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Modeling of photonic crystals using a real-valued transmission line matrix method

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2 Author(s)
Romo, G. ; Department of Electronics, Carleton University, Ottawa K1S 5B6, Ontario, Canada ; Smy, T.

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In this article, we present a stable real-valued transmission line matrix (TLM) method for simulating periodic photonic structures. Unique to this method is the circuit-type implementation of the periodicity (Bloch) condition at the sidewalls of the unit cell under simulation. Unlike previously published methods for implementing periodic boundary conditions in real-valued TLM networks, our circuit representation is shown to be passive since no energy is introduced from the boundaries of the simulation domain. The enforcement of Bloch boundary conditions at the sidewalls of the simulation domain, while preserving energy, results in an unconditionally stable TLM method free of high-frequency noise. Our approach is validated by simulating a two-dimensional array of dielectric materials, a structure usually referred to as a photonic crystal. The results are compared with those obtained by the plane wave expansion method and good agreement is found. © 2003 American Institute of Physics.

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Journal of Applied Physics  (Volume:94 ,  Issue: 4 )