The theory of Coherent Perfect Absorption¹ (time-reversed lasing) and Reflectionless Scattering Modes² has shown that there always exist discrete solutions to scattering of electromagnetic waves in multiple-scattering geometries that achieve perfect transduction or perfect (reflectionless) impedance matching. In general these are transient (complex frequency) solutions, but, typically, with tuning of a one system parameter it is possible to achieve steady- state, reflectionless excitation of arbitrary systems. Here we focus on the case of reflectionless excitation of a lossless multiport/multi-channel system, and show³ that it is possible not only to eliminate reflection, but also to control the scattering into the output channels to perform routing or filtering functions. This is achieved by creating a degeneracy of d complex eigenvalues of the wave equation, tuned to the real frequency; and we find that the number of tuning parameters needed to achieve such routing at a given frequency to be 2(d+1). For heuristic reasons we expect an open low-loss wave-chaotic cavity with tunable scattering elements to be optimal for achieving routing functions, since such a cavity has overlapping, pseudo-random resonances, making it frequency agnostic, and easily reprogrammable. We will present the results of recent experiments⁴ and simulations^3,4 of such a cavity that have confirmed this conjecture in the microwave frequency range. These systems are easily reprogrammable, making them uniquely effective for applications where frequency- agile performance is required and implying robustness to perturbations and defects in fabrication.

1. “Coherent Perfect Absorbers: Time-reversed Lasers”, D. Chong, L. Ge, H. Cao, and A. D. Stone, Physical Review Letters, 105, 053901 (2010).
2. “Theory of Reflectionless Scattering Modes”, William Sweeney, Chia Wei Hsu, and A. Douglas Stone, Phys. Rev. A, 2020, https://link.aps.org/doi/10.1103/PhysRevA.102.063511
3. “Coherent Control of Scattering of Guided Waves”, in preparation, A. Alhulaymi, Pyvovar, P. Del Hougne, O. D. Miller, A. D. Stone.
4. “Agile Free-Form Signal Filtering with a Chaotic-Cavity-Backed Non-Local Programmable Metasurface”, T. Faul, L. Cronier, A. Alhulaymi, A. D. Stone, P. del Hougne, submitted to Advanced Materials.