Parametric down conversion in li inse2 double pump pass singly resonant oscillator

1. INTERNATIONAL JOURNAL OF COMPUTER ENGINEERING & International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 9, September (2014), pp. 105-114 © IAEME TECHNOLOGY (IJCET) ISSN 0976 – 6367(Print) ISSN 0976 – 6375(Online) Volume 5, Issue 9, September (2014), pp. 105-114 © IAEME: www.iaeme.com/IJCET.asp Journal Impact Factor (2014): 8.5328 (Calculated by GISI) www.jifactor.com 105 IJCET © I A E M E PARAMETRIC DOWN - CONVERSION IN LiInSe2: DOUBLE-PUMP PASS SINGLY-RESONANT OSCILLATOR Rena J. Kasumova Baku State University, 23 acad. Z. Khalilov Str., Baku, AZ1148, Azerbaijan ABSTRACT In the present work investigation is carried out for parametric intracavity oscillation for two pump passage through resonator with account for phase change of interacting waves of pump, signal and idler waves in the materials for mid-IR range of spectrum in case of LiInSe2 crystal. In this work there has been made an analysis of threshold character of parametric generation in this crystal under the conditions of the existing experiment. The more correct values for refractive indices, and angle of phase matching is obtained for LiInSe2 crystal at wavelength of 6.5 mcm. Comparison of results obtained in the constant-intensity, constant-field approximations and experiment is also carried out. Keywords: Intracavity Frequency Conversion, Parametric Oscillation, Mid-IR Crystals, Constant- Intensity Approximation. OCIS codes: 190.2620, 190.4400 INTRODUCTION The current level of progress of society is determined by volume of transmitted information. Development of information technologies and the necessity of creating of global computer networking aid in its promotion. One of the most promising and rapidly growing orientations of science and technology for implantation of these tasks is elaboration of relatively inexpensive compact sources of frequency tunable radiation throughout the all spectral regions. Optical parametric frequency converters are known for the amplification and generation of tunable light in a wide frequency range and therefore are attractive for these kinds of problems. By present, there have been reached the considerable achievements in application of tuning parametrical sources of optical coherent radiation in the mid-infrared spectral range. The results of some investigations have shown that one of perspective in this direction is the elaboration of optical

2. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 9, September (2014), pp. 105-114 © IAEME parametric oscillators (OPO) where the just one nonlinear crystal which is pumped up by one-micron radiation is used [1-6]. Thus important there is a choice of a nonlinear crystal. 106 As is known by the choice of crystals-converters of frequency-the main selection condition is, on the one hand, their transparency in the broad region of spectrum and on the other hand, their high nonlinear susceptibility in comparison with the existing crystals. The most suitable one as OPOs for the middle IR mcm are chalcogenide non-oxide nonlinear crystals. with a pumping near 1 One can note among them the prospect Ag3AsS3, AgGaS2, HgGa2S4, Hg1-xCdxGa2S4, CdSiP2, BaGa4S7, LiGaS2, LiInSe2, as being effective nonlinear crystals for mid IR – range of spectrum [4-15]. To study the nonlinear optical properties of the investigated type of crystal, it is expedient to resort to the constant–intensity approximation [16-17], in contrast to the constant–field approximation [18-19], which permits taking into account the influence of phase effects on the process of frequency conversion of laser radiation in the given crystals of mixed type. At parametric interaction it is necessary to take into account the threshold character of parametric generation to which the losses and phase mismatch of interacting waves make considerable contribution. The simultaneous account of these two factors may be provided by theoretical analysis of wave interaction in the constant-intensity approximation. The second-harmonic generation for CdGeAs2 and Zn1-xMgxSe crystals and also the parametric wave interaction for Zn1-xMgxSe have been studied in the constant-intensity approximation by us [20-22]. In the present work, parametric light generation for chalcogenide nonlinear LiInSe2 crystal is investigated in the case of doubly pump pass. The analysis of threshold intensity of pumping for LiInSe2 in conditions of real experiment is offered. In present work it is considered not only changes of phases of interacting waves and losses, but also partial reduction of intensity for interacting waves. The values of refraction indices and angle of phase-matching have been calculated at parametric generation at 6.5 mcm for LiInSe2. Theory. Let us consider the parametric generation in LiInSe2 according to experimental scheme suggested in [1, 13 and 15]. As a pump source authors employed a diode-pumped Nd:YAG laser at lp=1.064 mcm with pulse duration of 14 ns, pump energy of 100 mJ, an average power of 10 W and the pump beam diameter equal to 3.8 mm. According to experience a crystal sample with 17.6 mm in length was placed into a resonator consisting of two mirrors. The singly-resonant oscillator has been investigated in the case of doubly pump pass in Refs. [1, 13, 15]. The input (left) mirror of resonator had a transmissions of 73-84% and 18-22% for idler and signal waves, respectively. The right mirror was used as a total reflector (R 98.5 %) for all three waves (pump, signal and idler waves). The crystal was pumped through left mirror, which transmitted 82 %. For output of the idler wave semiconductor mirror was used with the transmission coefficient of 67 % at idler wavelength and reflection coefficient of 98 % at pump wavelength. Biaxial LiInSe2 was employed as nonlinear crystal for radiation generation at l=6.5 mcm. It was cut in the x-y plane at j=41.60 for scalar interaction, to ensure maximum effective nonlinearity deff=10.6 pm/V [9]. Let us now consider the situation, in which optical waves at frequencies p (conventionally, the strong wave is known as the pump wave) and i (idler wave) interact in a dissipative nonlinear optical medium of length l to produce an output signal wave at the frequency s (p = s + i). The coupled amplitude equations describe the parametric interaction to have the form [18]

3. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 9, September (2014), pp. 105-114 © IAEME s n n + exp( ), + = − D s s s s p i + = − D i i i i p s p p p p s A are the complex amplitudes of the signal, idler and pump waves at respective D = − + + ( ) exp( 2 ) cosh

4. = G − G − , 2 2 , s i p so p s i po G = I G = I . 107 = = = − I A A A e t k r 1 * 1 * 1 2 i n n + exp( ), 2 p n n + exp( ). 2 i dA A I A i A A i z dz dA A I A i A A i z dz dA A I A i A A i z dz g g g − − − + = − − D (1) Here s,i , p frequencies s,i,p w in direction of axis z. The nonlinear coefficients and loss parameters for j-th wave ( j = s, i, p ) are labeled as j and j , respectively; n g is the constant of n photon absorption, 2 , ; j i , , j j j j s i p b b w = r r . In general case it is supposed that the crystal has linear and two-photon absorption ( n =2). And phase mismatch between the interacting waves is given by p s i D = k − k − k . According to [1, 7-15], LiInSe2 is some orders of magnitude less prone to two-photon absorption process affecting the other existing mid-IR nonlinear crystals (Ag3AsS3, AgGaS2, HgGa2S4, CdSiP2). As a result, in our theoretical analysis for LiInSe2 the two-photon absorption coefficients were neglected. Thus, let's analyze the process of parametric wave interaction in considering crystals without taking two-photon absorption of a pump wavelength of 1.064 mcm into consideration. We carry on the task in general case, when at the entry all three waves with frequencies of p,i,s w are present, so the boundary conditions become as follows , , , , , , ( 0) exp( ) p i s po io so po io so A z = = A ij , (2) where po,io,so j are an initial phases of pump, idler and signal waves at the entry of the medium and z = 0 corresponds to the entry of crystal. We first have analytically investigated the general case further at the numerical account we will consider that po io,so A ˇ A , i.e. on an input in a crystal practically there is only a strong pump wave, and single and idler waves are at level of noise, i.e. experimental conditions [1, 13, 15] are carried out, that is realized only double pump-pass condition. Now we solve the system of Eqs. (1) for the complex amplitudes of the idler wave Ai using constant–intensity approximation in the standard way by applying the boundary conditions (2). Then for the idler wave intensity at the output of crystal (which is determined by 1 1 1 ( ) ( ) ( ) i i i I A A* l = l × l ) we obtain the following [23] 2 * 2 sinh A A q 2 1 1 1 1 2 2 i so po i io i io I I q A q l l l l , (3) where 2 2 2 2 D 4 p s q

5. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 9, September (2014), pp. 105-114 © IAEME ( 0) ( )exp[ (2 ) ], ( 0) ( )exp[ (2 ) ], ( 0) ( )exp[ (2 ) ], = = + = = + = = + A z R A l i d i A z R A i d i A z R A i d i s s s s rs l i i i i ri = × − + − + D cosh sinh sinh I q q q l l l = × so × − × − i × + ×

7. 108 As is known, the parametric process has threshold character. From (3) it is possible to determine threshold value of pumping wave amplitude in the constant – intensity approximation. From the condition of parametric gain, which is Ii (l) ³ Iio at phase matching the threshold amplitude of pumping looks as ( s p i d =d +d ) [23] 2 , ( ) / po thresh s i s p i s A = G + + (4) As seen from (4) the po,thresh A value increases with an increase in mismatch and losses (d). It is seen from the result that the account of the depletion effects ( 2 s p i so G =g g I ), i.e. of the reverse reaction of excited waves on the pump wave, leads to a raise in the threshold pumping amplitude. After reflection from right mirror of a resonator interacting waves propagate now in the opposite direction. The boundary conditions at the entry to crystal look as: 2 1 2 1 l 2 1 p p p p rp (5) where rs,ri ,rp j are the variations of the wave phase at . , p i s frequencies while reflecting from second mirror, , , (2 ) s i p j d are the phase shift of waves at the above frequencies in the air gap of length d between the medium and second mirror, z=0 again corresponds to the entrance into the nonlinear medium, 2i ,2s,2 p R signify coefficients from right mirror for idler, signal and pump waves, respectively and , , 1 ( ) s i p A l are the complex amplitudes of the interacting waves at the exit from the crystal after a single pass through the crystal. After a double pass through the crystal at its exit we obtain the following expression for the intensity of the idler wave ( 1 1, i p i s e = = − − − Dl ): ( ) 2 2 2 2 2 2 2 1 2 2 1 2 D 2 2 2 2 2 2 2 2 sinh ( ) ( )exp( 2 ) cosh cth sinh 1 4 res res s p i i i i i res i res s p res i R R q I R I q q q R q R R q R q −

8. l l l l l l l (6) where 2 2 2 2 4 res res res p s q D = G − G − , 2 2 1 1 ( ), ( ), res res s s p s p s i p G = I l G = I l 2 2 2 1 1 1 l l 1 2 1 1 1 1 ( ) ' exp( 2 ) p p sinh ' sinh ' 2 sinh ' s io I q I q q q q q l l l ,

9. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 9, September (2014), pp. 105-114 © IAEME D = − + + I ( ) exp( 2 ) cosh '

