Special Section on Fundamental and Applied Nanoelectromagnetics

Dynamical diffraction theory of waves in photonic crystals built from anisotropically scattering elements

[+] Author Affiliations
Vladimir G. Baryshevsky

Belarusian State University, Research Institute for Nuclear Problems, 11 Bobruiskaya Street, Minsk 220050, Belarus

Evgeny A. Gurnevich

Belarusian State University, Research Institute for Nuclear Problems, 11 Bobruiskaya Street, Minsk 220050, Belarus

J. Nanophoton. 6(1), 061713 (Oct 29, 2012). doi:10.1117/1.JNP.6.061713
History: Received June 30, 2012; Revised October 2, 2012; Accepted October 3, 2012
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Abstract.  Analyzing scattering of electromagnetic waves in a two-dimensional photonic crystal from the viewpoint of scattering theory, we come to the conclusion that multiple rescattering of waves by the centers (wires) composing the crystal significantly affects the imaginary part of the crystal refractive index. As a result, it appears that, in the case of crystals, the classical expression relating the refractive index of a random medium to the amplitude of scattering by a single center has limited application, because it does not properly describe the attenuation of waves. We derive an expression that, unlike the classical one, includes the effective amplitude of scattering by a wire in a crystal, instead of the amplitude of scattering by a single wire in vacuum. The same effective amplitude must appear in the equation describing the dynamical diffraction of waves in crystals. We also derive the expression for the effective amplitude in the case when scattering by a single center is anisotropic. Because a most general approach is applied to the description of the scattering process, the results are valid for a wide range of cases without being restricted to either electromagnetic waves or crystals built from wires.

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© 2012 Society of Photo-Optical Instrumentation Engineers

Citation

Vladimir G. Baryshevsky and Evgeny A. Gurnevich
"Dynamical diffraction theory of waves in photonic crystals built from anisotropically scattering elements", J. Nanophoton. 6(1), 061713 (Oct 29, 2012). ; http://dx.doi.org/10.1117/1.JNP.6.061713


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