1. INTRODUCTION

The newly developed nonlinear crystal ${{\rm BaGa}_2}{{\rm GeSe}_6}$ (point symmetry 3) has been already successfully employed for frequency doubling of ${{\rm CO}_2}$ laser radiation at 10.5910 µm [1], a mid-IR optical parametric oscillator (OPO) pumped by a Rb-doped periodically-poled ${{\rm KTiOPO}_4}$ (Rb:PPKTP) OPO at 1.85 µm [2], mid-IR difference-frequency generation (DFG) between the signal and idler outputs of a 1.035-µm-pumped femtosecond periodically poled ${{\rm LiNbO}_3}$ (PPLN) OPO [3], and mid-IR femtosecond optical parametric amplification (OPA) pumped by a 1.96-µm Tm-fiber laser system [4]. However, in any nonlinear crystal, refractive index variation due to residual absorption of some of the interacting wavelengths may result not only in thermal lensing effects but also in noticeable phase mismatch, which will strongly affect the conversion efficiency of harmonic generation, OPO, DFG, or OPA. To investigate these deleterious effects that may occur in ${{\rm BaGa}_2}{{\rm GeSe}_6}$ for high-average-power operation, we have studied the temperature-dependent phase-matching properties for second-harmonic generation (SHG) and sum-frequency generation (SFG) by using Nd:YAG laser-pumped KTP and ${{\rm RbTiOAsO}_4}$ (RTA) OPOs and a ${{\rm CO}_2}$ laser and its harmonics as pump sources. In addition, we have measured the thermo-optic constants ${\rm d}{n_o}/{\rm d}T$ and ${\rm d}{n_e}/{\rm d}T$ of this uniaxial crystal at 0.7993–3.3913 µm by using a prism method and constructed the thermo-optic dispersion formula. This formula, combined with our Sellmeier equations reported in Ref. [5], accurately reproduces the experimentally obtained temperature-dependent SHG and SFG phase-matching conditions in the 0.805–10.5910 µm range and indicates that ${{\rm BaGa}_2}{{\rm GeSe}_6}$ is less temperature sensitive than ${{\rm BaGa}_4}{{\rm Se}_7}$ [6] for OPOs and chirped-pulse OPA systems pumped by high-average-power Ho:YAG and Ho:YLF lasers and regenerative amplifiers at 2.052 and 2.091 µm, respectively.

2. EXPERIMENTS AND DISCUSSION

Prior to the thermo-optic constant measurements, we investigated the temperature-dependent phase-matching conditions for nonlinear frequency conversions in ${{\rm BaGa}_2}{{\rm GeSe}_6}$. In this experiment, we used a $\theta = {90}^\circ$ and $\varphi = {49.1}^\circ $ cut crystal that had been used in our previous work [5]. The crystal was mounted in a temperature-controlled copper oven (stability: ${\pm 0.1^\circ {\rm C}}$) that was placed on a Nikon step motor-driven rotation stage (accuracy to vary the angle $\theta : {\pm 0.02}^\circ $). The phase-matching angles and wavelengths were measured at different crystal temperatures from 20°C to 120°C at ${10^\circ {\rm C}} \sim {20^\circ {\rm C}}$ intervals.

We first configured KTP and RTA OPOs pumped with the pulsed output of a Nd:YAG laser at 1.0642 µm and performed temperature-dependent phase-matched frequency-doubling of their outputs in ${{\rm BaGa}_2}{{\rm GeSe}_6}$. By tuning the idler wavelength of the KTP OPO in the 2.140–2.180 µm range, the 90° phase-matching condition was obtained for the type-2 process in the 20–120°C range, giving a linear increase of the phase-matching wavelength with a slope of ${\rm d}{\lambda _1}/{\rm d}T = + {0.15}\,\,{\rm nm/^\circ {\rm C}}$ (Fig. 1). For the type 1 process, studied with the signal wavelength of 1.6100 µm from the RTA OPO, the phase-matching angle was found to change rapidly with a slope of ${\rm d}\theta /{\rm d}T = + {0.074}$ at 50°C, increasing to ${\rm d}\theta /{\rm d}T = + {0.14}\,\, {\rm deg}/^\circ {\rm C}$ at 120°C, owing to the near-90° phase-matching condition at higher temperatures (Fig. 2).

 

Fig. 1. 90° phase-matching wavelength versus temperature for type 2 SHG of a Nd:YAG laser-pumped KTP OPO in ${{\rm BaGa}_2}{{\rm GeSe}_6}$. The solid line is a theoretical calculation with Eqs. (1) and (2). The temperature bandwidth at 20°C is $\Delta T \cdot l = {6.8^\circ {\rm C}} \cdot {\rm cm}$. Open circles represent our experimental data.

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Fig. 2. Phase-matching angle versus temperature for type 1 SHG of a Nd:YAG laser pumped RTA OPO at 1.6100 µm in ${{\rm BaGa}_2}{{\rm GeSe}_6}$. The solid curve is a theoretical calculation with Eqs. (1) and (2). The temperature bandwidth at 20°C is $\Delta T \cdot l = {1.2^\circ {\rm C}} \cdot {\rm cm}$. Open circles represent our experimental data.

