Simulation of frequency dependent photonic crystals using the transmission line matrix method

In this paper, we present a transmission line matrix method capable of modeling photonic crystals composed of frequency dependent materials using a nonuniform mesh. First, the necessary modifications of the standard hybrid-node are described. The method is then validated by computing the photonic band structure of two photonic crystals. The first simulated structure is composed of pure metallic cylinders, and the second one of semiconducting rods of InSb. In both cases, the results are compared with those predicted by alternative methods and good agreement is found. The method is also suitable for the simulation of the temperature dependence of the permittivity of semiconductors and a tunable in-line photonic filter is simulated.