Absolute value of the d_36 nonlinear coefficient of AgGaS_2: prospect for a low-threshold doubly resonant oscillator-based 3:1 frequency divider

We report the measurement of the absolute $d_{36}$ nonlinear coefficient of silver gallium sulfide $({\mathrm{AgGaS}}_2)$ from three phase-matched nonlinear interactions spanning from 10.2 to 0.78 µm: the sum-frequency of a ${\mathrm{CO}}_2$ laser (10.2 µm) and a near-IR AlGaAs diode laser (0.842 µm), the second-harmonic generation of a KCl:Li color-center laser (2.53 µm), and the noncritically phase-matched $3\omega -\omega \to 2\omega$ difference frequency between the AlGaAs diode laser and the KCl:Li laser to generate 1.265 µm. From the theoretical evaluation of the Gaussian-beam aperture functions for these type I interactions with arbitrary focusing parameters, beam-waist locations, and absorption losses, we have deduced from the three processes the same consistent value $d_{36}=13\hspace{0.5em}(\pm 2) \mathrm{pm}/\mathrm{V}$ for ${\mathrm{AgGaS}}_2.$ Our value is independent of the growth origin of the material. In light of the trustworthy value of $d_{36}$ measured from our experiments we analyze the feasibility of a continuous-wave doubly resonant parametric oscillator-(DRO-)based 3:1 frequency divider pumped by a near-IR diode laser. The predicted pump power threshold for the ring-resonator DRO lies in the range of 70–140 mW for a 14–18-mm-long sample with an absorption loss near the level of $1\% {\mathrm{cm}}^{-1}$ at the output frequencies.