An optical analog of the Borrmann effect in photonic crystals
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An Optical Analog of the Borrmann Effect in Photonic Crystals M. V. Bogdanova*, Yu. E. Lozovik, and S. L. Eiderman Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow oblast, 142190 Russia *email: [email protected] Received March 18, 2009
Abstract—Numerical simulation using the layered Korringa–Kohn–Rostoker (LKKR) method is applied to calculate the reflection and absorption spectra of an spolarized electromagnetic wave incident on a faced centered cubic photonic crystal (PC) with opal structure whose sites are occupied by twolayer metal–dielec tric spheres. The reflection and absorption coefficients of the PC are analyzed as a function of the angle of incidence of the electromagnetic wave on the crystal surface. A range of wavelengths λ and angles of inclina tion θ to the normal is found in which the absorption experiences a sharp change under small variations of the above parameters. The appearance of peaks in the absorption spectrum of the PC is analyzed, and the spec trum is compared with the behavior of the reduced density of states. By the finite difference time domain (FDTD) method applied to the Maxwell equations, the spatial distribution of the energy density of electro magnetic field inside each of five layers of the PC is obtained at angles of incidence of 23° and 30° for a wave length of 455 nm. It is demonstrated that the sharp maxima of the density of electromagneticfield energy that are localized on the surfaces of absorbing metal spheres correspond to the absorption maximum. At the same time, at the absorption minimum, the maxima of the field energy density in each of the five layers are local ized mainly between the lattice sites of the PC. An analogy between this phenomenon and the Borrmann effect, which is known in Xray spectroscopy of ordinary crystals, is analyzed. DOI: 10.1134/S1063776110040072
1. INTRODUCTION Photonic crystals (PCs) [1] are structures (as a rule, artificial) with periodically modulated dielectric con stant on scales comparable with the wavelength of an electromagnetic wave in the visible and nearinfrared ranges. Due to the periodicity of the medium, the propagation of radiation in a PC is similar to the motion of an electron in an ordinary crystal under a periodic potential. Owing to the translation symmetry of PCs, the normal modes of the electromagnetic field in the PC are Bloch functions. Thus, electromagnetic waves in PCs are characterized by a band gap spectrum and by a coordinate dependence similar to that of Bloch electron waves in ordinary crystals. In particu lar, the abovementioned periodicity is responsible for a photonic band gap—a spectral domain that depends on the geometrical parameters of the PC and on the properties of the material [2]—in which the propaga tion of light in the PC is suppressed in all (complete photonic band gap) or in some distinguished direc tions. PCs are of interest both from the viewpoint of fun damental science (for example, to control quantum electrodynamic processes) and
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