Theoretical Consideration on Influences of Cavity or Pillar Shape on Band Structures of Silicon-Based Photonic Crystals

This paper describes the physical manifestations of the various influences of cavity (or pillar) shape and the filling factor of dielectric material on band structures in two-dimensional photonic crystals. The influences of circular or rectangular cross-sections of cavity (or pillar) arrays on photonic band structures are considered theoretically, and significant aspects of square and triangular lattices are compared. It is shown that both the averaged dielectric constant of the photonic crystal and the distribution profile of photon energy play important roles in defining optical properties. For the triangular lattice, especially, it is shown that cavity array with a rectangular cross-section breaks the band structure symmetry. So, we go on to discuss this from the perspective of band structure, and consider the optical properties of a lattice with a circular cross-section cavity