The approach based on investigation of characteristic properties of the resolving operators (resolvents) of stationary boundary value problems of the theory of wave diffraction by gratings is used for the analysis of the basic regularities running the formation of resonant non-stationary scattered fields. Information about singularities provides the description of the anomalous effects connected with possibility of existence, in the structures under consideration, of eigen modes having super high Q-factor, with linear "interaction" of modes in the parameter regions of spectrum crowding.
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