PBG structures of novel two-dimensional annular photonic crystals with triangular lattice

Abstract

The photonic band gap (PBG) structures of four types of annular photonic crystals (PCs) with inner-scatter of rectangular, square, hexagonal and circle shapes are respectively calculated by the plane wave expansion method. The optimal samples with the largest gap-midgap ratio for each structure are obtained by scanning the four parameters: filling ratio f, dielectric constant 1 , rotating angle of inner-scatters and outside radius R of the air ring. The results show that the band gap can be further maximized by adjusting the structural parameters, and a wide PBG with the gap-midgap ratio of 20.4% is gained in the annular photonic crystal with rectangular inner-scatters.The PBG of photonic crystals (PCs) is a range of frequencies where the modes are evanescent and thus not allowed to propagate through the crystals irrespective of the propagation direction and polarization type. It is significant to study the characteristics of the PBG and design the structure with PBG as wide as possible.Employing an anisotropic material [1,2] or magnetic material [3,4] , changing the shape of scatter [2] , structural deformation [5][6][7][8][9] and composite structures [10][11][12] are all the approaches to obtain wide PBG. A new type of two-dimensional structure called annular photonic crystal has been proposed by Hamza Kurt and D. S. Citrin [13] , which is composed of a dielectric-rod and a circular-air-hole array in a square or triangular lattice, and a PBG with the gap-midgap ratio of 18.3% has been gained. Kong Lingkai [14,15] has studied negative refraction and focusing properties of two-dimensional annular photonic crystals. In this letter, three kinds of new quasi annular photonic crystals are proposed, of which inner-scatter shapes are rectangular, square and hexagonal, respectively. The PBG structures of these kinds of photonic crystals are studied in detail by the plane wave expansion method, and for comparison, the standard annular structure is also studied, of which the inner-scatter shape is circle. The optimal parameter of each structure is gained, and it is discovered that the quasi annular photonic crystal with rectangular inner-scatters has a PBG with gap-midgap ratio of 20.4%, which exceeds the result got by Hamza Kurt and D. S. Citrin [13] .The schematic diagrams of the structures are shown in Fig.1. The scatters with the dielectric permittivity of 1 are inserted in the middle of the holes with radius R and permitFig.1 Cross sections of four kinds of annular photonic crystals with different inner-scatter shapes: (a) Rectangular; (b) Square; (c) Hexagonal; (d) CircleC