Coupling theory of quasinormal modes for lossy and dispersive plasmonic nanoresonators

A quasinormal mode (QNM) coupling theory is proposed for a system of coupled resonators. The theory is generally applicable to systems with energy loss and arbitrary frequency dispersion of permittivity such as plasmonic nanoresonators. The QNM coupling coefficients in the theory are obtained with first-principle calculations without fitting the full-wave numerical results or experimental data. The theory is built up based on the Green's-function formalism, which shows that the coupling between resonators originates from the mutual excitation of scattered field of each resonator. With the theory, the source-excited scattered field or the source-free QNMs of the coupled system can be obtained as an expansion in terms of QNMs of each individual resonator in the system. The theory provides an intuitive physical picture and also shows superior computational efficiency compared with the full-wave numerical method if the scattered field of each resonator in the system can be expanded with a small set of QNMs. The theory is tested against full-wave numerical method and is used to design metallic nanoantennas with a broadband enhancement of the spontaneous emission rate.