Dispersion relation calculation of photonic crystals using the transmission line matrix method

Abstract

In this paper we present the use of the transmission line matrix (TLM) method as a modelling tool for the computation of the dispersion relation of photonic crystals (PCs). First, the formulation of a complex-valued TLM algorithm for the implementation of the periodicity condition on the sidewalls of the simulation domain (unit cell), is presented in detail. Then, the stability issues of this formulation are analysed from energy considerations. The analysis shows that the TLM method remains unconditionally stable since the equations enforcing the periodicity condition allow for the energy to be preserved as a constant during the simulations. Finally, the complex-valued TLM algorithm is validated by simulating two PCs and by comparing the results with those predicted by alternative methods. Copyright © 2004 John Wiley & Sons, Ltd.