The effects of focusing in the three‐frequency parametric upconverter

This paper extends the theory of parametric upconversion to describe the mixing of two focused optical beams with unequal confocal parameters. The results of this paper have greatest applicability when focusing of one input beam is limited by physical constraints, e.g., damage. The effects of phase matching, walk‐off, and diffraction are treated herein. The analysis shows that if the beams have fixed confocal parameters b₁ and b₂, optimum mixing generally occurs with b₂≠b₁. If both confocal parameters can be arbitrarily chosen, maximum efficiency occurs with b₁=b₂= (crystal length)/2.84 in the absence of Poynting vector walk‐off, and with b₁≠b₂ in the presence of walk‐off. For weak focusing upconversion efficiency is written in a closed form which shows explicitly the effect of walk‐off.