Journal ArticleDOI
Photonic bands: Convergence problems with the plane-wave method.
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TLDR
It is found that when ∈(r) is sharply peaked, photonic levels become almost degenerate throughout the Brillouin zone, corresponding to standing waves.Abstract:
The problems associated with the poor convergence of the Fourier transform of the hard-sphere dielectric function are discussed. A significant band gap between the eighth and ninth levels has been found for air spheres in fcc. We also consider a periodic array of Gaussian spheres, which converges well and allows a consistent and reliable determination of the general features of photonic bands. It is found that when \ensuremath{\epsilon}(r) is sharply peaked, photonic levels become almost degenerate throughout the Brillouin zone, corresponding to standing waves.read more
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Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis
TL;DR: A fully-vectorial, three-dimensional algorithm to compute the definite-frequency eigenstates of Maxwell's equations in arbitrary periodic dielectric structures, including systems with anisotropy or magnetic materials, using preconditioned block-iterative eigensolvers in a planewave basis is described.
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On-chip natural assembly of silicon photonic bandgap crystals
TL;DR: By assembling a thin layer of colloidal spheres on a silicon substrate, this work can obtain planar, single-crystalline silicon photonic crystals that have defect densities sufficiently low that the bandgap survives.
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Preparation of photonic crystals made of air spheres in titania
TL;DR: Three-dimensional crystals of air spheres in titania with radii between 120 and 1000 nanometers were made by filling the voids in artificial opals by precipitation from a liquid-phase chemical reaction and subsequently removing the original opal material by calcination and are a new class of photonic band gap crystals for the optical spectrum.
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Photonic band-gap structures
TL;DR: In this article, the photonic band gap structures, those three-dimensional periodic dielectric structures that are to photon waves as semiconductor crystals are to electron waves, are discussed.
Journal ArticleDOI
Photonic band gaps in three dimensions: New layer-by-layer periodic structures
TL;DR: In this article, a 3D periodic dielectric structure with circular, elliptical, or rectangular shape is introduced. But the 3D layer structure can be easily fabricated using conventional microfabrication techniques on the scale of optical wavelengths.