## Abstract

We report new experimental results on the phase-matching properties of AgGa_{0.86}In_{0.14}S_{2} for second-harmonic generation (SHG) and sum-frequency generation (SFG) of a Nd:YAG laser-pumped KTiOPO_{4} (KTP), AgGaS_{2} optical parametric oscillators (OPOs), and a CO_{2} laser in the 0.615−10.5910 µm spectral range. In addition, we present Sellmeier equations that provide a good reproduction of the present experimental results and the value of the nonlinear optical constant d_{36}(AgGa_{0.86}In_{0.14}S_{2}) = 13.4 pm/V measured by SHG method.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Owing to the extended IR transmission up to 14.3 µm (Fig. 1) and the decreased birefringence and thermo-optic constants (Δ*n* = *n*_{o} – *n*_{e} = 0.0451 and *d*(Δ*n*)/*dT* = −4.732 × 10^{−6} °C^{−1} at 1.0642 µm) compared to those (12.4 µm, Δ*n* = 0.0529 and *d*(Δ*n*)/*dT* = −5.030 × 10^{−6} °C^{−1} at 1.0642 µm) of AgGaS_{2} [1–5], AgGa_{0.86}In_{0.14}S_{2} appears to be more efficient than AgGaS_{2} for generating mid-IR pulses when pumped by near-IR lasers such as a Nd:YAG laser and a Yb:YAG laser.

We have already reported the 90° phase-matched difference-frequency generation (DFG) in the 4.04–6.98 µm spectral range in this material by using a Nd:YAG laser and a tunable Ti:Al_{2}O_{3} laser as pump sources [2,3]. We also reported the 90° phase-matched up-conversion of a CO_{2} laser at 9.2714–10.5910 µm to the visible range by mixing with a Nd:YAG laser-pumped β-BaB_{2}O_{4} (BBO) OPO [4]. However, no attempt was made to compare these data with those of AgGaS_{2}. In order to assess the potential of this crystal against AgGaS_{2}, we have further studied its phase-matching properties for SHG and SFG in the 0.8428 − 10.5910 µm spectral range by using a Nd:YAG laser-pumped KTP and AgGaS_{2} OPOs and a CO_{2} laser as pump sources. Therefore, we analyzed them by using the refined Sellmeier and thermo-optic dispersion formulas presented in [4]. In addition, we measured the nonlinear optical constant of this crystal as *d*_{36} = 13.4 pm/V by the SHG method at *λ*_{1} = 1.9710 µm. These results strongly suggested that AgGa_{0.86}In_{0.14}S_{2} is more useful than AgGaS_{2} for generating mid-IR pulses above ∼8 µm by OPO and optical parametric amplifier (OPA).

## 2. Experiments and discussion

The 7 mm long, *θ* = 90° and *ϕ* = 45° cut AgGa_{0.86}In_{0.14}S_{2} crystal used in the present experiments is the same one that had been used for the previous experiments [4]. This crystal was mounted on a temperature-controlled copper oven set on a Nikon stepmotor-driven rotation stage having an accuracy of ± 0.02° [6].

The temperature stability of the oven is ± 0.1°C. By using the signal and idler outputs of a Nd:YAG laser-pumped KTP OPO as a pump source, we once again measured the SHG and SFG cut-off wavelengths at 20°C. The shortest SHG wavelength was measured to be *λ*_{2} = 0.9855 µm (*λ*_{1} = 1.9710 µm). For SFG between the fundamental and second harmonic, the fundamental wavelength was *λ*_{1} = 2.8236 µm (*λ*_{2} = 1.4118 µm, *λ*_{3} = 0.9412 µm). Moreover, the 90°phase-matched SFG wavelength between a Nd:YAG laser and the idler output of a Nd:YAG laser-pumped AgGaS_{2} OPO was *λ*_{3} = 0.8428 µm (*λ*_{1} = 4.0511 µm, *λ*_{2} = 1.0642 µm). We also measured the temperature phase-matching bandwidths (Δ*T*·*l*) at full-width at half-maximum (FWHM) for SHG from the temperature variation of the phase-matching wavelengths by heating the crystal from 20 °C to 140 °C at 20 °C intervals, and those for SFG by measuring directly the output powers at the fixed wavelengths by heating the crystal from 20 °C to 40 °C at 2 °C intervals. These results are tabulated in Table 1 together with the data for SFG between a CO_{2} laser and a Nd:YAG laser-pumped BBO OPO at *λ*_{3} = 0.6164 µm [4] and the theoretical values calculated with the following refined Sellmeier equations that were constructed by using the refractive indices given by the single-pole Sellmeier equations presented in Ref. [4].

