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A flexible Bloch mode method for computing complex band structures and impedances of two-dimensional photonic crystals
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10.1063/1.3674281
/content/aip/journal/jap/111/1/10.1063/1.3674281
http://aip.metastore.ingenta.com/content/aip/journal/jap/111/1/10.1063/1.3674281
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Figures

Image of FIG. 1.
FIG. 1.

Schematic of L = 5 PC structures for a square and a triangular PC lattice. The squares with solid edges are the unit cells used by our method. For the triangular lattice PC, the field in the solid-edge unit cells are calculated from the unit cells of the simulated structure (dashed edges) using Bloch’s theorem, with the ratio between adjacent cells’ fields.

Image of FIG. 2.
FIG. 2.

(Color online) Complex band structure for the PC. The Wood anomaly (a/λ = 0.333) is marked. The modes are sorted into colors by |μ|; where two modes are propagating (i.e., have |μ| = 1), they are sorted by |arg(μ)|. (a) Magnitude of Bloch factors |μ|, with three Bloch modes found at all frequencies. (b) |μ| with two Bloch modes found below the Wood anomaly, three above. (c) Argument of Bloch factors. (d) Complex band structure in 3D.

Image of FIG. 3.
FIG. 3.

(Color online) Reflectance of the coated PC as a function of ay 1 and ay 2, the relative thicknesses of the two coating layers, calculated using PC impedances from BlochCode. The minimum reflectance is marked.

Image of FIG. 4.
FIG. 4.

Schematic of the all-polarization antireflection coating. r 1 and r 2 are the radii of the holes in the first two layers, and d 1 and d 2 are the thicknesses of the extra silicon background layers between the first few rows of holes. For this coating, r 1 = 0.13 a, d 1 = 0.89 a, r 2 = 0.17 a, and d 2 = 0.9 a.

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/content/aip/journal/jap/111/1/10.1063/1.3674281
2012-01-11
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A flexible Bloch mode method for computing complex band structures and impedances of two-dimensional photonic crystals
http://aip.metastore.ingenta.com/content/aip/journal/jap/111/1/10.1063/1.3674281
10.1063/1.3674281
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