Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities

We develop a general temporal coupled-mode theory for multimode optical resonators. This theory incorporates a formal description of a direct transmission pathway, and is therefore capable of describing Fano interference phenomena in multimode cavities. Using this theory, we prove a general criterion that governs the existence of nonorthogonal modes. The presence of nonorthogonal modes creates interesting transport properties which can not be obtained in normal resonator systems. We validate our theory by comparing its predictions with first-principles finite-difference time-domain simulations and obtaining excellent agreement between the two.