The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method

TL;DR

This paper explores the connection between the Wigner-Weyl kinetic formalism and the complex geometrical optics method, showing they can produce equivalent wavefield intensities in wave propagation scenarios.

Contribution

It establishes a direct relationship between two asymptotic wave propagation techniques and provides analytical solutions linking them.

Findings

Wavefield intensity equivalence demonstrated

Analytical solutions for Gaussian beams obtained

Relationship confirmed in lens-like media

Abstract

The relationship between two different asymptotic techniques developed in order to describe the propagation of waves beyond the standard geometrical optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex geometrical optics method, is addressed. More specifically, a solution of the wave kinetic equation, relevant to the Wigner-Weyl formalism, is obtained which yields the same wavefield intensity as the complex geometrical optics method. Such a relationship is also discussed on the basis of the analytical solution of the wave kinetic equation specific to Gaussian beams of electromagnetic waves propagating in a ``lens-like'' medium for which the complex geometrical optics solution is already available.