Wide frequency band expansion of permittivity normal modes

Normal modes are valuable tools for modeling electromagnetic resonators, since all their electromagnetic properties can be extracted from a small set of modes. To extend the utility of normal modes to open systems, a set of modes was developed where permittivity is designated to be the eigenvalue. However, these modes, also known as generalized normal modes, are defined at only a single frequency, which limits their utility for spectral applications. In this paper,we present a simple way to extend the validity of permittivity modes to neighboring frequencies. This enables the evaluation of spectral lineshapes and scattering of short pulses from open nanophotonic structures using knowledge of the generalized normal modes at only a single frequency.