Speckle Memory Effect in the Frequency Domain and Stability in Time-Reversal Experiments

TL;DR

This paper investigates the speckle memory effect in the frequency domain and its impact on the stability of time-reversal wave refocusing in complex media, providing new analytical insights and quantitative stability measures.

Contribution

It introduces a detailed analysis of the frequency memory effect using fourth-order moments and quantifies the statistical stability of time-reversal focusing in scattering media.

Findings

Characterizes the frequency memory effect and its governing factors.

Provides a quantitative description of the stability of time-reversal wave refocusing.

Derives explicit formulas for the mean and variance of the refocused wave.

Abstract

When waves propagate through a complex medium like the turbulent atmosphere the wave field becomes incoherent and the wave intensity forms a complex speckle pattern. In this paper we study a speckle memory effect in the frequency domain and some of its consequences. This effect means that certain properties of the speckle pattern produced by wave transmission through a randomly scattering medium is preserved when shifting the frequency of the illumination. The speckle memory effect is characterized via a detailed novel analysis of the fourth-order moment of the random paraxial Green's function at four different frequencies. We arrive at a precise characterization of the frequency memory effect and what governs the strength of the memory. As an application we quantify the statistical stability of time-reversal wave refocusing through a randomly scattering medium in the paraxial or beam regime. Time reversal refers to the situation when a transmitted wave field is recorded on a time-reversal mirror then time reversed and sent back into the complex medium. The reemitted wave field then refocuses at the original source point. We compute the mean of the refocused wave and identify a novel quantitative description of its variance in terms of the radius of the time-reversal mirror, the size of its elements, the source bandwidth and the statistics of the random medium fluctuations.