Localized Resonances Beyond the Quasi-Static Approximation

Based on the results in Chaps. 2–4, it is natural to consider the plasmon and polariton resonances beyond the quasi-static approximation. This can be obtained via considering the spectral properties of the layer potential operators introduced in the previous chapters with frequencies attached to integral kernels. This makes the spectral analysis much radically more challenging. In fact, the relevant layer potential operators are no longer self-adjoint in any function space and many classical spectral tools, say e.g. diagonalization, do not apply. Nevertheless, one still can manage to establish the resonance conditions which couple the geometric and medium parameters of the material structure as well as the frequency in a highly intricate and delicate manner. It turns out that the resonant fields possess distinct properties with some of them similar to the quasi-static resonances and some different.