Time-Reversal Symmetry Bounds in Temporal Coupled-Mode Theory

TL;DR

This paper develops a comprehensive framework for temporal coupled-mode theory, deriving bounds on coupling phases and strengths imposed by time-reversal symmetry, revealing fundamental trade-offs and symmetry-induced cancellations in resonant systems.

Contribution

It introduces tight bounds on coupling phases and strengths in temporal coupled-mode theory under time-reversal symmetry, expanding understanding of reciprocal and nonreciprocal interactions.

Findings

Time-reversal symmetry enforces cancellation of projected generalized reflections.

Derived tight bounds for coupling phases and strengths in arbitrary multi-mode, multi-port systems.

Identified trade-offs between reciprocal regions of coupling strengths and phases.

Abstract

We provide a general treatment for the temporal coupled-mode theory with arbitrary numbers of modes and ports, and derive tight bounds for the coupling phases in addition to coupling strengths under time-reversal symmetry. We report trade-offs between the cardinalities of the reciprocal regions of the resonant coupling strengths versus phases. We discover that time-reversal symmetry enforces projected generalized reflections in the background to cancel out completely. In double-port systems, the reciprocal regions of the coupling phases span a quarter of the nonreciprocal regions for any non-hidden mode.