Partially-coherent waves with binominal coherence

TL;DR

This paper provides a detailed spectral analysis of non-diffracting optical waves with binominal two-point coherence functions, establishing conditions for their physical validity and examining their maximum contrast properties.

Contribution

It introduces a comprehensive framework for analyzing binominal coherence functions, including conditions for non-negativity and spectral properties, which was not previously detailed.

Findings

Derived necessary and sufficient conditions for non-negative definiteness.

Calculated eigenvalues and eigenfunctions for general binominal coherence functions.

Analyzed maximum irradiance contrast conditions for specific BCF examples.

Abstract

Comprehensive analysis of non-diffracting optical waves with binominal two-point coherence function (BCF) is presented. This coherence function consist of two terms, each depending on either separation of points or central point. We established the necessary and sufficient conditions for non-negative definiteness of the binominal coherence functions. Spectral analysis, including calculations of the eigenvalues and eigenfunctions for the general BCF case is presented. We considered two simple BCF examples of and analyzed the conditions leading to the maximum irradiance contrast.