Temporal coupled-mode theory for resonators

We present a general formalism of the temporal coupled-mode theory (TCMT) for resonators which are dielectric resonators or metal-shielded dielectric ones. The temporal coupled-mode equations (TCME) are derived directly from Maxwell Equations, and applicable for the analysis of various perturbed resonators as well as resonant scatterers. The resonators with metallic loss and inhomogeneous dielectric medium are taken as two typical examples from various perturbed resonators, and analyzed in detail, respectively. The scattering of electromagnetic waves by a resonant scatterer which has either three-dimensional (3D) spherical or 2D cylindrical symmetry, or else is sufficiently smaller than the resonant wavelength of the incident wave, is formulated by combining TCMT with the electromagnetic induction theorem. The present analysis is mathematically simple and physically intuitive.