Improvement of the modal expansion of electromagnetic fields through interpolation

We consider optical structures where the dielectric permittivity is described as a rational function of the pulsation ω (Lorentz model). The electromagnetic fields can be computed on a large number of frequencies by computing the eigenmodes of the optical device and reconstructing the solution by expanding it on these eigenmodes. This modal expansion suffers from numerous limitations that are detailed in this report. In order to overcome these limitations, an interpolation procedure is proposed such that the direct computation of the electric field is needed only for a small number of interpolation points. Numerical experiments in 2-D and 3-D exhibit the efficiency of this approach.