Focusing through random media in space and time: a transmission matrix approach

TL;DR

This paper introduces a method to focus microwave radiation in space and time through a random medium by analyzing the evolution of the transmission matrix, enabling precise control of pulse timing and position.

Contribution

It presents a novel approach using the transmission matrix evolution to achieve spatiotemporal focusing in random media, linking contrast to eigenvalue participation and mode decay rates.

Findings

Temporal profile of focused pulse matches incident Gaussian pulse

Contrast depends on participation number and matrix size

Decay rates of quasi-normal modes influence contrast dynamics

Abstract

We exploit the evolution in time of the transmission matrix following pulse excitation of a random medium to focus radiation at a selected time delay t' and position r. The temporal profile of a focused microwave pulse is the same as the incident Gaussian pulse. The contrast in space at time t' of the focused wave is determined by the participation number of transmission eigenvalues M' and the size N' of the measured transmission matrix. The initial rise and subsequent decay in contrast observed reflects the distribution of decay rates of the quasi-normal modes within the sample.