*λ*is in micrometers. As shown in Table 1, the experimentally observed 90° phase-matching wavelengths and the temperature phase-matching bandwidths (Δ

*T*·

*l*) agree well with the theoretically calculated values.

We also measured the nonlinear optical constant of this crystal from the ratio of SHG output powers observed in this crystal and a 5 mm long, *θ* = 58.2° and *ϕ* = 45° cut reference AgGaS_{2} crystal by pumping with a Nd:YAG laser-pumped KTP OPO tuned at 1.9710 µm. By neglecting the absorption at 1.9710 µm and 0.9855 µm and taking the Fresnel reflection losses at the crystal surfaces and the reference value of *d*_{36}(AgGaS_{2}) = 14.1 pm/V at a phase-matching angle of *θ _{pm }*= 62.5° for AgGaS

_{2}, we found

*d*

_{36}(AgGa

_{0.86}In

_{0.14}S

_{2}) = (13.4 ± 0.7) pm/V.

After these experiments, we have cut the present crystal into *θ* = 39.9° and measured the phase-matching angles for SHG and SFG of a CO_{2} laser at 1.7652 − 10.5910 µm by using a waveguide CO_{2} laser (Coherent DEOS, Model EOM-10) as a pump source. Since the CO_{2} laser was operated at low power when measuring the phase-matching angles, the thermal lensing effect was not observed in this experiment.

The results are tabulated in Table 1 together with the temperature phase-matching bandwidths (Δ*T*·*l*) determined from the temperature variation of the phase-matching angles (Δ*θ _{ext}/*Δ

*T*) observed by heating the crystal from 20 °C to 140 °C at 20 °C intervals and the acceptance angles (Δ

*θ*

_{ex}_{t}·

*l*) given by Eq. (2). As shown in Table 1, the experimentally observed values agree well with the theoretical values given by Eqs. (1) and (2).

In the meantime, we calculated the phase-matching angles for type-1 and type-2 SHG of this crystal at 20 °C. The resulting tuning curves (solid lines) are shown in Fig. 2 together with our experimental points (open circles) measured at *λ*_{1} = 1.9710, 3.5303, 5.2955, and 10.5910 µm. For comparison, we also inserted the tuning curves (dashed lines) of AgGaS_{2} calculated with the following refined Sellmeier equations [7] that were transformed from the single-pole Sellmeier equations presented in Ref. [5].

_{0.86}In

_{0.14}S

_{2}increased from those of AgGaS

_{2}owing to the decreased birefringence. We subsequently calculated the 90° phase-matching curve of this crystal for type-1 three-wave interactions (1/

*λ*

_{1}+ 1/

*λ*

_{2}= 1/

*λ*

_{3}) for SFG and DFG at 20 °C. The resulting tuning curve (solid line) is shown in Fig. 3 together with our experimental points (open circles/not all) measured at

*λ*

_{1 }= 1.9710–10.5910 µm [2,4]. For comparison, we also inserted the tuning curve (dashed line) of AgGaS

_{2}calculated with Eq. (3) together with our experimental points (open circles) at

*λ*

_{1}= 1.7718 − 3.1428 µm, those (open triangles) of Chen

*et al*. [8] at

*λ*

_{1}= 4.8912 and 5.3333 µm, and those (closed circles and closed triangles/not all) at

*λ*

_{1}= 7.04 − 10.5910 µm taken from Refs. [9–11]. As can be seen from this figure, the tuning curve of AgGa

_{0.86}In

_{0.14}S

_{2}shifted towards longer wavelengths owing to the decreased birefringence of this crystal as noted in the preceding.

