Abstract
We present a fundamental result on the role of time-reversal symmetry in the temporal coupled-mode theory (TCMT). The TCMT is a phenomenological theory that describes resonant wave scattering in photonics, acoustics, and other fields. Modifications to the canonical formulation of the TCMT are required for nonreciprocal devices where time-reversal symmetry is usually absent. We discover that previous results on reciprocity for the TCMT are incomplete, and we provide a mathematical proof to clarify the roles of time-reversal symmetry and reciprocity in the TCMT. The new result leads to a general treatment of nonreciprocity in the TCMT. The theoretical result has many practical applications, including the design of nonreciprocal devices such as optical circulators and isolators.
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