Lattice symmetry applied in transfer-matrix methods for photonic crystals

Transfer-matrix methods have been routinely used to calculate the transmission and reflection spectra of electromagnetic waves propagating through a photonic crystal slab. In this article we show that the intrinsic lattice symmetries within a photonic crystal can be used to reduce numerical computations of the electromagnetic problem. We have employed this lattice-symmetry enhanced transfer-matrix method to handle two-dimensional photonic crystal slabs of square and triangular lattices and three-dimensional layer-by-layer photonic crystal slabs. The calculated transmission spectra agree excellently with the photonic band structures in predicting the photonic band gap positions, indicating the accuracy and efficiency of this proposed approach.