In addition, the refractive indices of AgInS_{2} are obtained from the well-known relationship Eq. (4) in mixed crystals. From Eqs. (1), (3), and (4), it is found to be a positive uniaxial crystal below 1.127 µm.

Since AgGa_{0.86}In_{0.14}S_{2} is more transparent than AgGaS_{2} at wavelengths longer than ∼8 µm (*α* = 0.35 cm^{−1} at 10 µm for AgGa_{0.86}In_{0.14}S_{2} and *α* = 0.6 cm^{−1} at 10 µm for AgGaS_{2}) and its nonlinear optical constant does not differ from *d*_{36} = 14.1 pm/V of AgGaS_{2}, AgGa_{0.86}In_{0.14}S_{2} seems to be more efficient than AgGaS_{2} when used as a Nd:YAG laser-pumped OPO and OPA. The laser-induced damage threshold of AgGa_{0.86}In_{0.14}S_{2} is almost as high as that of AgGaS_{2} (>2.2J/cm^{2} at 9.2714 µm [12]). Thus, we calculated the type-1 and type-2 phase-matching angles for this process by using Eq. (1). The resulting tuning curve (dashed line) for type-2 OPO is shown in Fig. 4 together with the tuning curve (solid line) and the experimental points of Vodopyanov *et al*. for AgGaS_{2} OPO taken from Ref. [13]. For comparison, we also inserted our tuning curve (dotted line) of AgGaS_{2} calculated with Eq. (3) into this figure. As can be seen from this figure, the tuning curve of AgGa_{0.86}In_{0.14}S_{2} shifted towards longer wavelengths at fixed phase-matching angles as expected from the decreased birefringence. The acceptance angle and temperature phase-matching bandwidth of AgGa_{0.86}In_{0.14}S_{2} for generating 10.50 µm pulses at *θ _{pm }*= 44° are calculated to be Δ

*θ*·

_{ext}*l*= 0.33 deg·cm and Δ

*T*·

*l*= 24.0 °C·cm, which are ∼10% larger than Δ

*θ*·

_{ext}*l*= 0.28 deg·cm and Δ

*T*·

*l*= 19.6 °C·cm of AgGaS

_{2}at

*θ*= 38.4° (The Sellmeier equations of Roberts [14] for AgGaS

_{pm}_{2}give Δ

*θ*·

_{ext}*l*= 0.27 deg·cm at

*θ*= 38°). Thus, AgGa

_{pm }_{0.86}In

_{0.14}S

_{2}is thought to be more stable than AgGaS

_{2}to generate mid-IR pulses up to 14.3 µm when pumped by a high-repetition-rate Nd:YAG laser operating in the picosecond and femtosecond regimes.

## 3. Conclusions

We have reported the phase-matching properties of AgGa_{0.86}In_{0.14}S_{2} for SHG and SFG in the 0.615 − 10.5910 µm spectral range, which are precisely reproduced by the Sellmeier and thermo-optic dispersion formulas presented in this paper. Since the nonlinear optical constant (*d*_{36} = 13.4 pm/V) of this crystal does not differ from that of AgGaS_{2} and it is more transparent than AgGaS_{2} at wavelengths longer than ∼ 8 µm, AgGa_{0.86}In_{0.14}S_{2} is thought to be more useful than AgGaS_{2} for synchronously pumped high-repetition-rate OPO and chirped-pulse high-repetition-rate OPA to generate mid-IR pulses up to 14.3 µm under Nd:YAG laser excitation.

