Maximizing band gaps in two-dimensional photonic crystals in square lattices.

This paper is devoted to a numerical algorithm for the maximization of band gaps in two-dimensional photonic crystals in square lattices. We first apply the finite element method to solve the eigenvalue problem, then use the piecewise constant level set (PCLS) method to maximize the band gaps. The PCLS method is very powerful for representing and modeling regions of different structures. Extremely large gaps are realized with gallium arsenide material, for transverse magnetic field (TM), transverse electric field (TE), and for complete band gaps. When the mean gap frequency is below 1, the biggest gap is about 0.2922 for the TE.