Electromagnetic beam propagation in nonlinear media

V.V Semak,M.N Shneider

doi:10.1017/hpl.2015.3

Abstract

We deduce a 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 narrow fields such as radio wave propagation in the ionosphere and electromagnetic and acoustic wave propagation in stratified media, we develop here a novel approach of using such equations in the modeling of laser beam propagation in nonlinear media. Our approach satisfies the correspondence principle since in the limit of zero-length wavelength it reduces from physical to geometrical optics.

Highlights

The science of nonlinear optics is one of the rapidly growing fields driven by multiple important technological applications
As we show below, neglecting the third term is a significant mistake that leads to an inadequate description of wave propagation in nonlinear media
It is usual practice in the majority of nonspecialized educational courses and textbooks to ignore the contribution of the term containing ∇ε and describe electromagnetic wave propagation using the equation deduced for uniform media

Summary

Introduction and other extraordinary particularities of nonlinear beam

The science of nonlinear optics is one of the rapidly growing fields driven by multiple important technological applications. Being unable to find either errors or invalidating assumptions in our forthright approach we journeyed back to the source (Maxwell’s equations) in order to review the foundational scientific principles This examination exposed the assumptions in the original physical concept that, in our nonlinear media have been published since the concept of opinion, are inconsistent and self-contradictory. [11, 12], has a solution represented by the blending of the solution of the Helmholtz equation for propagation of a laser beam in a medium with a uniform and irradiance independent refractive index similar to the one obtained by Kogelnik and Li[14] and a correction term that represents nonlinear field perturbation expressed in terms of paraxial ray optics (the eikonal equation)[15] We will demonstrate that, within paraxial approximation and considering the propagation range in which variation of the spatial profile of laser beam irradiance due to the effect of nonlinear induced refraction is small and, can be considered as perturbation, the propagation Equations (10) or (11) can be straightforwardly modified into an equation that, as proposed in Refs. [11, 12], has a solution represented by the blending of the solution of the Helmholtz equation for propagation of a laser beam in a medium with a uniform and irradiance independent refractive index similar to the one obtained by Kogelnik and Li[14] and a correction term that represents nonlinear field perturbation expressed in terms of paraxial ray optics (the eikonal equation)[15]

Examination of current theory for laser beam propagation in nonlinear media

Revised propagation equation for slowly varying amplitude

Concluding remarks