The paper discusses the methodological questions arising in the study of open electrodynamic structures of resonance quasi optics via time-domain technique. As demonstrated, all of the interesting physical characteristics inherent in these objects (including the objects with various frequency-selective elements) can be obtained through the numerical solution of the relevant model initial bowldaryvalue probhxns. For the first time, a finite difference method equipped with the exact local 'absorbing' conditions on artificial boundaries has been applied for the solution of this kind of open problems. The results of the computational experiments performed have verified the possibility of the efficient selection of oscillations in dispersive open resonators with diffraction gratings, among them the resonators with gratings operating in the quasitotal nonspecular reflection mode.

Abstract-The paper is concerned with the development and mathematical justification of the methodology for applying the timedomain methods in the study of spectral characteristics of open electrodynamic resonant structures.

Abstract-The efficiency of different ways for controlled changes of spectral characteristics of open electrodynamic resonant structures are studied and evaluated in the paper.

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