A stable real-valued transmission line matrix (TLM) method for simulating periodic photonic structures was presented. The method was the circuit-type implementation of the periodicity (Bloch) condition at the sidewalls of the unit cell under simulation. It was observed that the enforcement of Bloch boundary conditions at the sidewalls while preserving energy, results in a stable TLM scheme free of high-frequency noise.

Journal of Applied Physics
Department of Electronics

Romo, G., & Smy, T. (2003). Modeling of photonic crystals using a real-valued transmission line matrix method. Journal of Applied Physics, 94(4), 2177–2182. doi:10.1063/1.1593214