The exact dispersive quasi-normal mode (DQNM) expansion for photonic structures with highly dispersive media in unbounded geometries

In this paper, we present recent developments in our modal expansion technique for electromagnetic structures with highly dispersive media and its application for unbounded geometries. The expansion formula, based on a simple version of Keldys’s theorem, make use of Dispersive Quasi-Normal Modes (DQNMs), also known as natural modes of photonic structures, obtained by solving spectral problems associated to the Maxwell's equations. Such structures can be defined very generally by their geometry (bounded or unbounded), and the electromagnetic properties of various media (permeability and permittivity can be dispersive, anisotropic, and even possibly non reciprocal). As an example, a dispersive benchmark case, a diffraction grating, made of a periodic slit array etched in a free-standing silver membrane, is presented.