Non-orthogonal FDTD simulations for photonic band structures, states density, and transmission/reflection of photonic crystals

摘要

Photonic crystals have been widely studied in the fields of physics, material science and optical information technology. In general, the standard rectangular finite difference time domain (FDTD) method is used to predict the performances of photonic crystals. It is however very time consuming and inefficient. The current authors developed a software called GCFE, which is based on a non-orthogonal FDTD method. The software can be used to predict the photonic band structures, photonic states density and transmission and/or reflection coefficients for one-dimensional to three-dimensional photonic crystals. In the present paper, the derivations of the discrete Maxwell's equations in time-domain and space-domain and the derivation of the discrete transfer matrix in real-space domain are briefly described firstly. In addition, the design idea and the functions of GCFE version 2.0.00 are introduced. Moreover, the band structures, transmission and reflection coefficients and photonic states density for the photonic crystal with cube lattice are calculated by our GCFE software, and numerical application results are also shown.