Rigorous modal analysis of plasmonic nanoresonators

TL;DR

This paper develops a rigorous modal analysis framework for plasmonic nanoresonators, extending modal-expansion methods to non-Hermitian systems with material dispersion, enabling accurate, efficient, and physically interpretable modeling of complex nanophotonic phenomena.

Contribution

It introduces an extended modal formalism with auxiliary fields, an efficient finite element solver, and new expressions for modal excitation coefficients, enhancing analysis of plasmonic resonators.

Findings

Achieves convergence with increasing modal states for accurate predictions

Enables analysis of Fano interference and quenching effects

Provides rapid and physically interpretable modal analysis

Abstract

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 new 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 towards accurate predictions is achieved, offering a solid theoretical foundation for analyzing important issues, e.g. Fano interference, quenching, coupling with the continuum, which are critical in nanophotonic research.