## Disclosures

The authors declare that there are no conflicts of interest related to this article.

## Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

## References

**1. **V. V. Badikov, I. N. Matveev, V. L. Panyutin, S. M. Pshenichnikov, A. E. Rozenson, S. V. Skrebneva, N. K. Trotsenko, and N. D. Ustinov, “Growth and optical properties of the AgGa_{1-x}In* _{x}*S

_{2}system,” Sov. J. Quantum Electron.

**10**(10), 1302–1303 (1980). [CrossRef]

**2. **S. Banerjee, K. Miyata, K. Kato, N. Saito, and S. Wada, “90° phase-matched parametric frequency conversion in AgGa_{1-x}In* _{x}*S

_{2},” Appl. Phys. B

**87**(1), 101–103 (2007). [CrossRef]

**3. **S. Banerjee, K. Miyata, and K. Kato, “Temperature phase-matching properties of mixed chalcopyrite AgGa_{1-x}In* _{x}*S

_{2}crystal,” Opt. Commun.

**277**(1), 202–204 (2007). [CrossRef]

**4. **F. Tanno and K. Kato, “90° phase-matched up-conversion of CO_{2} laser radiation in AgGa_{0.86}In_{0.14}S_{2},” Appl. Phys. B **109**(2), 367–369 (2012). [CrossRef]

**5. **K. Kato, T. Okamoto, S. Grechin, and N. Umemura, “New Sellmeier and thermo-optic dispersion formulas for AgGaS_{2},” Crystals **9**(3), 129 (2019). [CrossRef]

**6. **K. Kato, K. Miyata, V. V. Badikov, and V. Petrov, “Thermo-optic dispersion formula for BaGa_{4}Se_{7},” Appl. Opt. **57**(11), 2935–2938 (2018). [CrossRef]

**7. **K. Kato, V. Petrov, and K. Miyata, “Accurate Sellmeier equations for AgGaS_{2} in the 0.565–10.6321 μm spectral range,” Proc. SPIE **11670**, 11670–54 (2021).

**8. **W. Chen, J. Burie, and D. Boucher, “Midinfrared cw difference-frequency generation using a synchronous scanning technique for continuous tuning of the full spectral region from 4.7 to 6.5 μm,” Rev. Sci. Instrum. **67**(10), 3411–3415 (1996). [CrossRef]

**9. **W. Jantz and P. Koidl, “Efficient up-conversion of 10.6-μm radiation into the green spectral range,” Appl. Phys. Lett. **31**(2), 99–101 (1977). [CrossRef]

**10. **T. Itabe and J. L. Bufton, “Phase-matching measurements for 10-μm upconversion in AgGaS_{2},” Appl. Opt. **23**(18), 3044–3047 (1984). [CrossRef]

**11. **P. Canarelli, Z. Benko, R. Curl, and F. K. Tittel, “Continuous-wave infrared laser spectrometer based on difference frequency generation in AgGaS_{2} for high-resolution spectroscopy,” J. Opt. Soc. Am. B **9**(2), 197–202 (1992). [CrossRef]

**12. **A. Harasaki and K. Kato, “New data on the nonlinear optical constant, phase-matching, and optical damage of AgGaS_{2},” Jpn. J. Appl. Phys. **36**(Part 1, No. 2), 700–703 (1997). [CrossRef]

**13. **K. L. Vodopyanov, J. P. Maffetone, I. Zwieback, and W. Ruderman, “AgGaS_{2} optical parametric oscillator continuously tunable from 3.9 to 11.3 μm,” Appl. Phys. Lett. **75**(9), 1204–1206 (1999). [CrossRef]

**14. **D. A. Roberts, “Dispersion equations for nonlinear optical crystals: KDP, AgGaSe_{2}, and AgGaS_{2},” Appl. Opt. **35**(24), 4677–4688 (1996). [CrossRef]