous line broadening cannot be ne-glected in Nd:CGG, so that hL

CGG 5 0.6(T8/T81 LCGG)hc

CGGhe . The coupling efficiency factor hC (seeSubsection 3.A), does not depend on the particular lasermaterial but on the experimental conditions (pump andlaser beam waists). Therefore, we can assume hc

YAG

5 hcCGG (this is valid only if the circulating power is the

same, i.e., same output power and mirror transmittance).In addition, from Table 1 we have LYAG ' LCGG . As aconsequence we can estimate he by a direct comparisonbetween the laser slope efficiencies obtained fromNd:YAG and Nd:CGG crystals:

he 'hL

CGG

hLYAG

. (10)

Fig. 8. Spectral shape of the laser emission (obtained for the2-at.%-doped sample) as a function of output mirror transmit-tance.

Fig. 9. Spectral shape of the laser emission (obtained for the2-at.%-doped sample) as a function of diode temperature.

Thus from this equation and the experimental data dis-played in Fig. 2 we have estimated the extraction effi-ciency factor he as a function of the saturation parameter.Results (obtained for the 2-at.%-doped sample) are shownin Fig. 7 (solid circles). As predicted by expressions (8)and (9), the he factor increases with the circulating power.By comparing theoretical curves (dotted curves) and ex-perimental data displayed in Fig. 7, it is possible to esti-mate the ratio between the inhomogeneous and homoge-neous line widths as Dn inh /Dnh ' 2.5 6 0.5. This valueis similar to those obtained previously for otherinhomogeneous-line-broadened, Nd31-doped lasers (rang-ing between 2 and 3).16

The ratio Dn inh /Dnh can also be calculated from spec-troscopic measurements. Since we do not know the valueof the homogeneous line width Dnh we shall assume, in afirst-order approximation, that it is equal to the fluores-cence line width associated with the laser transition inYAG, i.e., Dnh ' 6 cm21.16 On the other hand the inho-mogeneous line width Dn inh can be directly estimatedfrom the emission spectrum shown in Fig. 5(a). It isfound Dn inh ' 18 cm21, which leads to Dn inh /Dnh ' 3, inreasonably good agreement with the value obtained fromthe analysis of the laser efficiencies (see Fig. 7).

D. Influence of Inhomogeneous Broadening on LaserSpectraThe Nd31 multicenter distribution in CGG crystals alsoinfluences the spectral properties of the 1.3-mm laseremission. All the centers with a gain larger than cavitylosses can contribute to the output spectrum.16 If similarspectroscopic parameters (fluorescence lifetime and emis-sion cross section) are assumed for all the centers, as issuggested by site selective experiments,12 the optical gainassociated with each center can be assumed to be propor-tional to the corresponding density of excited ions. As aconsequence changes in the cavity losses or in the relativepopulation of different centers should influence the lineshape of laser emission.

Figure 8 shows the influence of output mirror transmit-tance on the spectral distribution of the laser line ob-tained from a 2-at.%-doped sample. It should be notedthat in the experiments concerning laser line shape, anti-reflection coatings were deposited on crystal surfaces tominimize the influence of the etalon effect caused by thespace between input mirror and crystal faces. Neverthe-less, we obtained the same results with and without an-tireflection coatings, indicating that the spectral shape ofthe laser radiation is not influenced by this effect. FromFig. 8 it is clear that the width of the laser line decreasesas the output mirror transmission is increased (and thusthe intracavity circulating power decreased). It shouldnow be mentioned that this effect was not observed in thecase of Nd:YAG (homogeneous broadening) when similarexperiments were performed. Thus, the behavior ob-served in Fig. 8 is again attributed to the inhomogeneousnature of the fluorescence line. When the output mirrortransmittance (cavity losses) is increased, the total num-ber of Nd31 ions contributing to laser oscillation de-creases (only those centers showing the highest gain par-ticipate in the stimulated emission). This leads to areduction in the laser line width and also in the fraction of

2082 J. Opt. Soc. Am. B/Vol. 20, No. 10 /October 2003 Jaque et al.

pump power that is converted into 1.3-mm laser radiation(causing a reduction in the pump-to-laser conversion effi-ciency).

Figure 9 shows the spectral distribution of the laserline (obtained for the 2-at.%-doped sample) for differentpump laser diode temperatures. The T 5 0.3% outputmirror was used. Pump power was 600 mW. Because ofthe broad Nd31 absorption bands shown by these crystals,output power was found to be almost independent of thediode temperature (pump wavelength). However, as canbe observed, the spectral shape of the laser emission isstrongly dependent on diode temperature (pump wave-length). Because of the different environments, the spec-tral position of absorption bands slightly varies from onecenter to another. As a consequence when the pumpwavelength is changed, the density of excited ions of eachcenter is also modified. Since the shape and position ofthe emission bands also depends on the relative popula-tion of Nd31 centers, any change in the pump wavelengthleads to a variation in the profile of the output laser spec-trum. This spectrum changes in such a way that thegain increases at the emission wavelengths correspondingto the Nd31 centers, which are now more populated.

Figures 8 and 9 indicate that although the broad ab-sorption bands of Nd31 ions in CGG ensure stable outputpower, special care in the stabilization of diode tempera-ture must be taken to avoid spectral changes in the out-put laser radiation.

4. CONCLUSIONSIn this work diode-pumped laser oscillation around 1.3mm from the Nd:CGG system is demonstrated. Experi-ments have been performed on crystals with Nd31 concen-trations varying between 0.1 and 8 at.% showing that op-timum Nd31 concentration is ;2 at.%. The pump powersat threshold obtained for different output mirror trans-mittances have been used to determine the parameters ofrelevance in laser dynamics (net emission cross sectionand optical losses). The laser slope efficiencies ofNd:CGG crystals have been found to be lower than thoseobtained for Nd:YAG. The possible mechanisms for theselow efficiencies have been investigated. We have con-cluded that the laser performance of the Nd:CGG systemis not influenced by the presence of energy transfer up-conversion processes. ESA cross sections at both pumpand infrared wavelengths have also been determined.We have concluded that although ESA cannot be ne-glected, its influence on the laser slope efficiency can beconsidered negligible. On the other hand we have foundthat variations of the laser slope efficiency with outputmirror transmission are correctly described if the inhomo-geneous nature of fluorescence lines (caused by the mul-tisite distribution of Nd31 ions) is taken into account.The comparison between experimental data and theoret-ical predictions has been used to estimate the ratio of theinhomogeneous over the homogeneous line widths asDn inh /Dnh ' 2.5 6 0.5, this value being in good agree-ment with that obtained from spectroscopy. Finally, theinfluence of multicenter distribution on the spectral shapeof the laser radiation has been investigated. Resultsshow that although thermal control of pump diode is not

necessary for 1.3-mm power stabilization, it is of criticalimportance in the spectral properties of output radiation.

ACKNOWLEDGMENTSThis work has been supported by the Comunidad Au-tonoma de Madrid (CAM) under projects 07M/0065/2001and 07N/0020/2002. D. Jaque acknowledges the Minis-terio de Ciencia y Tecnologia for a Ramon y Cajal con-tract.

Corresponding author D. Jaque may be reached bye-mail to daniel.jaque@uam.es.

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