Improved Plane-Wave Expansion Method for Band Structure Calculation of Metal Photonic Crystal

We combine Cartesian coordinates and polar coordinates wave number eigenvalue equations based on the plane-wave expansion (PWE) method to calculate and optimize the band structures of the two-dimensional (2D) metal photonic crystals (PhCs). Compared with the traditional PWE methods for metal PhCs, the band structures can be calculated directly in our method and no further procedures are needed to handle the folded band structures. With this method, we optimize the large gap-midgap ratio of the 2D square lattice of square metal rods and circular metal rods. The TM gap-midgap ratio of the 2D square lattice of square metal rods reaches 7.6246% with the side length L=0.71a with a being the lattice constant. The TM gap-midgap ratio of the 2D square lattice of circular metal rods reaches 16.3934% with radius R= 0.45a. Our method can be easily used in both square lattice and triangular lattice directly.