Long-time asymptotic of temporal-spatial coherence function for light propagation through time dependent disorder

TL;DR

This paper analyzes the long-time behavior of the coherence function for light traveling through a randomly scattering medium, revealing a power-logarithmic decay law influenced by scattering angles.

Contribution

It introduces a detailed asymptotic analysis of the field correlator using the Bethe-Salpeter equation, highlighting decay laws and spatial moment behaviors in time-dependent disorder.

Findings

Fluctuation intensity decays as a power-logarithmic stretched exponential.

Spatial moments of the correlator diverge weakly over time.

Decay characteristics depend on scattering angles.

Abstract

Long-time asymptotic of field-field correlator for radiation propagated through a medium composed of random point-like scatterers is studied using Bete-Salpeter equation. It is shown that for plane source the fluctuation intensity (zero spatial moment of the correlator) obeys a power-logarithmic stretched exponential decay law, the exponent and preexponent being dependent on the scattering angle. Spatial center of gravity and dispersion of the correlator (normalized first and second spatial moments, respectively) prove to weakly diverge as time tends to infinity. A spin analogy of this problem is discussed.