Power Eigenchannels of Non-Hermitian Media

Controlling the transmission of waves through complex media, has always been a challenging and fundamental problem in optics [1]. Recently, experimental methods have made possible to obtain the transmission matrix of a complex structure, which is of crucial importance in achieving maximal transmission through such disordered media [2]. In another direction, the notion of parity-time
$(\mathscr{PT})$
-symmetry, that was recently introduced in the context of optical physics [3], has led to the discovery of synthetic structures that can utilize loss as an advantage in many applications. Since the energy is not conserved, controlling the optical power is a challenging problem.