Diffraction Problem and Amplitudes-Phases Dispersion of Eigen Fields of a Nonlinear Dielectric Layer

TL;DR

This paper analyzes the amplitudes and phases dispersion of eigen fields in a nonlinear dielectric layer, highlighting self-organization phenomena and eigenmode properties in a nonlinear electrodynamic system.

Contribution

It introduces a constructive approach to analyze eigen oscillation-wave fields in a nonlinear dielectric layer with Kerr-like nonlinearity.

Findings

Eigen fields are characterized through a diffraction problem solution.

Self-organization effects are linked to energy flow from external sources.

Eigen mode norms are derived from the diffraction problem.

Abstract

The open nonlinear electrodynamic system - nonlinear transverse non-homogeneous dielectric layer, is an example of inorganic system having the properties of self-organization, peculiar to biological systems. The necessary precondition of effects of self-organization is the presence of a flow of energy acting in system from an external source, due to which the system gets ability to independent formation of structures. On an example of the transverse non-homogeneous, isotropic, nonmagnetic, linearly polarized, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer the constructive approach of the analysis of amplitudes-phases dispersion of eigen oscillation-wave fields of nonlinear object are shown. The norm of an eigen field is defined from the solution of a diffraction problem of plane waves or excitation of point or compact source of a nonlinear layer.