Abstract
This chapter presents a series of analytical results that serves as theoretical basis for numerical study of electromagnetic wave transformations in two-dimensionally periodic structures. Among them is the solution of the important problem of truncation of the computational space by artificial boundaries. The author establishes and analyzes fundamental characteristics of transient and steady-state fields in the regular part of the rectangular Floquet channel. For the first time, strict corollaries of Poynting’s complex power theorem and Lorentz’s lemma (the energy-balance equations and reciprocity relations) is presented for two-dimensionally periodic gratings of finite thickness illuminated by transverse-electric or transverse-magnetic plane waves. The method of transport operators (a space-time analogue of the generalized scattering matrices), developed in the chapter, can significantly reduce the computational resources required for calculation of wave scattering by multilayer periodic structures or by the structures on thick substrates. A number of questions concerning the spectral theory of two-dimensionally periodic gratings is answered—it is the result, which is essential for a reliable physical analysis of the resonant scattering of pulsed and monochromatic waves.
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Velychko, L. (2016). Two-Dimensionally Periodic Gratings: Pulsed and Steady-State Waves in an Irregular Floquet Channel. In: Sirenko, Y., Velychko, L. (eds) Electromagnetic Waves in Complex Systems. Springer Series on Atomic, Optical, and Plasma Physics, vol 91. Springer, Cham. https://doi.org/10.1007/978-3-319-31631-4_4
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DOI: https://doi.org/10.1007/978-3-319-31631-4_4
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