Multibeam interference model for predicting 3D photonic crystal structures

Photonic crystals (PCs) have been intensively investigated both theoretically and experimentally in recent years due to their possibility to manipulate and control light. A number of different methods have been proposed and demonstrated to fabricate two- or three-dimensional photonic crystal structures. Among them, the holographic lithography method, in which multi-beam interference is employed, offers a number of advantages, including its ability to create large volume of periodic structures through an irradiation process, the uniformity of period, and more degrees of freedom to control the structures. In this study, a multi-beam interference model is presented for predicting the three-dimensional photonic crystal structures. Various parameters, including beam propagation and polarization directions, beam intensities, and phase shifts are considered. Calculations have been carried out to simulate a four-beam configuration which has been popularly used in the fabrication of photonic crystals. It has been demonstrated that the contours of the interference pattern are related to the polarization states and the intensity ratios among the four beams. Therefore, by controlling the beam intensities and polarization directions, different structures can be obtained. The results presented in this study provide a useful guide for choosing various optical parameters and selecting proper photoresists to fabricate three-dimensional photonic crystals.