Universal embedding of a non-Hermitian reciprocal scattering optical system into a Hermitian time-reversal-invariant system

Abstract

For Hermitian optical systems, reciprocity and time-reversal symmetry are equivalent. In non-Hermitian systems that have gain and/or loss, however, they are not equivalent. Here, we point out a connection between reciprocity and time-reversal symmetry in general. For a non-Hermitian system, we show that reciprocity can be viewed as a manifestation of the time-reversal symmetry of an enclosing Hermitian system. Our work deepens the understanding of the general constraints on the scattering matrix of non-Hermitian optical systems.