The influence of nonlinear spectral bandwidth on single longitudinal mode intra-cavity second harmonic generation

We investigate intra-cavity second harmonic generation (SHG) under single longitudinal mode operation while considering the effect of the finite spectral bandwidth of the phase matching. We develop a simple model that takes into account the spectral bandwidth of both the laser gain and the doubling process and show that the theoretical limit of SHG is strongly dependent on the ratio between the doubling crystal spectral bandwidth and the gain bandwidth of the laser. In order to achieve optimal SHG conversion efficiency this ratio should be as high as possible.