Optimization of band gap of photonic crystals fabricated by holographic lithography

Generally the photonic band gap (PBG) is a multi-variable function of several parameters related to the shape and size of the dielectric columns of photonic crystals (PhCs), and a time-consuming step-by-step scanning process for each parameter has to be used to find their best combination yielding maximum PBG. In this letter, the widely used Nelder-Mead simplex algorithm is introduced to optimize these parameters simultaneously to find a larger PBG for a new kind of two-dimensional (2D) hexagonal GaAs-Air PhC. This structure can be conveniently produced by the single-exposure holographic lithography, and the specific holographic design is also systematically investigated. This study reveals that the band gaps of PhCs made by holographic lithography may be widened by introducing irregularity of the columns and lowering the symmetry of the structure.