10. D = G − G − , 2 . i s p io G = I 109 2 * 2 A A sinh q ' s io po 2 1 1 1 1 2 2 ' s so s so I q A q l l l l , 2 2 2 2 ' 4 p i q Here l p i s Y =j −j −j − D is phase ratio between interacting optical waves. In practice by choice of values for reflection coefficient of right mirror and of phase mismatching D for all three interacting waves it can be realized the condition 1 i e = . Other words, undesirable phase mismatching Y can be compensated by choice of interference layers (reflection coefficient) of right mirror. It should be noted that during analysis the constant –intensity approximation was applied separately to each passage of the crystal. Thus, for example, at propagating wave from left to right and study of signal wave (or idler wave) the intensities of pump and idler (or signal) waves is considered constant and equal to the entry values respectively , po io I I (or so I ). Whereas at displacement of wave in opposite direction, wave intensity are considered again constant, but already equal to their corresponding entry values 2 2 2 1 2 1 ( ), ( ) p p i i R × I l R × I l (or 2 2 1 ( ) i s R × I l ). At such approach we take the partial decrease of intensities of pump wave and idler (or signal) waves into account because of energy transfer from exciting waves to excited one, that is 1 1 ( ) , ( ) p po s so I l I I l I or 1 ( ( ) ) i io I l I . Usually as a rule, in practice it used propagation of the radiation in the x-y, x-z or y-z planes for biaxial crystals. The samples of LiInSe2 used in experiments [1, 13, 15] were cut for propagation in the x-y plane (type-II phase-matching), which characterized by maximum effective nonlinearity deff. The sample under study was cut at j=41.6o for idler wavelength ~6.5 mcm at normal incidence (q=90o). As is known, at condition x y z n n n biaxial crystal in the x-y plane operates as uniaxial crystal where z o n = n . Thus for given geometry of crystal it realized OPO (for interaction) with maximum effective nonlinearity. Here the equation of 1 1 1 e e o = + should p i s be established for the sake of parametric generation of radiation at an idler wavelength 6.5 mcm and at pumping wavelength of 1.0642 mcm. From here we can get the proper value of 1.2723 mcm for wavelength of signal wave. The main values of refraction indices for wavelength of waves under study are derived from Sellmeyer equation [9], and ( ), ( ), ( ) e e o x i y p z s n n n n n n () e n are given in Table. Table. Calculated data for LiInSe2 at parametric generation of idler wave in the mid-IR Wave type l, mcm () e n

11. , pm/V Phase matching type js, degree pump 1.0642 2.29023 2.330345 2.33898 2.31228 10.6 [9] 41.575 41.6 [1, 13] signal 1.2723 2.27697 2.314298 2.32330 2.32330 idler 6.5 2.22844 2.260755 2.27043 2.25526

12. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 9, September (2014), pp. 105-114 © IAEME 110 RESULTS AND DISCUSSION To study the parametrical frequency conversion in LiInSe2, we will make the numerical calculation of the analytical expression (6) that is derived from the constant-intensity and constant-field approximations for parametric generation with two pump pass of resonator. To choose the parameters for calculation we used the exact information that we have from the experiment for LiInSe2 crystals [1, 13, 15]. The theoretical analysis of nonlinear interaction of optical waves in LiInSe2 with account for phase effects has been made in comparison with existing experimental data. According to existing experiment dissipation for all interacting waves include: effective dissipation in unit length of crystal while scattering is considered; dissipation of diffraction ( 2 a L , , d s i p s i p , , 2 L a L , , 1 ln ( ) 2 s i p − = − where a, L are the radius of plane-parallel circular mirror and length of optical resonator respectively); losses on mirrors due to reflection from mirrors; Fresnel losses for each surface ( 2 − = , , +

13. , , , , 1 1 n n Fresnel s i p s i p s i p for waves which are perpendicular to the crystal). In experiment reflection coefficients that are mentioned above for laser mirrors will make the resonator to have high quality for signal wave than idler wave. Even the high value of transmission coefficient of crystal faces in experiment did not remove the Fresnel losses at the experiment for normal incidence of waves. In [9, 13, 15] effective losses were estimated by interpolation of the experimental measurements and losses are equal to 0.16 -1 for pump wave, 0.07 -1 for signal wave and 0.04 -1 for idler wave. From Fig. 1 we see that parametric generation for different losses begins at various values of pump intensity (curves 1-3). The curve 1 obtained with account of all existing losses while curves 2 and 3, with ignoring the dissipation of diffraction and Fresnel losses. The curves 1 and 3 correspond to the same value of i = 0.04 -1 while curve 2 was estimated at i = 0.089 -1. With an increase of pumping intensity there is an observed first horizontal section of dependence, i.e., parametric reinforcement is absent. Then at the definite value of pumping intensity, i.e., at threshold amplitude of pumping, the notable raising of dependence begins. With the increase of losses, the growth of dependence takes place at greater values of threshold intensity of pumping (compare curves 1 and 3), which is in the consent with (4). So, from the numerical analysis (4) (for D/2

