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Method of transfer relations in the theory of multiple resonant scattering of waves as applied to diffraction gratings and photonic crystals

  • Atoms, Spectra, Radiation
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Abstract

An approach is proposed in the theory of multiple scattering of wave fields in two-dimensional inhomogeneous media, which provides a universal description for wave scattering from one-dimensional periodic interfaces between two dielectric media (optical gratings) and from two-dimensional periodic dielectric structures (photonic crystals). The approach is based on the transfer matrix methodology, which involves sub-dividing the scattering medium into elementary layers with gaps; however, in contrast to the transfer matrix method, it leads to invariant imbedding equations for the matrix coefficients of reflection and transmission of an inhomogeneous medium. The developed approach is applied in a quantitative analysis of two optical effects: resonant decrease in the light reflection coefficient from the grating, associated with the profile depth effect, and exponential-power decay of optical radiation in the forbidden band of a 2D photonic crystal upon an increase in the number of its layers starting from one layer. The frequency spectrum for the electromagnetic radiation power transmission through a 2D photonic crystal formed by parallel layers of infinitely long cylinders is interpreted taking into account the spectral dependence of the total cross section of scattering from a single cylinder. Such an interpretation of the frequency spectrum with two forbidden gaps combined with the analysis of layer-by-layer dynamics of its formation makes it possible to reveal the role of microscopic resonant scattering of waves from a single cylinder and of macroscopic Bragg-type resonant scattering from a periodic system of cylinders during the formation of the spectrum of radiation transmission through a photonic crystal. A physical explanation is given for the transparency peaks in one of the forbidden gaps in the spectra of radiation transmission through a perfectly ordered system of cylinders in terms of multipole resonances of scattering from a single cylinder.

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Authors and Affiliations

  1. Eldis Research Center For Electronic Diagnostic Systems, Russian Academy of Sciences, Moscow, 101000, Russia

    Yu. N. Barabanenkov

  2. Institute of Microelectronic Technology and Ultra-High-Purity Materials, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432, Russia

    M. Yu. Barabanenkov

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  1. Yu. N. Barabanenkov
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  2. M. Yu. Barabanenkov
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__________

Translated from Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) Fiziki, Vol. 123, No. 4, 2003, pp. 763–774.

Original Russian Text Copyright © 2003 by Yu. Barabanenkov, M. Barabanenkov.

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Barabanenkov, Y.N., Barabanenkov, M.Y. Method of transfer relations in the theory of multiple resonant scattering of waves as applied to diffraction gratings and photonic crystals. J. Exp. Theor. Phys. 96, 674–683 (2003). https://doi.org/10.1134/1.1574541

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