Study of symmetric and asymmetric defect positions in a photonic crystal supercell

Abstract

A 2D supercell photonic crystal consisting of dielectric cylindrical rods in air medium was used to study the effect of symmetry of the defects on the resonance modes. A single defect was introduced at every possible position in the crystal and the transmission properties were studied. When a defect is introduced on an axis which passes through the centre of the crystal and is perpendicular to the direction of propagation of EM wave, the mirror symmetry along an axis passing through the centre of the supercell (Soy axis) is preserved. When a defect is introduced on an axis that passes through the centre of the crystal and is parallel to the direction of propagation of EM wave, the mirror symmetry along the axis Sox passing through the centre of the supercell is preserved but the mirror symmetry along Soy is broken. However, when the defect is placed at the centre of the crystal, the mirror symmetries is preserved along both the axes defined in the supercell. It is seen that TM mode needs to see mirror symmetry in the direction of propagation within the supercell, (mirror symmetry of defects with respect to Soyaxis) in order to produce a strong resonance peak. However the presence of mirror symmetry along Sox seems to have little to no effect on the resonance peak. The single defects placed on the E∥ and E⊥ axes passing through the centre of the crystal and their respective supercell defect modes have been discussed in this paper.