Statistics of diffusive and localized fields in the vortex core

TL;DR

This paper investigates the statistical properties of fields in vortex cores within random wave fields, comparing diffusive and localized regimes, and finds universal and deterministic features supported by experimental and theoretical agreement.

Contribution

It provides a comprehensive analysis of vortex core field statistics, revealing universal distributions and deterministic phase variations dependent on elliptical intensity contours.

Findings

Excellent agreement between experiment and theory.

Phase variation depends solely on elliptical contour eccentricity.

Vorticity distribution reflects Gaussian and mesoscopic transmission properties.

Abstract

The statistics of the field structure in the vortex core surrounding phase singularities in random wave fields are measured and calculated for diffusive and localized waves. Excellent agreement is found between experiment and theory. The variation of phase with geometric angle is deterministic, depending only upon the eccentricity of elliptical intensity contours, whose probability distribution is shown to be universal. The distribution of vorticity is shown to reflect both the vorticity distribution in the Gaussian limit and the mesoscopic distribution of total transmission.