Rigorous modal analysis of plasmonic nanoresonators

The specificity of modal-expansion formalisms is their capabilities to model the physical properties in the natural resonance-state basis of the system in question, leading to a transparent interpretation of the numerical results. In electromagnetism, modal-expansion formalisms are routinely used for optical waveguides. In contrast, they are much less mature for analyzing open non-Hermitian systems, such as micro- and nanoresonators. Here, by accounting for material dispersion with auxiliary fields, we considerably extend the capabilities of these formalisms, in terms of computational effectiveness, number of states handled, and range of validity. We implement an efficient finite-element solver to compute the resonance states, and derive closed-form expressions of the modal excitation coefficients for reconstructing the scattered fields. Together, these two achievements allow us to perform rigorous modal analysis of complicated plasmonic resonators, being not limited to a few resonance states, with straightforward physical interpretations and remarkable computation speeds. We particularly show that, when the number of states retained in the expansion increases, convergence toward accurate predictions is achieved, offering a solid theoretical foundation for analyzing important issues, e.g., Fano interference, quenching, and coupling with the continuum, which are critical in nanophotonic research.