Connection of temporal coupled-mode-theory formalisms for a resonant optical system and its time-reversal conjugate

Temporal coupled-mode theory has been widely used to describe the physics of resonant optical systems. In general, an optical system can be constrained by energy conservation, time-reversal symmetry, and reciprocity. Most previous developments of temporal coupled-mode theory made use of all three constraints. In this paper, we consider separately the implication of each of these constraints on the parameters of temporal coupled-mode theory. For this purpose we made extensive use of the connection between a physical system and its time-reversal conjugate. This connection also indicates some of the nontrivial implications of the relation between the resonant properties of a physical system and its time-reversal conjugate. We validate these implications numerically by direct electromagnetic simulations of a guided resonance system. This work should enable the application of temporal coupled-mode theory to a wider range of resonant systems.