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2017 | 132 | 4 | 1227-1229
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Symmetry of Two-Dimensional Hybrid Metal-Dielectric Photonic Crystal within Maple

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2D-photonic crystal has the close packed hexagonal structure of metallized spheres. The selection rules are first necessary thing for understanding of interactions between differently polarized light and artificial photonic structure. This problem is the object of our paper. Known methods of group theory allow to solve such problems. However, the knowledge about symmetry of structure is the starting point of them. Usually the X-ray diffraction provides such information about natural 3D-crystals. Such assumptions so far have to do after the visual research of photonic structures in practice. Further these assumptions may be confirmed (or vice versa) by experimental research of optical response of photonic structures. We assumed that the symmetry of photonic structure is close to 2D (P6mm) group. Group-theoretical calculations were provided using the system of computer mathematics Maple. Both polarizations, normal to surface and parallel to that plane, were taken into consideration. The obtained selections rules were confirmed later by independent experiments.
  • Department of Computer Engineering, Petro Mohyla Black Sea State University, Mykolayiv, 54003, Ukraine
  • Department of Computer Engineering, Petro Mohyla Black Sea State University, Mykolayiv, 54003, Ukraine
  • [1] G.P. Chuiko, O.V. Dvornik, Symmetry of two-dimensional hybrid metal-dielectric photonic crystal within MAPLE, Maplesoft, 2013
  • [2] S.G. Romanov, N. Vogel, K. Bley, K. Landfester, C.K. Weiss, S. Orlov, Phys. Rev. B 86, 195145 (2012), doi: 10.1103/PhysRevB.86.195145
  • [3] S.G. Romanov, A.V. Korovin, A. Regensburger, U. Peschel, Adv. Mater. 23, 2515 (2011), doi: 10.1002/adma.201100460
  • [4] B.K. Weinstein, in: Modern Crystallography, Vol. 1, Eds. B.K. Weinstein, A.A. Chernov, L.E. Shuvalov, Nauka, Moscow 1979, (in Russian)
  • [5] Y.K. Yegorov-Tismenko, G.P. Litvinskaya, Theory of Crystal Symmetry, GEOS, Moscow 2000, (in Russian)
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