A study of radiation propagation in a medium with quadratic inhomogeneity

The propagation of Hermitian beams in a medium with a distributed quadratic inhomogeneity is studied and is shown that any solution can be represented as a function of some particular solution. This is accomplished by establishing a one-to-one correspondence between optical fields in a homogeneous medium and in a medium with an arbitrary quadratic inhomogeneity. The stability of optical resonators is studied and the condition for their stability is found. Several solutions are found using the method developed.