Coupled Mode Theory and Its Applications on Computational Nanophotonics
Coupled-mode theory (CMT) has been widely utilized in the analysis of electromagnetic wave coupling and conversions due to its mathematical simplicity and physical intuitiveness. The early version of CMT was proposed by Pierce and Miller in the 1950s to study microwaves, and was mathematically formulated by Schelkunoff using mode expansion, and by Haus with variational principles. The CMT was later introduced to the investigation of optical waveguides by Marcuse , Snyder , and Kogelnik  in the early 1970s. Since then a series of formulations and applications in optical waveguide has been proposed and studied. The physical model of CMT is expanding the total eld inside and optical waveguide in terms of the eld of a reference waveguide structure, by applying the orthogonality condition, a set of ordinary differential equations are obtained. Generally, the CMT focused on the guided modes with the assumption that only a limited number of guided modes (usually one or two) close to phase matching play signicant roles in the interaction of the modal elds. In situations of applications involving the radiation mode coupling, the application of CMT becomes cumbersome due to the continuous spectrum of radiation modes. One possible solution to circumvent the problem of radiation modes is to introduce leaky modes to approximate the radiation modes [9-20].