1722 OPTICS LETTERS / Vol. 32, No. 12 / June 15, 2007

Frequency doubling of CO2 laser radiation at10.6 �m in the highly nonlinear

chalcopyrite LiGaTe2

Jean-Jacques Zondy,1 Franck Bielsa,2 Albane Douillet,2 Laurent Hilico,2 Ouali Acef,3 Valentin Petrov,4,*Alexander Yelisseyev,5 Ludmila Isaenko,5 and Pavel Krinitsin5

1Institut National de Métrologie, CNAM, 61 rue du Landy, F-93210 La Plaine St Denis, France2Laboratoire Kastler Brossel, Université d’Evry Val d’Essonne, rue du Père André Jarlan, F-91025 Evry, France

3LNE-SYRTE, Observatoire de Paris, 61 rue de l’Observatoire, F-75014 Paris, France4Max-Born-Institute for Nonlinear Optics and Ultrafast Spectroscopy, 2A Max-Born-Strasse, D-12489 Berlin, Germany

5Institute of Geology and Mineralogy, Russian Academy of Sciences, S 43 Russkaya Street,630058 Novosibirsk, Russia

*Corresponding author: petrov@mbi-berlin.de

Received February 27, 2007; accepted April 9, 2007;posted April 19, 2007 (Doc. ID 80459); published June 6, 2007

Type-I phase matching for second-harmonic generation at 10.6 �m in LiGaTe2 is demonstrated by using atunable single-frequency continuous-wave CO2 laser, and the nonlinear coefficient of LiGaTe2 is determinedfrom comparison with AgGaSe2. The effective nonlinearity of LiGaTe2 for this process amounts to34.5 pm/V. © 2007 Optical Society of America

OCIS codes: 190.4400, 190.2620.

It seems strange, but in fact the optimum nonlinearchalcogenide crystal for second-harmonic generation(SHG) of the technologically important CO2 laserlines at 10.6 �m still does not exist [1]: whileAgGaSe2 (AGSe) has a relatively low thermal conduc-tivity and rather anisotropic thermal expansion,Tl3AsSe3 has a relatively low nonlinear coefficientand low thermal conductivity and damage threshold,and ZnGeP2 has a very low effective nonlinearity deffor is not phase matchable at all for this process, inaddition to its intrinsic multiphonon absorption at10.6 �m. GaSe has an extremely low damage thresh-old and poor mechanical properties (soft and withlayered structure), while CdSe has low nonlinearityand insufficient birefringence for SHG [1,2]. Sul-phides such as Ag3AsS3, Ag3SbS3, LiInS2, LiGaS2,AgGaS2, or HgGa2S4 are in general absorbing at10.6 �m or not phase matchable (LiInS2, LiGaS2,HgGa2S4,) [2–4]. Some recently developed selenidessuch as LiInSe2 and LiGaSe2 have a rather low defffor this process [4,5], while AgGaTe2 also does nothave enough birefringence for it [6]. CdGeAs2 exhib-its an extremely large nonlinear coefficient(�155 pm/V� but requires cryogenic cooling for re-duction of its residual absorption losses [7]. Linearabsorption is another basic limitation in some el-emental nonlinear crystals previously used for SHGat 10.6 �m (Se, Te), while the growth technology ofbinary HgS was never developed [2]. Moreover, fromthe chalcogenides, most adequate for SHG at10.6 �m, only AGSe is commercially available, whileCdGeAs2 and Tl3AsSe3 can be obtained only fromsome laboratories. New approaches that are underdevelopment include the engineering of quaternarycompounds as solid solutions [3], from which the non-critically phase-matchable AgGaxIn1−xSe2 seemsmost promising [8], or quasi phase matching in ori-entation patterned GaAs [9]; however, both technolo-

0146-9592/07/121722-3/$15.00 ©

gies are still in their premature stage. Here we reportthe first experimental realization of continuous-wave(CW) CO2 laser SHG at 10.6 �m with the recentlydiscovered chalcopyrite LiGaTe2 (LGT) and provide arelative estimation of deff for this nonlinear process.

The successful growth of single crystals of LGT andtheir structure were reported in [5]. The clear trans-parency range �2.5–12 �m� and the relatively largebandgap �2.41 eV� make LGT very interesting forhigh-power applications in the mid-IR [10]. The firstexperimental realization of SHG at 4.5 �m showedthat its nonlinear coefficient d36 is rather high [10];the result transformed to the 10.6 �m→5.3 �m SHGprocess by using Miller’s rule is 39.3 pm/V±10%[11]. Thus LGT possesses roughly a two-times higherfigure of merit (FM=deff

2 /n3, where deff=d36 sin 2� for�=0°, and n is the refractive index) than the crystalnormally selected for SHG at 10.6 �m, AGSe: 74.6against 33.6 pm2/V2 [11,12].

