Wave Scattering Properties of Complex and Ray-Chaotic Graphs, Billiards, and Enclosure

The dream of completely controlling scattering in complex non-Hermitian settings, such as strongly scattering media and chaotic enclosures, has intrigued researchers for decades and motivated many studies in wavefront shaping, perfect absorption, metasurface development for cavity shaping, etc. We generalize the concept of singularity speckle patterns of light to arbitrary two-dimensional parameter spaces and any complex scalar function that describes wave phenomena involving complicated scattering. We utilize experimental scattering (S-)matrix data from microwave graphs, billiards and enclosures to generate complex scalar functions that are projected into parameter spaces constructed from control signals on embedded metasurfaces, and frequency, to identify new classes of scattering singularities beyond the common ones (coherent perfect absorption, S-matrix exceptional points, reflection-/transmission-less modes, etc.). We can also manipulate the singularities using embedded metasurfaces and combine them to form new scattering singularities. We introduce a complex generalization of time delay (CTD) and show that every type of scattering singularity has an associated CTD that diverges at that point. The CTD shows universal statistical properties with -3 power-law tails in the PDF of both the real and imaginary parts of CTD, independent of wave propagation dimension, number of scattering channels, presence or absence of reciprocity, and degree of uniform loss. We support our empirical results from microwave experiments with Random Matrix Theory simulations and conclude that all results presented are found in all generic scattering systems.