Coherent Control of Wave Scattering via Coincidences of Complex Spectra

We introduce and validate a theoretical framework for coherent control of multichannel scattering of linear waves to route waves through complex geometries with multiple scattering. We show that steady-state perfect routing solutions are achievable at any frequency via tuning geometric param- eters so that multiple complex eigenfrequencies coincide on the real axis. The relevant complex spectra describe critically constrained scattering processes (CCONs), where a specific number of generically accessible outgoing channels are not excited due to destructive interference. Focusing on electromagnetic waves, we demonstrate in simulations high discrimination routing and demulti- plexing of signals in a multiport chaotic cavity with a number of tunable scatterers which can be predicted from theory. A similar approach can be used to implement other interesting functional- ities, such as filtering, power division and directional lasing. The method can be applied to other classical waves and also to quantum matter waves.