Matrix approach for optimal spatio-temporal coherent control of wave scattering

TL;DR

This paper introduces a matrix-based method for optimally shaping wavefronts in space and time to control wave scattering, validated through microwave experiments for various wave-control tasks in complex environments.

Contribution

It develops a singular value decomposition approach to determine optimal wavefront shaping in complex scattering media, applicable to multiple wave-control objectives.

Findings

Successfully achieved reflectionless transient excitation.

Demonstrated optimal energy deposition.

Controlled scattering-invariant time-varying states.

Abstract

We present and experimentally verify a matrix approach for determining how to optimally sculpt an input wavefront both in space and time for any desired wave-control functionality, irrespective of the complexity of the wave scattering. We leverage a singular value decomposition of the transport matrix that fully captures how both the spatial and temporal degrees of freedom available to shape the input wavefront impact the output wavefront's spatial and temporal form. In our experiments in the microwave domain, we use our formalism to successfully tackle three iconic wave-control tasks in a disordered cavity: (i) reflectionless transient excitation (``virtual perfect absorption''), (ii) optimal energy deposition, and (iii) scattering-invariant time-varying states.