Temporal coupled-mode theory for the Fano resonance in optical resonators

TLDR

We present a theory of the Fano resonance for optical resonators based on a temporal coupled‑mode formalism. The theory applies to a single resonance coupled to multiple input and output ports and is validated against 3‑D FDTD simulations of guided resonance in photonic crystal slabs. The analysis shows that energy‑conservation and time‑reversal symmetry tightly constrain the coupling constants, enabling a symmetry‑based derivation of the Fano line shape for two‑port symmetric structures and suggesting utility for filter and sensor design.

Abstract

We present a theory of the Fano resonance for optical resonators, based on a temporal coupled-mode formalism. This theory is applicable to the general scheme of a single optical resonance coupled with multiple input and output ports. We show that the coupling constants in such a theory are strongly constrained by energy-conservation and time-reversal symmetry considerations. In particular, for a two-port symmetric structure, Fano-resonant line shape can be derived by using only these symmetry considerations. We validate the analysis by comparing the theoretical predictions with three-dimensional finite-difference time-domain simulations of guided resonance in photonic crystal slabs. Such a theory may prove to be useful for response-function synthesis in filter and sensor applications.