In this paper we theoretically study (with plane wave expansion and finite-difference time- domain models) optical properties of 2D hexagonal  dielectric photonic crystal of the p6mm plane symmetry group. The structure is made of GaAs dielectric rods in air. We perform the calculations of the band structures, equi-frequency contours and electromagnetic propagation through the basic structure and waveguide.

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1. Coordinate transformation based design of confined metamaterial structures