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Novel numerical method for the analysis of 2D photonic crystals: the cell method

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Abstract

The Cell Method, a new efficient numerical method suitable for working with periodic structures having anisotropic inhomogeneous media with curved shapes, is proposed in order to calculate the band gap of 2D photonic crystals for in-plane propagation of TM and TE waves. Moreover some numerical comparisons with other numerical methods will be provided.

©2002 Optical Society of America

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Figures (6)

Fig. 1.
Fig. 1. (a)Inner and outer orientations of the space cells in the 3D space (b)Primal and dual complexes and global variables associated with their primal and dual space cells respectively.
Fig. 2.
Fig. 2. Examples of 2D photonic crystals and periodicity of the unit cells in the xy-plane (a) for rectangular unit cells (b) for quadrangular unit cells. (c) Dependence of some voltages on the boundary of a rectangular unit cell by the periodic boundary condition.
Fig. 3.
Fig. 3. TMz case
Fig. 4.
Fig. 4. Examples of 2Dprimal and dual grids (a) Triangular primal cell complex, barycentric dual cell complex for the TMz cases (b) Barycentric primal cell complex, triangular dual cell complex for the TEz cases
Fig. 5.
Fig. 5. (a) Results of the test 1 (b) A comparison of some CM and FEM results in the test 1.
Fig. 6.
Fig. 6. (a) Results of the test 2 (b) Results of the test 3.

Equations (8)

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G T M ν GV = ω 2 M ε V
V ( x + a , y + b ) = e j β x a j β y b V x y
V = T ( β x , β y ) V
AV = ω 2 BV
M TM V = ω 2 V
G ˜ T M ε 1 G ˜ V = ω 2 M μ F
F ( x + a , y + b ) = e j β x a j β y b F x y
M TM F = ω 2 F
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