For this SHG study we employed a sealed-off, low-pressure (15 torr of a mixture of CO2-He-N2), dual-discharge-arm, single-longitudinal-mode CO2 laserthat could be tuned by the end grating. The nonlinearcrystals (LGT and a reference sample of AGSe) wereplaced between two crossed broadband grid polariz-ers (with extinction ratio �1%), as in Fig. 1: the firstpolarizer in combination with a half-wave plateserved as a variable attenuator, while the second onestrongly rejected the unconverted fundamental (F)transmitting the generated second harmonic (SH).The latter was possible because in both crystalstype-I SHG was realized. Several additional CaF2plates were used to totally suppress the F wave infront of the InSb detector (connected to a current-to-voltage preamplifier) used for direct measurement ofthe chopped SH power.

The CO2 laser delivered an output power of

�1.3 W in a Gaussian transverse mode. It was lin-

2007 Optical Society of America

June 15, 2007 / Vol. 32, No. 12 / OPTICS LETTERS 1723

early polarized by the end grating. For estimation ofthe relative conversion efficiency and the phase-matching angle we used the 10P�20� line at 10.6 �m.The 9R�20� line at 9.27 �m was used to infer the signof the phase-matching angle deviation from the givencut. The LGT sample and the reference AGSe samplehad an equal aperture of 4 mm�4 mm and thicknessof 2 mm. The LGT was cut at �=31.4° ��=0° � fortype-I ee-o SHG, and the AGSe was cut at �=55.5°��=45° � for type-I oo-e SHG. Both were uncoated.

With loose focusing of the F beam (Gaussian waistw0=230 �m obtained by f=20 cm lens L1) we firstverified the phase-matching capability of LGT. Theexperimentally obtained internal phase-matchingangles (�=32.85° ±0.5° at 10.6 �m and �=29.33°±0.5° at 9.27 �m) were very close to the values cal-culated by the existing Sellmeier equations [10]:32.07° and 29.00° at 10.6 and 9.27 �m, respectively.

Fig. 1. Schematic of the setup for SHG. C, mechanicalchopper; HWP, CdS half-wave plate; GP, Ge grid polarizer;L1, ZnSe focusing lens; L2, ZnSe collecting lens �f=35 mm�; InSb, indium antimonide liquid-N2-cooled photo-voltaic detector.

The measured angular acceptance of LGT for SHG at

effect of bulk absorption–scattering losses, which are

10.6 �m is shown by the symbols in Fig. 2 for two Fbeam waists.

For estimation of the conversion efficiency and deffwe used a standard analytical approach taking intoaccount the Fresnel losses as well as absorption-scattering losses at both the F and SH wavelengths,the different index of refraction, the focusing func-tion, and the spatial walk-off [13]. To eliminate errorsrelated to the exact determination of the collection ef-ficiency we based the estimation of deff on a relativemeasurement:

�deff

deff��2

=�

��

T2��

T2��T��

T��2n�n2�

n��n2��

h�

hexp�Lc��2� − �2�� ��,

�1�

Fig. 2. (Color online) Angular acceptance of LGT mea-sured for two different focusing conditions (symbols) andtheoretical calculation (curves).

with

h�a,l,,� =1

2l�−l/2

l/2 � d�d��exp�− a�� + �� + l� − 2�� − ���2 − i�� − ����

�1 + i���1 − i���,

where �=P2� /P�2 is the measured power conversion

efficiency; T=1−R=4n / �n+1�2 is the Fresnel trans-mission at the F ��� and SH �2��; h is the aperturefunction that takes into account the effects of focus-ing, walk-off, and losses; Lc is the physical crystallength, assumed here to be equal for the two samples;� denotes the absorption–scattering loss; a= ���

−�2� /2�zR; and l=Lc /zR, also called the focusing pa-rameter, is the crystal length scaled to the F beamRayleigh length zR=k�w0

2 /2. The function h is theGaussian beam focusing function that accounts forthe deleterious effects of the finite beam aperture: (a)the effect of Poynting vector walk-off [�2��AGSe�=0.67° =11.7 mrad or ���LGT�=2.057° =35.9 mrad]at =10.6 �m via the walk-off parameter =� /�0,which is merely the walk-off angle scaled to the Fbeam divergence �0= /�n�w0, (b) the effect of dif-fraction via the kernel of the h function, and (c) the

often neglected but are important in our imperfectLGT sample [10,11]. The argument =�k ·zR of thefocusing function is the reduced wave-vector mis-match ��k=k2�−2k�� that can be angularly tuned fora peak phase-matching search. The h function is re-lated to a G mismatch function �G��=2h�� / l� thattends (when a→0) to the well-known sinc2��kLc /2�as the focusing parameter l→0 (plane-wave limitwith w0→�). In particular, the comparison of thebandwidth of G�w0 ,� as function of for a givenwaist with the experimental angular tuning band-width allows one to refine accurately the actual waistof the F beam [14], otherwise determined in thiswork from the power transmission through cali-brated pinholes [13].

