  It is demonstrated that current theoretical models utilize equations for
description of laser beam propagation in nonlinear media that were deduced
under the assumption of homogeneity of dielectric constant of the media and for
the case of planar wave front. Here, we deduce complete wave propagation
equation that includes inhomogeneity of the dielectric constant and present
this propagation equation in compact vector form. Although similar equations
are known in the narrow fields, such as, radio wave propagation in ionosphere
and electro-magnetic and acoustic wave propagation in stratified media, we
develop here a novel approach of using such equations in modeling of laser beam
propagation in nonlinear media. The inadequacy of the assumptions under which
the propagation equations are derived in the current model is demonstrated.
Also, mathematical derivation is presented that describes foundation and
validates our previously reported method for modeling of laser beam propagation
in nonlinear media by blending solution of linear Helmholtz equation with a
correction term representing nonlinear field perturbation expressed in terms of
paraxial ray-optics (eikonal) equation. Unlike all previous theoretical
approaches developed during past five decades, our approach satisfies
correspondence principle since in the limit of zero-length wavelength it
reduces from physical to geometrical optics.
