Analytical Solution of Band Gaps in 2-D Photonic Crystals Made by Multi-Beam Interference

Analytical solution of band gaps in two-dimensional (2-D) photonic crystals made by multi-beam interference was put forward. This solution gives concise analytical expression of every band gap. The quantitative relationship between the characters of band gaps and parameters of the materials of 2-D PC is different from that of one-dimensional (1-D) PC. For structures satisfying some conditions, the properties of band gaps obtained by the analytical solution are in good consistency with that obtained by the numerical simulations using plane wave expansion method. It showed why both TE and TM waves should have the same band structure in certain direction of 2-D PC with low refractive index. Also, it should be noted that the presented approach is accurate only for low index structures.