Resonant frequencies for diffraction gratings Original Research Article

This note is devoted to a study of resonance phenomena in electromagnetic gratings. In particular, a characterization of the scattering frequencies (the complex values of the frequency inducing resonant behaviors) is given by using a variational method. After the diffraction problem is reduced to a bounded domain, we extend it to complex values of the frequency. The existence of the resolvant of the diffraction problem is established in the upper complex half-plane. It is shown that this resolvant can be extended meromorphically to the domain C/R+. In addition, the scattering frequencies, which correspond to the poles of this extension, solve a nonlinear eigenvalue problem.