Analytical functions for the optimization of second-harmonic generation and parametric generation by focused Gaussian beams

Abstract

An analytical function involving four parameters is proposed to express the second-harmonic generation efficiency as well as the parametric generation gain coefficient in the Boyd-Kleinman theory. The analytical function clearly reveals the dependence of conversion efficiency on the focusing parameter and the walk-off parameter. Moreover, the optimum focusing parameter and its corresponding maximum efficiency are explicitly given in the analytical function, leading to a straightforward evaluation of a given crystal performance.