Modelling of the Self Sum-Frequency-Mixing Laser

A theoretical model of the self sum-frequency-mixing (SFM) laser generated by a single crystal is proposed, in which spatial distribution of the pump and circulating fundamental lasers with arbitrary beam waists are taken into account. The model is then applied to two kinds of crystals of current interest, Nd:YAI₃(BO₃)₄ and Nd:Ca₄GdO(BO₃)₃. Numerical analyses of the self-SFM laser properties predict and confirm some experimental results. The model proposed is not limited to self-SFM lasers and may be applied to general analyses of the fundamental or nonlinear laser generation with Gaussian beams.