Some questions of optimal focusing during second harmonics generation in nonlinear crystals. Part 1. Mathematical apparatus
The problem of second harmonics generation (SHG) of monochromatic spatially coherent paraxial radiation in homogeneous quadratic nonlinear uniaxial crystals is considered theoretically. It is assumed that the laser radiation is focused into a crystal by two crossed cylindrical lenses with different focal lengths. The aim of this study is to find dependences of optical focusing parameters on the primary radiation power. The work consists of two parts. Part 1 describes the mathematical apparatus required for the study. It is suggested to transform a set of nonlinear wave equations to a form, more convenient for further use. Some important particular cases are considered. An asymptotically exact analytical solution of the SHG problem is presented.