Singularities in Speckled Speckle

TL;DR

This paper investigates the complex singularity structures in speckled speckle fields with multiple correlation lengths, revealing anomalous clustering and statistical behaviors through simulations and theory.

Contribution

It provides new insights into the singularity patterns and statistics in speckled speckle fields, highlighting their anomalous clustering and distribution compared to single correlation length fields.

Findings

Singularities form giant clusters or chains depending on source parameters.

Phase extrema can outnumber vortices by factors exceeding 10^4.

Azimuthal extrema can outnumber C points significantly.

Abstract

Speckle patterns produced by random optical fields with two (or more) widely different correlation lengths exhibit speckle spots that are themselves highly speckled. Using computer simulations and analytic theory we present results for the point singularities of speckled speckle fields: optical vortices in scalar (one polarization component) fields; C points in vector (two polarization component) fields. In single correlation length fields both types of singularities tend to be more{}-or{}-less uniformly distributed. In contrast, the singularity structure of speckled speckle is anomalous: for some sets of source parameters vortices and C points tend to form widely separated giant clusters, for other parameter sets these singularities tend to form chains that surround large empty regions. The critical point statistics of speckled speckle is also anomalous. In scalar (vector) single correlation length fields phase (azimuthal) extrema are always outnumbered by vortices (C points). In contrast, in speckled speckle fields, phase extrema can outnumber vortices, and azimuthal extrema can outnumber C points, by factors that can easily exceed $10^{4}$ for experimentally realistic source parameters.