The relation between Time Reversal focusing and Coherent Backscattering in multiple scattering media: a diagrammatic approach

TL;DR

This paper develops a diagrammatic theoretical framework to analyze one-channel time reversal in multiple scattering media, revealing the roles of different scattering diagrams and linking TR to Coherent Backscattering, with experimental validation.

Contribution

It introduces a self-consistent multiple scattering theory for time reversal, clarifying the roles of ladder and most-crossed diagrams and establishing a novel connection between TR and CBS.

Findings

Time-reversed amplitude doubles when source and TR point coincide.

Ladder diagrams, not most-crossed, cause the observed enhancement.

Experimental ultrasonic results confirm theoretical predictions.

Abstract

In this paper, we revisit one-channel time reversal (TR) experiments through multiple scattering media in the framework of the self-consistent multiple scattering theory. The hyper resolution and the self-averaging property are retrieved. The developed formalism leads to a deeper understanding of the role of the ladder and most-crossed diagrams in a TR experiment, and also establishes the link between TR and Coherent Backscattering (CBS). Especially, we show that when the initial source and the time reversal point are at the same location, the time-reversed amplitude is twice higher. Surprisingly, this enhancement is due to the ladder diagrams and not to the most-crossed ones, contrary to CBS. These theoretical predictions are confirmed by experimental results. The experiments are performed with ultrasonic waves propagating through a random collection of parallel steel rods.