Temporal Coupled Mode Theory for a Single Floquet-Sheet Resonator

TL;DR

This paper introduces a rigorous Temporal Coupled-Mode Theory for a Floquet-sheet resonator with time-modulated conductivities, providing analytical tools for understanding and designing time-varying photonic interfaces.

Contribution

It develops a systematic TCMT framework for Floquet resonators, linking it to the Floquet Transfer Matrix Method and deriving analytical expressions for scattering parameters.

Findings

Validated by COMSOL simulations.

Explicitly models resonant coupling between channels.

Robust even with material loss included.

Abstract

We develop a rigorous Temporal Coupled-Mode Theory (TCMT) specifically tailored for a single Floquet-sheet resonator governed by time-modulated conductivities. By invoking photon-number conservation during frequency conversion, we derive characteristic radiative decay rates and coupling coefficients that account for the frequency ratio between channels. We establish a systematic bridge to the Floquet Transfer Matrix Method (TMM), providing closed-form analytical expressions that map scattering parameters to the Drude-type physics of the sheet. Our model explicitly captures the resonant coupling between the 0th-order propagating channel and the -1st-order surface-mode channel. Validated by COMSOL numerical simulations, the theory remains robust even when intrinsic material loss is incorporated. This framework offers an intuitive pole-expansion representation for designing time-varying photonic interfaces.