  A quasimodal expansion method (QMEM) is developed to model and understand the
scattering properties of arbitrary shaped two-dimensional (2-D) open
structures. In contrast with the bounded case which have only 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 (PMLs) 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 which eigenvectors are bi-orthogonal 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 new
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 (LDOS).
