Open Periodic Resonators and Waveguides: Novel Results in Electromagnetic Theory of Gratings

Abstract

Transient resonance wave scattering by gratings is rather complicated phenomenon; it depends on numerous parameters and has not been studied thoroughly yet. The numerical simulation that takes into account diverse properties of the spectrum (various eigenmodes: natural oscillations and eigenwaves) may serve as the most reliable tool for such investigation. The components of the grating’s spectrum may be found through analytical continuation of the solutions to diffraction problems into the domain of complex values of the real physical parameters (such as frequency, propagation constants, and geometrical dimensions). When the parameters vary within the domain of real values (diffraction theory in the frequency domain) properties of complex spectrum usually stay out of the focus of intrest. However, it turns out that spectral properties play the principal role in the formation of the response of an electromagnetic structure to every external excitation. The approach, based on the study of the singularities (spectrum) of resolvent operators of boundary value problems in the frequency domain, allows us to consider and treat various mathematical, electromagnetic, and applied problems of resonant wave scattering using the same methodological background. In this chapter we apply this approach to the analysis of regularities in transient resonance wave scatterings and for the description and treatment of irregular effects and anomalous phenomena associated with the ability of a grating to support regimes with complicated nonclassical dispersion laws.