A Phase-Space Approach for Propagating Field-Field Correlation Functions

TL;DR

This paper introduces a phase-space method based on the Wigner distribution function to efficiently model and analyze the propagation of correlation functions in complex, random, and coherent wave sources, including wave-like effects.

Contribution

It develops a phase-space approach using the Wigner function for propagating field correlation functions, incorporating wave effects like diffraction and evanescent decay.

Findings

Explicit expressions for correlation length growth with distance.

Analysis of evanescent waves in near-field sources.

Reflection behavior of partially coherent sources on flat mirrors.

Abstract

We show that radiation from complex and inherently random but correlated wave sources can be modelled efficiently by using an approach based on the Wigner distribution function. Our method exploits the connection between correlation functions and theWigner function and admits in its simplest approximation a direct representation in terms of the evolution of ray densities in phase space. We show that next leading order corrections to the ray-tracing approximation lead to Airy-function type phase space propagators. By exploiting the exact Wigner function propagator, inherently wave-like effects such as evanescent decay or radiation from more heterogeneous sources as well as diffraction and reflections can be included and analysed. We discuss in particular the role of evanescent waves in the near-field of non-paraxial sources and give explicit expressions for the growth rate of the correlation length as function of the distance from the source. Furthermore, results for the reflection of partially coherent sources from flat mirrors are given. We focus here on electromagnetic sources at microwave frequencies and modelling efforts in the context of electromagnetic compatibility.