Two-Dimensionally Periodic Gratings. Part 2: Some Regularities in the Behavior of Nonstationary and Steady-State Fields in the Rectangular Floquet Channel

Elements of the spectral theory of double-periodic gratings

“…From here on, all notations are determined in [3,4]. In the problems of this kind but with arbitrary right-hand sides in the Helmholtz equation, for the case of the simplest periodic structure (any material scatterers are absent), we consider monochromatic waves generated by quasi-periodic current sources located in the range z L  : …”

“…The main results of the spectral theory for two-dimensionally periodic structures are presented in [1,2]. We formulate some general statements of spectral theory for two-dimensionally periodic gratings based on these results and on the results presented in [3,4]. The frequency parameter 2 k    (  is the wavelength in a free space) plays a role of spectrum parameter, and a two-dimensionally periodic grating is considered as an open periodic resonator.…”

“…The results allowing one to construct and test rigorous algorithms for solving vector initial boundary-value problems of electromagnetic theory of two-dimensionally periodic gratings have been obtained in [3,4]. It has been proved that all pulsed fields generated in the reflection and transmission areas of a grating (in regular regions of the Floquet channel) are uniquely determined by their longitudinal components.…”