Inverse design of the transmission matrix in a random system using Reinforcement Learning

This work presents a n approach to the inverse design of scattering systems by modifying the transmission matrix u sing reinforcement learning . We utilize Proximal Policy Optimization to navigate the highly non - convex landscape of the object function to achieve three types of transmission matri ces: (1) F ixed - ratio power conversion and z ero - transmission mode in r ank - 1 matri ces, (2) exceptional points with degenerate eigenvalues and unidirectional mode conversion, and (3) uniform channel participation is enforced when transmission eigenvalues are degenerate . Engineering wave propagation is a fast - moving domain. S ingularit ies of the scattering matrix (SM), or sub - SM, such as the transmission matrix (TM) or reflection matrix (RM) encode the scattering behavior of a n open system and can be exploited in sensing, switching, lasing and energy deposition [1,2] . Open system s can be described by effective non - Hermitian Hamiltonians, and their resonance frequencies corresponds to poles of SM. Frequency points at which the response vanishes are described by zeros, which are also usually complex value. Incident radiation is completely absorbed when a zero of the SM is brought to the real axis. Such coherent perfect absorption (CPA) is the time reversal of an outgoing wave at the lasing threshold [4] .