General treatment of sum-frequency mixing with elliptical Gaussian beams

Optical sum-frequency mixing offers an efficient way to generate coherent light at wavelengths that are not directly accessible by lasing transitions. The efficiency of these mixing processes can be enhanced by using elliptical rather than spherical Gaussian beams. In this paper, an expression for the nonlinear conversion efficiency in these processes is derived. Numerical results are presented that allow maximizing the obtainable output power by an optimization of the input beam parameters.