16 November 2004 Time domain simulation of photonic crystals using the transmission line matrix method
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Abstract
This paper presents the transmission line matrix method (TLM) as an alternative efficient simulation tool for the analysis of photonic crystals (PCs). The paper describes important aspects for the computation of the photonic band structures of infinitely periodic PCs within the formulation of the TLM method. In addition, we propose two methods for reducing the computational effort involved in the simulations of PCs. One method is based on a real-valued implementation of the periodicity (Bloch) condition, and the other one is based on the use of a multi-grid mesh. Depending on the physical geometry of the crystal, computational savings of over 50% can be easily achieved. The advantages and limitations of these methods are described. Given the popularity of the finite differences time domain (FDTD) method for the simulation of PCs, we briefly compare the performance of the TLM method with that of the FDTD and show that under various circumstances, the use of the TLM method can be advantageous. The suitability of the TLM method to handle PCs with more general material properties such as frequency dependent metals and semiconductors is also demonstrated. Finally, we validate these simulation aspects of the TLM method by simulating various photonic crystals composed of dielectric, metallic and semiconducting materials using uniform and multi-grid meshes. The results are compared with those predicted by alternative methods such as the plane wave expansion method for verification.
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Gerardo Romo, Gerardo Romo, Tom J. Smy, Tom J. Smy, } "Time domain simulation of photonic crystals using the transmission line matrix method", Proc. SPIE 5579, Photonics North 2004: Photonic Applications in Telecommunications, Sensors, Software, and Lasers, (16 November 2004); doi: 10.1117/12.566468; https://doi.org/10.1117/12.566468
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