Accurate derivation of THG conversion efficiency in periodically poled nonlinear medium and optimizing conversion parameters

Abstract

We have derived a novel equation to accurately predict the third harmonic generation (THG) conversion efficiency in hybrid periodically poled nonlinear medium. Our equation considers the general case that takes both depleted pump regime and phase mismatching cases, resulting in more precise predictions of efficiency. This level of accuracy is crucial for certain applications like high-power THG lasers. Moreover, accurate calculation of THG power density is essential to prevent exceeding the crystal damage threshold. We applied our equation on hybrid MgO:PPLN crystal to determine the optimal SHG region length corresponding to two different power densities, namely, $0.25$ and $0.5MW/c{m}^2$. The effect of crystal temperature on efficiency was also studies. Furthermore, a comparison between the derived equation and the commonly used nondepleted pump regime equation was performed. We found that the latter equation is significantly less accurate, particularly at high power densities, with the efficiency of the depleted pump regime being 50.6% less than nondepleted one. To demonstrate the effectiveness of the equation, our results were compared with experimental data, and we observed a good agreement between them.