Predication of multi-dimensional photonic crystal structures generated by multi-beam interference in holographic lithography

Photonic crystals (PCs) are synthetic micro-structures which have periodical refraction index variations and produce photonic band gaps similar to electronic band gaps produced by the crystal potentials of semiconductors. 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 mulit-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 two four-beam configurations which have 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, the intensity ratios among the four beams, and the phase delays. Therefore, by controlling the beam intensities, polarization directions, and phase delays, 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 2D and 3D photonic crystal structures.