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We determined the temperature phase-matching acceptance bandwidths ($\Delta T \cdot \ell$) in terms of full width at half-maximum (FWHM) under eight different phase-matching conditions by using the measured temperature dependence of the phase-matching angles ($\Delta {\theta _{\rm ext}}/\Delta T$) and the calculated angular acceptance ($\Delta {\theta _{\rm ext}} \cdot \ell$) given by the following Sellmeier equations [5]:

Table 1. Temperature Phase-Matching Properties for Type 1 and Type 2 SHG and SFG of a ${{\rm CO}_2}$ Laser and Its Harmonics and Nd:YAG Laser-Pumped KTP and RTA OPOs in ${{\rm BaGa}_2}{{\rm GeSe}_6}$ at 20°C

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Meanwhile, we used a ${{\rm BaGa}_2}{{\rm GeSe}_6}$ prism with an apex angle of 14°31’42” and entrance surface dimensions of ${10.78} \times {12.32}\,\,{{\rm mm}^2}$ that was employed for the measurements of the refractive indices [1], and we measured ${\rm d}{n_o}/{\rm d}T$ and ${\rm d}{n_e}/{\rm d}T$ at 0.7993, 1.0642, 1.1523, 2.052, and 3.3913 µm versus temperature from 20°C to 180°C at an interval of 20°C.

From the raw data, a tentative thermo-optic dispersion formula was first constructed and used to extrapolate ${\rm d}{n_o}/{\rm d}T$ and ${\rm d}{n_e}/{\rm d}T$ at 5.2955 µm and 10.5910 µm. The interpolated and extrapolated values were then iteratively adjusted to obtain the best fit to the measured temperature phase-matching acceptance bandwidths ($\Delta T \cdot \ell$) in Table 1. The refined thermo-optic dispersion formula reads as follows:

To test the validity of Eqs. (1) and (2), we finally performed the phase-matched DFG between the signal ($\lambda_s = 1.8045 \,\, \unicode{x00B5}{\rm m}$) and idler ($\lambda_i = 2.4793 \,\, \unicode{x00B5}{\rm m}$) outputs of a Nd:YAG laser-pumped 90° phase-matched ${{\rm CsTiOAsO}_4}$ (CTA) OPO [6,7] by using the $\theta = {32.1}^\circ $ cut entrance face. Figure 3 shows the experimental values of the phase-matching angles versus temperature for the type 1 and type 2 processes (open circles) together with the tuning curves calculated using Eqs. (1) and (2). The resulting temperature variations are ${\rm d}{\theta _{\rm pm}}/{\rm d}T = + {0.005}\,\,{\rm deg/^\circ {\rm C}}$ for the type 1 process and ${\rm d}{\theta _{\rm pm}}/{\rm d}T = + {0.007}\;{\rm deg/^\circ {\rm C}}$ for the type 2 process, which are smaller than the ${\rm d}{\theta _{\rm pm}}/{\rm d}T = + {0.010}\,\, {\rm deg/^\circ {\rm C}}$ observed for the type 1 process in the $xz\,( = bc)$ plane of ${{\rm BaGa}_4}{{\rm Se}_7}$ (Fig. 3 of [6]). Thus, ${{\rm BaGa}_2}{{\rm GeSe}_6}$ is thought to be more stable than ${{\rm BaGa}_4}{{\rm Se}_7}$ for high-average-power OPOs pumped by a Ho:YLF laser at 2.052 µm and a Ho:YAG laser at 2.091 µm [8]. Similar advantages are expected for mid-IR chirped-pulse OPA at high repetition rates [4].

 

Fig. 3. Phase-matching angle versus temperature for type 1 and type 2 SFG between the signal ($\lambda_s = 1.8045 \,\, \unicode{x00B5}{\rm m}$) and idler ($\lambda_i = 2.4793 \,\, \unicode{x00B5}{\rm m}$) outputs of a Nd:YAG laser-pumped CTA OPO in ${{\rm BaGa}_2}{{\rm GeSe}_6}$. The solid curves are calculated using Eqs. (1) and (2). The temperature bandwidths at 20°C are $\Delta T \cdot \ell = \;{35.1^\circ {\rm C}} \cdot {\rm cm}$ for both type 1 and type 2 processes. Open circles represent our experimental data.

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3. CONCLUSION

We have presented a thermo-optic dispersion formula for ${{\rm BaGa}_2}{{\rm GeSe}_6}$ that proves to be very useful in reproducing the temperature dependence of the experimental phase-matching conditions for the nonlinear frequency-conversion processes in the 0.805–10.5910 µm range, in combination with our Sellmeier equations. We believe that these two formulas will play an essential role in the prediction and investigation of self-induced thermal effects for OPOs and OPAs pumped by high-average-power laser systems in the 2-µm wavelength range.