The primed symbols in Eq. (1) refer to the refer-ence sample (AGSe). For two materials of almostidentical index of refraction (n�=n2�=2.4945 for LGTand n =n =2.5912 for AGSe) this ratio depends

� 2�

1724 OPTICS LETTERS / Vol. 32, No. 12 / June 15, 2007

mainly on the evaluation of h� /h and the careful es-timation of the loss coefficients at the F and SH. TheSH loss of each material was measured in transmis-sion by positioning one of the samples right behindthe phase-matched one and removing the contribu-tion of the Fresnel reflection at normal incidence. Thelosses at the F were estimated at the Brewster anglefor the corresponding polarization.

The dashed curve in Fig. 2 is a sinc2 function cal-culated with the LGT parameters. The black curve isnot a fit either: it is a calculation of the h��kLc /2� ap-erture function. To link the computed normalizedwave-vector mismatch =�k ·zR to measured inter-nal angles �, �k��� is expanded to first order as�k���= ���k /����PM

�� by using the approximate rela-tion ���k /����PM

=2�k�����PM=0.106 �m−1 rad−1. It

can be seen that the experimental angular band-width ���=1.72° � matches extremely well the valuegiven by the dispersion relations of LGT.

We compared the SHG efficiencies of LGT andAGSe, using focusing lenses with f=20 cm and f=7.5 cm (Fig. 3). The loose focusing �w0=230 �m�corresponds to a focusing parameter of l=0.051 ap-proaching the plane-wave limit. The walk-off lengthsare L�=�w0 /�=35 mm for AGSe and 11.3 mm forLGT, well beyond the crystal thickness. In the case ofloose focusing, however, an etalon effect of the AGSesample, which was phase-matched at strictly normalincidence, had an enhancement effect and precludedan accurate estimation of the relative efficiency. Un-wanted intensity fluctuations due to optical feedbackto the laser were avoided with tighter focusing �f=7.5 cm�. The waist measured with this lens (L1 inFig. 1) was w0=124 �m, corresponding to l=0.176,whereas L��AGSe�=18.8 mm and L��LGT�=6 mm,which is now comparable with the crystal thickness.Owing to the stronger F beam divergence, the etaloneffect was no longer noticed for the AGSe samplewhen it was slightly tilted in the uncritical plane (noF or SH power fluctuations). The SH signal wasstable, allowing a better comparison of the conver-sion efficiency. The result is plotted in the upper partof Fig. 3, now revealing a net difference in the twoslopes of the efficiency curves � /��=1.437. Wechecked that within the uncertainties in the esti-

Fig. 3. (Color online) Comparison of the conversion effi-ciencies of LGT and AGSe for SHG at 10.6 �m under the

same two focusing conditions as in Fig. 2.

mated loss coefficients, the ratio h� /h does not sig-nificantly deviate from unity and thus the influenceof the losses in the exponential factor in Eq. (1) ispredominant over the ratio of the focusing functions.When the losses, ���AGSe�=0.75 cm−1, �2��AGSe�=1.22 cm−1, ���LGT�=1.95 cm−1, a2��LGT�=3.38 cm−1, are accounted for, then h�=0.08167 �G�=0.9644� and h=0.07912 �G=0.8994�, yielding aratio of the effective nonlinearities of deff /deff�=1.42�±10% �. This leads to d36�LGT�=1.285d36�AGSe�=37.9 pm/V [12], which is in fullagreement with the value previously estimated bySHG of fs pulses at 4.5 �m in the plane-wave limit[10,11]. Thus deff�LGT�=34.5 pm/V for SHG at10.6 �m.

This work was supported in the frame of ProjectD/0427481 by the German-French bilateral pro-gramme PROCOPE. Financial support by the Accessto Research Infrastructures activity in the SixthFramework Programme of the EU (contract RII3-CT-2003-506350, Laserlab Europe) for conducting the re-search is also gratefully acknowledged. The crystalgrowth work was supported by the Russian Founda-tion for Basic Research (grant 04-02-16334).

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