Analysis of structure and band gap evolution of photonic crystals formed holographically by symmetric umbrella configuration with varying apex angles

Abstract

A theoretical investigation of the possible three-dimensional photonic crystal structures that can be created by holographic interference using the symmetric umbrella configuration of four plane waves is made. The irreducible Brillouin zones and the photonic band gap (PBG) properties of the possible resulting crystal lattices when the apex angle is varied from 10° to nearly 180° are investigated. Our calculations indicate that a complete PBG can exist in the resulting structure in a very wide range of the apex angle, from 33° to 135° except a narrow region at 49° to 55°. The study has also shown that a larger band gap may be obtained in a structure that slightly deviates from the standard cubic lattice and that the optimum exposure threshold or optimum filling ratio of the dielectric material is roughly a step-like function of apex angle. These results may give a general outlook on this method and relax some requirements in experiments.