Orateur
Description
Quasi-normal modes, also known as resonant states, are modes of the electromagnetic field satisfying the source free harmonic Maxwell's equations. They generally appear for complex-valued frequencies and extend the notion of eigenmodes from Hermitian to non-Hermitian systems. The real part of the frequency represents the oscillation frequency of the time harmonic field while the imaginary part is related to the mode finite life time. Quasi-normal modes are particularly suited for studying open systems, i.e., systems for which the energy is free to escape towards infinity. These modes are, however, delicate to handle due to their exponentially divergent nature at infinity and the difficulty in normalising them.
In this talk I will present a research activity which we have just started on the simulation of electromagnetic wave scattering by a large ensemble of particles based on quasi-normal modes. Our approach consists in first computing the quasi-normal modes of single particles and then coupling these modes via the electromagnetic Green's tensor. The proposed formulation derives from an integral representation of the multiple-scattering problem and an expansion of the electromagnetic field in a quasi-normal modes "basis" valid inside each particle. The resulting formulation promises to be numerically advantageous for systems made of a large number of isolated objects as the number of degrees of freedom would scale as the number of particles times the number of modes used in the truncated single-particle field expansion. I will present results obtained in our team in the case of a one-dimensional problem, i.e., a set of coupled Fabry-Perot slabs, and our perspectives to extend the method to two- and three dimensional systems.