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

Abstract

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.

SU-8: a photoresist for high-aspect-ratio and 3D submicron lithography

“…Theoretical works have predicted the appropriate laser beam configurations to achieve different periodic 3D structures (e.g. bcc, fcc, gyroid or diamond symmetries) [123,124]. Among them, only a few have been manufactured [125][126][127][128][129][130][131][132].…”

Fabrication Approaches for Generating Complex Micro- and Nanopatterns on Polymeric Surfaces

“…[90][91][92] Theoretical works have predicted the appropriate laser beam configurations to achieve different periodic 3D structures (e.g., bcc, fcc, gyroid, or diamond symmetries). 93,94 Among them, only a few have been manufactured up to now. Four-beam IL has proven to give fcc 95,96 (Figure 8), simple cubic, bcc, 97 and diamond-like 98,99 patterns.…”

“…IL has now been successfully applied for two decades to manufacturing of periodic structures for a wide variety of uses. Surface gratings were produced by interference of three beams or overlaying two sequential exposures at 90°. , Using additional beams in a single exposure or overlaying multiple exposures, 3D periodic structures have also been fabricated. − Theoretical works have predicted the appropriate laser beam configurations to achieve different periodic 3D structures (e.g., bcc, fcc, gyroid, or diamond symmetries). , Among them, only a few have been manufactured up to now. Four-beam IL has proven to give fcc , (Figure ), simple cubic, bcc, and diamond-like , patterns.…”

Multi-Beam Interference Advances and Applications: Nano-Electronics, Photonic Crystals, Metamaterials, Subwavelength Structures, Optical Trapping, and Biomedical Structures

“…For example, the lattice point geometry has been shown to affect the photonic-bandgap characteristics in photonic crystals [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45], selective plasmonic excitation in plasmonic crystals [46], photonic crystal laser beam pattern [47] and polarization mode control [48], birefringence of photonic crystal fibers [49], cell behavior in tissue engineering [50], tuning of surface textures [51], magnetization switching in periodic magnetic arrays [52], and, negative refraction and superlensing in metamaterials [53,54]. Accordingly, several studies report analytical and computational methods to select individual beam parameters to change the motif orientation and shape [34,42,55,56] from hemispherical to hemielliptical [57]; circular to triangular [58]; as well as, general structures including micro-cavities, micro-bumps, and rectangular bumps [51]. Most recently, research has focused on the exact analytical design and fabrication of motifs with 2D geometries that vary from the shape of an ellipse to that of a rhombus [59].…”