  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.
