Quasimodal expansion of electromagnetic fields in open two-dimensional structures

A quasimodal expansion method (QMEM) is developed to model and understand the scattering properties of arbitrary shaped two-dimensional open structures. In contrast with the bounded case which has only a discrete spectrum (real in the lossless media case), open resonators show a continuous spectrum composed of radiation modes and may also be characterized by resonances associated to complex eigenvalues (quasimodes). The use of a complex change of coordinates to build perfectly matched layers allows the numerical computation of those quasimodes and of approximate radiation modes. Unfortunately, the transformed operator at stake is no longer self-adjoint, and classical modal expansion fails. To cope with this issue, we consider an adjoint eigenvalue problem whose eigenvectors are biorthogonal to the eigenvectors of the initial problem. The scattered field is expanded on this complete set of modes leading to a reduced order model of the initial problem. The different contributions of the eigenmodes to the scattered field unambiguously appears through the modal coefficients, allowing us to analyze how a given mode is excited when changing incidence parameters. This gives physical insights to the spectral properties of different open structures such as nanoparticles and diffraction gratings. Moreover, the QMEM proves to be extremely efficient for the computation of local density of states.