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.
(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.
(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.
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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