# 90° phase-matched up-conversion of CO_{2} laser radiation in AgGa_{0.86}In_{0.14}S_{2}

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## Abstract

The CO_{2} laser radiation at 10.5910–9.2714 μm was up-converted to the visible in the 90° phase-matched AgGa_{0.86}In_{0.14}S_{2} crystal by mixing with the output of the 0.3547 μm pumped BBO optical parametric oscillator at 25–120 °C. The new Sellmeier and thermo-optic dispersion formulas that reproduce these experimental results correctly as well as the previously published data [Banerjee et al. in Appl Phys B 87:101, (2007); Opt Commun 227:202 (2007)] for difference-frequency generation at 4.05–6.98 μm and second-harmonic generation at 5.2955 μm are presented.

## 1 Introduction

In previous publications [1, 2], we have reported the Sellmeier and thermo-optic dispersion formulas for AgGa_{0.86}In_{0.14}S_{2} that provide a good reproduction for difference-frequency generation (DFG) at 4.05–6.98 μm and second-harmonic generation (SHG) at 5.2955 μm. However, a somewhat large discrepancy between theory and experiment was encountered for the 90° phase-matched up-conversion of the CO_{2} laser radiation achieved in this crystal. For instance, the experimentally observed OPO pump wavelengths for up-conversion of the 10.5910–9.2714 μm radiation are 14–17 nm shorter than the values given by the above-mentioned Sellmeier equations. In addition, a significant difference between theory and experiment was found for the temperature-dependent phase-matching conditions for this process. Thus, we have corrected these formulas so as to satisfy the new experimental results, and simultaneously fit the data points presented in [1, 2].

Here, we report the new experimental results on the 90° phase-matched up-conversion of the CO_{2} laser radiation in AgGa_{0.86}In_{0.14}S_{2} and the new Sellmeier and thermo-optic dispersion formulas for this crystal.

## 2 Experiments and discussions

The experiments were carried out with a step-tunable CW CO_{2} laser and a 0.3547 μm pumped BBO optical parametric oscillator (OPO) as the pump source. Both beams were combined with a ZnSe optical flat and collinearly incident on the refabricated, 7-mm-long, θ = 90° cut AgGa_{0.84}In_{0.16}S_{2} crystal mounted on the temperature controlled oven.

The OPO pump power was adjusted to 5–10 mJ at 10 Hz to avoid the surface damage of the AgGa_{0.84}In_{0.16}S_{2} crystal, and the CO_{2} laser power was adjusted to less than 20 mW to avoid local heating. The unfocused beam diameter was 4 mm for the former and 2 mm for the latter.

The pump and output wavelengths were measured by a 0.5-m spectrometer with an accuracy of less than 0.1 nm.

_{2}laser wavelengths at 9.2714–10.5910 μm, and by tuning the BBO/OPO wavelength from 0.65 to 0.70 μm, we have measured the 90° phase-matching pump wavelengths at 25 °C. The resulting experimental points (open circles) are shown in Fig. 1 together with the theoretical curves (A) and (B) that were calculated with the Sellmeier equations of Banerjee et al. [1, 2] for this crystal and those of Badikov et al. [3] for AgGa

_{1 − x }In

_{ x }S

_{2}(

*x*= 0.008 and 0.20), which differ significantly from the data points. The real line (C) is calculated with the following Sellmeier equations:

The measured acceptance angles and spectral phase-matching bandwidths at full-width at half-maximum (FWHM) are Δθ_{int}·ℓ^{½} = (2.3 ± 0.1) deg cm^{½} and Δλ_{p}·ℓ = (0.4 ± 0.1) nm cm, which agree well with the theoretical values of Δθ_{int}·ℓ^{½} = 2.35 deg cm^{½} and Δλ_{p}· ℓ = 0.39 nm cm for the CO_{2} laser wavelength of 10.5910 μm and Δθ_{int}·ℓ^{½} = 2.34 deg cm^{½} and Δλ_{p}·ℓ = 0.48 nm cm for the CO_{2} laser wavelength of 9.2714 μm.

Note that the ordinary and extraordinary refractive indices of AgGa_{1 − x }In_{ x }S_{2} increase and the birefringence decrease as a function of In concentrations [3] as in the case of AgGa_{1 − x }In_{ x }Se_{2} [4]. While the Sellmeier equations of Banerjee et al. [1, 2] give the ordinary refractive indices that are smaller than those of pure AgGaS_{2} [5] at wavelengths longer than 2.42 μm; in contrast, the new Sellmeier equations give the normal dispersion [*n*(AgGa_{0.86}In_{0.14}S_{2}) > *n*(AgGaS_{2})] throughout the whole spectral range. In addition, this index formula correctly reproduces the 90° phase-matched DFG between the Ti:Al_{2}O_{3} laser at 0.84274 μm and the Nd:YAG laser at 1.0642 μm as well as the phase-matching angle of θ_{PM} = 80.8° and 73.0° for SHG of the CO_{2} laser lines at 10.5910 [1, 2] and 10.2466 μm, respectively.

_{2}laser wavelengths of 10.5910 and 9.5525 μm are shown in Fig. 2.

_{p}/d

*T*= 0.101 and 0.108 nm/ °C for the CO

_{2}laser wavelength of 10.5910 and 9.5525 μm, respectively. The temperature phase-matching bandwidth (FWHM) for this process is Δ

*T*ℓ = (3.4 ± 0.1) °C cm, which agrees well with the calculated values of Δ

*T*ℓ = 3.3 and 3.5 °C cm for the respective CO

_{2}laser wavelengths of 10.5910 and 9.5525 μm.

_{2}laser line at 10.5910 μm given by Banerjee et al. [1, 2]. at 25–203 °C. However, because our calculated values for DFG based on the Nd:YAG laser do not fit their data points shown in Figs. 3 and 4 of [2] except at 120 °C, we have carefully checked these data points and found a distinct difference between the DFG wavelengths obtained at 25 °C by mixing the Ti:Al

_{2}O

_{3}laser the Nd:YAG laser [1] and by mixing the BBO/OPO and Nd:YAG laser [2] in the same crystal. The former is 4.0497 μm as noted in the preceding, while the latter is 4.0258 μm (Fig. 3 of [2]).

In order to clarify this inconsistency, we have once again measured DFG between the BBO/OPO and the Nd:YAG laser under the identical experimental conditions described in [2]. The resulting tuning points (open circles) are shown in Figs. 3 and 4 together with the data points (triangles) taken from [2]. As can be seen from these figures, our data points agree excellently with the theoretical values calculated with Eqs. (1) and (2). Thus, the data point shown in Fig. 3 of [2] is thought to be in error.

## 3 Conclusion

In summary, we have reported the 90° phase-matched up-conversion of the CO_{2} laser radiation at 9.2714–10.5910 μm in AgGa_{0.86}In_{0.14}S_{2}. These data were used to construct the new Sellmeier and thermo-optic dispersion formulas that provide the excellent reproduction of these experimental results as well as the previously published data [1, 2] of DFG at 4.05–6.98 μm and SHG of the CO_{2} laser at 10.5910 μm. We believe that these Sellmeier and thermo-optic dispersion formulas are highly useful for predicting the temperature-dependent phase-matching conditions for frequency conversion in the AgGa_{1−x }In_{ x }S_{2} (*x* ≦ 0.14) crystals when combined with our index and thermo-optic dispersion formulas for pure AgGaS_{2} [5].

## Notes

### Open Access

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