14. =0.1) it follows that in case of parametric interaction in LiInSe2 crystal, threshold energy of pumping will be equal to Ipo=6 mJ (in experiment corresponding value is equal to 6.8 mJ) at di=0.04 cm-1, dp= 0.16 cm-1 ( urve 1) and with account of dissipation of diffraction and Fresnel losses. Size of the beam spot is equal to 3.8 mm (corresponding to pump flow equal to 0.052 J/cm2 (in experiment 0.06 J/cm2)). As in experiment the used value of pulse duration of pump is equal to 14 ns, and then we obtain corresponding pump intensity equal to 3.781 MW/cm2 (in experiment 4.3 MW/cm2). In case of curve 3 the threshold energy of pumping is equal to Ipo=4.5-4.8 mJ (in experiment 0.039-0.042 J/cm2 or 2.84-3.025 MW/cm2). By comparing curves 2 and 3 we see, that by double increasing of losses for idler wave (up to 0.089 cm-1) the nonlinear growth of the threshold energy of pumping dependence takes place and at the same time the output intensity of idler wave decreases. At po I =8 mJ the output energy of idler wave falls with 0.7 to 0.6, i.e. on 15 %. In Fig. 2 the dynamic process of conversion of pump wave energy po I to the idler wave energy i I is depicted in the constant intensity (curves 1-5) and constant field (curve 6) approximations. Here in addition to the numerical calculation of the expression (6) (curves 1-6) experimental points are used from [1, 13 and 15]. By comparing curves 5 and 6 it is seen that the account of the phase change of all interacting waves and also partially change of pump intensity for

15. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 9, September (2014), pp. 105-114 © IAEME double pass resonator leads to the decrease of the output idler intensity in contrast to the constant-field 111 approximation. The curves 1 and 2 are obtained with account of all existing losses while curves 3-5 are calculated by ignoring the dissipation of diffraction and Fresnel losses. With the increase of phase mismatch, the conversion efficiency decreases (compare curves 1 and 2 or curves 3-5). The expressed maxima are observed in Fig. 2 (see curves 1-5). By having more correct values of experimental parameters (absolute value of different losses, the deviation angle from the direction of phase matching and others) we can estimate the optimal pump intensity. The best agreement between experimental and theoretical results (dots in Fig. 2) takes place for curve 3 at phase matching when D/2Gp is equal to 0.15 and we ignore the dissipation of diffraction and Fresnel losses. The discrepancy between estimated and experimental data for D can be explained by 1) lack of enough accurate measured value of losses which is obtained in [9] via interpolation, 2) the quality of bleaching and 3) degree of uncritical angular phase matching. In the experiment for real frequency converters, it is impossible to ensure a condition of phase agreement (phase matching = 0). An error in following the condition of phase matching determines the width of phase matching. Spectral width of pump radiation line, deviation from phase matching angle due to divergence of laser radiation, and instability of temperature for a crystal converter all contribute to mismatch. In future it can determine deviation angle from the direction of the phase matching Dq for biaxial LiInSe2 crystal in which parametric generation of idler radiation occurs at approximate wavelength of 6.45 mcm. Then in the constant-intensity approximation the condition for increasing degree of uncritical angular phase matching is possible to choose. This will draw nearer the creation of the efficient sources of coherent radiation, which is tunable by frequency in the middle-IR region of spectrum. Fig. 1: Dependences of output energy of idler wave in LiInSe2 crystal with 17.6 mm in length ( ) i I l as a function of the pump intensity po I 1.064 mcm) at reduced phase mismatch D/2Gp = 0, 4 / 10 so po I I − = , 5 / 10 io po I I − = , s = 0.07 -1, p = 0.16 -1, i = 0.04 -1 (curves 1 3) and 0.089 -1 (curve 2) with account of dissipation of diffraction and Fresnel losses (curve 1) and ignoring the dissipation of diffraction and Fresnel losses (curves 2 and 3)

16. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 9, September (2014), pp. 105-114 © IAEME 112 Fig. 2: Dependences of output energy of idler wave in LiInSe2 crystal with 17.6 mm in length ( ) i I l as a function of the pump intensity po I 1.064 mcm) at 4 / 10 so po I I − = , 5 / 10 io po I I − = , s = 0.07 -1, p = 0.16 -1, i = 0.04 -1, D/2Gp = 0 (curve 2 and experimental dots) and 0.05 (curves 5 and 6), 0.1 (curve 4) and 0.15 (curves 1 and 3) with account of dissipation of diffraction and Fresnel losses (curves 1 and 2) and ignoring the dissipation of diffraction and Fresnel losses (curves 3-6). Results obtained in the constant-intensity (curves 1-5), constant field (curve 6) approximations and experiment (dots) [1, 13, 15] CONCLUSION Thus, the analysis of nonlinear interaction of optical waves in LiInSe2 has considered with account for phase effects and losses but also with account partially change of interacting wave intensity. From the analysis of nonlinear interaction of optical waves and comparing them with existing experimental data, it is possible to choose optimal values of pumping intensity po I , which means the efficiency of parametric conversion could be increased for the considered crystal of mid- IR range and also make the increasing of the degree of uncritical angular phase matching possible. An absence of significant two-photon absorption makes this compound suitable for optical parametrical converters at 1.0642 nm. Therefore, based on these crystals we can produce parametric generation where technologically developed and popular Nd:YAG lasers could be used as pumping resource. It will make the development of the efficient sources of coherent radiation possible and it could be achieved by converters of frequency tuning in the mid-IR region of spectrum. REFERENCES 1. V. Petrov. “Parametric down-conversion devices: The coverage of the mid-infrared spectral range by solid-state laser sources,” Optical Materials, 34 (2012) 536-554.

17. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 9, September (2014), pp. 105-114 © IAEME 113 2. S.T. Yang, R.C. Eckardt, R.L. Byer, Continuous-wave singly resonant optical parametric oscillator pumped by a single-frequency resonantly doubled Nd:YAG laser. Optics Letters, 18 (12) (1993) 971-73. 3. K.L. Vodopyanov, F. Ganikhanov, J.P. Maffetone, I. Zwieback, and W. Ruderman, “ZnGeP2 optical parametric oscillator with 3.8–12.4-mm tenability,” Otics Express, 25 (2000) 841-843. 4. K.L. Vodopyanov, J.P. Maffetone, I. Zwieback, and W. Ruderman, “AgGaS2 optical parametric oscillator continuously tunable from 3.9 to 11.3 μm,” Appl. Phys. Lett. 75 (1999) 1204-1206. 5. S. Das, Line-tunable singly resonant optical parametric oscillator in mid-infrared spectral range based on KTA crystal. IEEE J. Quant. Electron., 45 (9) (2009) 1100-105. 6. T.-J. Wang, Z.-H. Kang, H.-Z. Zhang, Q.-Yi He, Yi Qu, Z.-S. Feng, Y. Jiang, and J.-Y. Gao, Y.M. Andreev, and G.V. Lanskii, “Wide tunable, high-energy AgGaS2 optical parametric oscillator,” Optics Express, 4 (26) (2006), 13001-13006. 7. L. Isaenko, A. Yelisseyev, S. Lobanov, P. Krinitsin, V. Petrov, and J.-J. Zondy, “Ternary chalcogenides LiBC2 (B=In, Ga; C=S, Se, Te) for mid-IR nonlinear optics”, J. Non-Cryst. Sol. 352 (2006) 2439-2443. 8. M.E. Doroshenko, H. Jelikova, P. Koranda, J. Sulc, T.T. Basiev, V.V. Osiko, V.K. Komar, A.S. Gerasimenko, V.M. Puzikov, V.V. Badikov, and D.V. Badikov. Tunable mid-infrared laser properties of Cr2+:ZnMgSe and Fe2+:ZnSe crystals. Laser Phys. Lett. 7 (2010) 38-45. 9. V. Petrov, J.-J. Zondy, O. Bidault, L. Isaenko, V. Vedenyapin, A. Yelisseyev, W. Chen, A. Tyazhev, S. Lobanov, G. Marchev, and D. Kolker, “Optical, thermal, electrical, damage, and phase-matching properties of lithiumselenoindate,” J. Opt. Soc. Am. B 27 (2010) 1902-1927. 10. L. Isaenko, A. Yelisseyev, S. Lobanov, A. Titov, V. Petrov, J.-J. Zondy, P. Krinitsin, A. Merkulov, V. Vedenyapin, and J. Smirnova, “Growth and properties of LiGaX2 (X=S, Se, Te) single crystals for nonlinear optical applications in the mid-IR”, Cryst. Res. Technol. 38 (2003) 379-387. 11. L. Isaenko, I. Vasilyeva, A. Merkulov, A. Yelisseyev, and S. Lobanov, “Growth of new nonlinear crystals LiMX2 (M=Al, In, Ga; X=S, Se, Te) for the mid-IR optics,” J. Cryst. Growth 275 (2005) 217-223. 12. Yu. M. Andreev, V. V. Atuchin, G. V. Lanskii, N. V. Pervukhina, V. V. Popov, and N. C. Trocenko, “Linear optical properties of LiIn(S1-xSex)2 crystals and tuning of phase matching conditions,” Sol. State Sci. 7 (2005) 1188-1193. 13. G. Marchev, A. Tyazhev, V. Vedenyapin, D. Kolker, A. Yelisseyev, S. Lobanov, L. Isaenko, J.-J. Zondy, V. Petrov, “Nd:YAG pumped nanosecond optical parametric oscillator based on LiInSe2 with tunability extending from 4.7 to 8.7 μm.” Optics Express, 17 (2009) 13441- 13446. 14. J.-J. Zondy, V. Petrov, A. Yelisseyev, L. Isaenko, S. Lobanov, “Orthorhombic crystals of lithium thioindate and selenoindate for nonlinear optics in the mid-IR,” In: Mid-Infrared Coherent Sources and Applications, ed. by M. Ebrahim-Zadeh and I. Sorokina, NATO Science for Peace and Security Series - B: Physics and Biophysics, Springer (2008) 67-104. 15. A. Tyazhev, G. Marchev, V. Vedenyapin, D. Kolker, A. Yelisseyev, S. Lobanov, L. Isaenko, J.-J. Zondy, V. Petrov, “LiInSe2 nanosecond optical parametric oscillator tunable from 4.7 to 8.7 μm.” Nonlinear Frequency Generation and Conversion: Materials, Devices, and Applications IX. Edited by Powers, Peter E. Proceedings of the SPIE, 7582 (2010) article id. 75820E, 11. 16. Z.H. Tagiev, and A.S. Chirkin, Fixed intensity approximation in the theory of nonlinear waves, Zh. Eksp. Teor. Fiz. 73 (1977) 1271-1282. 17. Z. H. Tagiev, R. J. Kasumova, R. A. Salmanova, and N. V. Kerimova, Constant-intensity approximation in a nonlinear wave theory, J. Opt. B: Quantum Semiclas. Opt. 3 (2001) 84-87.

18. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print), ISSN 0976 - 6375(Online), Volume 5, Issue 9, September (2014), pp. 105-114 © IAEME 114 18. S. A. Akhmanov, R. V. Khokhlov, Problemy Nelineynoy Optiki [The Problems of Nonlinear Optics] (VINITI, Moscow, 1965). 19. N. Blombergen, Nonlinear Optics (W.A. Benjamin, New York, 1965). 20. R.J. Kasumova. “Second optical harmonic generation of CO2 laser radiation in CGA crystal,” J. of Nonlinear Optical Physics Materials, 22 (2) (2013) 1350023-1-13. 21. R.J. Kasumova. “SHG in R region in mixed Zn1-xMgxSe crystals,” American J. of Optics and Photonics, 1 (4) (2013) 23-27. 22. R.J. Kasumova. “Optical parametric interaction in infrared region crystals,” J. of Nonlinear Optical Physics Materials, 22 (3) (2013) 1350033-1-9. 23. Z.A. Tagiev, Sh.Sh. Amirov, On the efficiency of the optical parametric oscillation in the prescribed intensity approximation, Soviet Journal of Quantum Electronics 16 (1989) 2243-2247.

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Parametric down conversion in li inse2 double pump pass singly resonant oscillator