Spatio-temporal Particle Manipulation with the Adiabatic Floquet Scattering Matrix

Abstract

The Generalized Wigner-Smith (GWS) matrix has recently emerged as a powerful tool for particle manipulation and wavefront shaping. Constructed solely from the scattering matrix and small variations in selected target parameters, the GWS matrix’s eigenstates provide a complete orthogonal basis of far-field input states for systems without gain and loss. This enables access to optimally shaped near fields of a target scatterer by manipulating the spatial degrees of freedom of the incident wave. Interestingly, while the GWS formalism was initially developed for static scattering systems, a generalization to periodically time-varying systems has been introduced lately. Numerical studies have been performed in one-dimensional systems, where the Generalized Wigner-Smith matrix was calculated using Floquet theory. This allows us to gain access to not only spatial, but also temporal degrees of freedom. Building on this, we investigate spatio-temporal particle manipulation in a two-dimensional disordered waveguide. The goal of this project is finding access to temporal and spatial degrees of freedom of a static target such that we can manipulating this target at one predefined moment in time. In a full-scale Floquet Wigner-Smith approach, however, the target must oscillate very fast and strongly. We therefore develop a formalism that uses Floquet theory only as a tool such that we solely need multispectral far-field information about the static target. Specifically, we utilize adiabatic Floquet theory in a post-processing step on the scattering information of the time-independent target and find optimal pulses. By choosing an appropriate parameter, which we use to calculate the GWS matrix, we can generate input wavefronts that exert a highly localized force on the target scatterer at a predefined moment in time. These results demonstrate that the adiabatic Floquet-GWS framework offers a pathway to spatio-temporal particle manipulation in strongly scattering environments. Due to the generality of this theory, it not only holds in electromagnetism, but can also be applied to acoustic systems, where first experiments are currently being set up to implement our predictions.