Correlated coherent states and propagation of arbitrary Gaussian beams in longitudinally homogeneous quadratic media exhibiting absorption or amplification

The methods of coherent states and integrals of motion are used to describe propagation of arbitrary Gaussian beams in focusing and defocusing nonlinear (quadratic) media exhibiting absorption or amplification. Analytic expressions for the beam parameters are obtained by purely algebraic procedures, i.e., without calculation of the relevant integrals. An operator theory of perturbations is used to find corrections to the beam path and width as a result of its nonparaxial propagation. The problem of propagation of arbitrary Gaussian beams in a quadratic medium is investigated in the case when the absorption (amplification) axis is shifted relative to the axis of a waveguide.