Eur. Phys. J. Special Topics 226, 1445-1455 (2017)
https://doi.org/10.1140/epjst/e2016-60254-0

Regular Article

Demystifying the memory effect: A geometrical approach to understanding speckle correlations^*

Center for Wave Phenomena, Department of Geophysics, Colorado School of Mines, Golden, CO, USA

^a e-mail: prunty@mines.edu

Received: 1 September 2016
Revised: 5 November 2016
Published online: 25 May 2017

Abstract

The memory effect has seen a surge of research into its fundamental properties and applications since its discovery by Feng et al. [Phys. Rev. Lett. 61, 834 (1988)]. While the wave trajectories for which the memory effect holds are hidden implicitly in the diffusion probability function [Phys. Rev. B 40, 737 (1989)], the physical intuition of why these trajectories satisfy the memory effect has often been masked by the derivation of the memory correlation function itself. In this paper, we explicitly derive the specific trajectories through a random medium for which the memory effect holds. Our approach shows that the memory effect follows from a simple conservation argument, which imposes geometrical constraints on the random trajectories that contribute to the memory effect. We illustrate the time-domain effects of these geometrical constraints with numerical simulations of pulse transmission through a random medium. The results of our derivation and numerical simulations are consistent with established theory and experimentation.