Study of Two Dimensional Photonic Crystal and Photonic Crystal Slabs of Triangular Air Holes in a Hexagonal Lattice

In this work, first we have done a study of band structures and eigenmodes of bidimensional photonic crystal of triangular air holes embedded in GaAs media in a hexagonal lattice. This study was done using the plane wave expansion method. In the perfect crystal, photonic band gap was find in both polarization modes (TE and TM) for different values of geometric parameters (size and orientacion) of air holes, then we introduce a defect in the crystal to create a cavity with confined eigenmodes which was studied too for different values of size and orientation. Second, we did a study of the same periodicitty array but in a slab of photonic crystal, for this we have used the formalism of the guided mode expansion method. In this system we find partial photonic band gap in the odd and even modes, and we studied the band structures, and the quality factor of a L3 cavity.