Modified Finite-Difference Time-Domain Method for Triangular Lattice Photonic Crystals

In this paper, a modified and easy finite-difference time-domain (FDTD) method based on a regular cartesian Yee´s lattice is developed for calculating the dispersion diagram of triangular lattice photonic crystals (PCs). Our method uses the standard central-difference equation, which is very easy to implement in any computing environment. The Bloch periodic boundary conditions are applied on the sides of the unit cell by translating the periodic boundary conditions to match with the directions of periodicity in the triangular lattice. Complete and accurate bandgap information is obtained by using this FDTD approach. Convergence, accuracy, and stability analysis were carried out, which ensures the reliability of this method. Numerical results for 2-D TE/TM modes in triangular lattice PC are in good agreement with results from 2-D plane wave expansion method. To ease the practical application of this method, clear explanations on the computer implementation are also provided.