Band Structure Engineering in 2D Photonic Crystal Waveguide with Rhombic Cross-Section Elements

Two-dimensional photonic crystal (2D PhC) waveguides with square lattice composed of dielectric rhombic cross-section elements in air background, by using plane wave expansion (PWE) method, are investigated. In order to study the change of photonic band gap (PBG) by changing of elongation of elements, the band structure of the used structure is plotted. We observe that the size of the PBG changes by variation of elongation of elements, but there is no any change in the magnitude of defect modes. However, the used structure does not have any TE defect modes but it has TM defect mode for any angle of elongation. So, the used structure can be used as optical polarizer. 1. Introduction PhCs are class of media represented by natural or artificial structures with periodic modulation of the refractive index [1–3]. Such optical media have some peculiar properties which gives an opportunity for a number of applications to be implemented on their basis. In 2D PhCs, the periodic modulation of the refractive index occurs in two directions, while in one other direction structure is uniform. When the refractive index contrast between elements of the PhC and background is high enough, a range of frequencies exists for which propagation is forbidden in the PhC and called photonic band gap (PBG). The PBG depends upon the arrangement and shape of elements of the PhC, fill factor, and dielectric contrast of the two mediums used in forming PhC. The most important feature of PhCs is ability to support spatially electromagnetic localized modes when a perfectly periodic PhC has spatial defects [4–6]. In recent years, a lot of researches are devoted to study 2D PhC with circular, square, and elliptic cross-section elements [7, 8]. However, less work was devoted to study of PhC with rhombic cross-section elements. In this paper, we study band structure for 2D PhC waveguide with dielectric rhombic cross-section elements with a square lattice and how band structure is affected by elongating of elements. 2. PWE Method and Numerical Analysis We consider 2D PhC waveguide as shown in Figure 1(a), consisting of a square lattice of GaAs rhombic cross-section elements in air background, having a lattice constant of ？nm. The rhombuses have side and a refractive index of [8]. The waveguide core is formed by substitution of a row of rhombuses with a row of different rhombuses with refractive index and side along the direction. Figure 1(b) shows the unit cell for the structure used which is composed of the elements as shown in Figure 1(c) [1]. Figure 1: (a) 2D PhC waveguide, (b) the unit