Frozen spatial coherence

TL;DR

This paper develops a theoretical framework for partially coherent frozen spatial coherence in optical fields, enabling the design of fields with controlled coherence properties along the propagation axis.

Contribution

It introduces a novel formalism for partially coherent frozen waves using superpositions of Bessel beams and Fourier series, extending the concept of coherence control.

Findings

The cross-spectral density is described by a 2D Fourier series.

A design method for fields with localized coherence properties.

The formalism allows creating fields highly coherent within a finite range.

Abstract

Inspired by the concept of coherent frozen waves, this paper introduces one possible theoretical framework of its partially coherent version, a frozen spatial coherence, in which a desired two-point correlation structure of an optical field is created on the propagation axis by superposing partially coherent zero-order Bessel beams. It is shown that the cross-spectral density can be given a description in terms of a two-dimensional Fourier series, analogous to the one-dimensional approach of coherent frozen waves. The formalism is applied to the design of a partially coherent field which is highly coherent only if the pair of points in the propagation axis belong to a predetermined and finite range and highly incoherent outside that range.