Temporal Coupled Mode Theory for a Single Floquet-Sheet Resonator

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.