Modeling of the self-sum-frequency mixing laser

A theoretical model of the self-sum-frequency mixing (self-SFM) laser generated by a single crystal is proposed in which the spatial distribution of the pump and circulating fundamental lasers with arbitrary beam waists is taken into account. The model is then applied to two kinds of crystal of current interest, $\mathrm{Nd}:{\mathrm{YAl}}_3({\mathrm{BO}}_3{)}_4$ and $\mathrm{Nd}:{\mathrm{Ca}}_4\mathrm{GdO}({\mathrm{BO}}_3{)}_3.$ Numerical analyses of the self-SFM laser’s properties predict and confirm some experimental results. Several ways to improve the self-SFM laser output are discussed and concluded. The model not only is applicable to self-SFM lasers but is also effective for general analyses of fundamental or nonlinear laser generation with Gaussian beams.