Numerical band calculation of holographically formed periodic structures with irregular motif

Abstract

Recently, two-dimensional and three-dimensional periodic dielectric structures have been directly fabricated by laser holographic lithography (HL) to create novel geometric structures with high-precision tolerances. Multiple beam interference via beam splitting mirrors or diffractive optical elements produce isointensity contours that can be accurately recorded in photoresist and subsequently used as a template for creating photonic crystals with a complete or partial bandgap. The periodic structures typically formed by HL comprise of highly convoluted contours that do not conform to typically known geometrical shapes and therefore preclude the use of analytic approaches such as the plane wave expansion (PWE) method to accurately generate the band-dispersion curves. In this paper, we present a numerical technique that decomposes the HL-formed structure into fine mesh grids and expands this material mesh into the PWE method to generate band-dispersion curves. Band diagrams obtained in this way are shown to accurately match the well known solutions for opal, inverted opal, and woodpile structures which have a regular motif. We extend the numerical technique to predict the band structure of HL templates which have an irregular motif and present band diagrams for structures formed by Ar-ion laser phasemask interference.