Splendeurs et mis\`eres de theory of laser beam propagation in nonlinear media

TL;DR

This paper develops a comprehensive wave propagation equation for laser beams in nonlinear media that accounts for inhomogeneity, offering a novel modeling approach that improves upon traditional assumptions and aligns with physical principles.

Contribution

It introduces a complete wave propagation equation including dielectric inhomogeneity and validates a new modeling method blending Helmholtz solutions with nonlinear corrections.

Findings

Derived a new wave propagation equation for inhomogeneous media.

Demonstrated the limitations of existing models based on homogeneous assumptions.

Validated the proposed model's consistency with physical optics principles.

Abstract

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.