The Time-Resolved S-matrix: spatial and temporal Focusing

Abstract

Spatial light modulators have recently opened up the possibility of accurate time-resolved measurements of the S-matrix of disordered scattering samples, allowing for precise imaging, as well as spatial and temporal focusing through such media. In this work we first recapitulate how time-delays can be appropriately assigned to multi-channel wave scattering processes by means of what is now known as the Wigner-Smith time-delay operator and discuss several interesting properties of its eigenstates. We then conjecture and analytically derive a connection to temporal focusing by means of the temporal focusing operator. Subsequently we turn our attention to this optimal focusing method, compare its performance to other approaches and systematically investigate the influence of several restrictions that will be present in most experimental setups. Finally we present some preliminary experimental results confirming our numerical findings and an interesting property regarding the spatial speckle properties of the temporal focusing eigenstates.