Dispersive Quasi-Normal Mode (DQNM) Expansion in Open and Periodic Nanophotonic Structures

This paper reviews recent developments in our modal expansion technique for the scattering problem of unbounded electromagnetic structures with highly dispersive media. The technique makes use of Dispersive Quasi-Normal Modes (DQNMs), also known as natural modes of photonic structures, obtained by solving spectral problems associated to Maxwell’s equations. The final expansion formula, based on a simple version of Keldysh’s theorem, reveals the contributions of eigenmodes onto the scattered field, allowing us to understand the scattering properties of arbitrary shaped nanophotonic structures (bounded or unbounded), where permeability and permittivity can be dispersive, anisotropic, and even possibly nonreciprocal. This provides complete physical insights to the spectral characteristics of given structures as well as a transparent interpretation of numerical results. We demonstrate this modal analysis on a 2-D model of diffraction grating, made of a periodic slit array etched in a free-standing silver membrane.