Photonic band structure of two-dimensional systems: The triangular lattice
TL;DR: By the use of a position-dependent dielectric constant and the plane-wave method, the photonic band structure for electromagnetic waves in a structure consisting of a periodic array of parallel dielectrics rods of circular cross section, whose intersections with a perpendicular plane form a triangular lattice is calculated.
Abstract: By the use of a position-dependent dielectric constant and the plane-wave method, we have calculated the photonic band structure for electromagnetic waves in a structure consisting of a periodic array of parallel dielectric rods of circular cross section, whose intersections with a perpendicular plane form a triangular lattice. The rods are embedded in a background medium with a different dielectric constant. The electromagnetic waves are assumed to propagate in a plane perpendicular to the rods, and two polarizations of the waves are considered. Absolute gaps in the resulting band structures are found for waves of both polarizations, and the dependence of the widths of these gaps on the ratio of the dielectric constants of the rods and of the background, and on the fraction of the total volume occupied by the rods, is investigated.
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TL;DR: This work shows that by employing accidental degeneracy, dielectric photonic crystals can be designed and fabricated that exhibit Dirac cone dispersion at the centre of the Brillouin zone at a finite frequency and numerically and experimentally demonstrates in the microwave regime that these crystals manipulate waves as if they had near-zero refractive indices at and near the Dirac point frequency.
Abstract: A zero-refractive-index metamaterial is one in which waves do not experience any spatial phase change, and such a peculiar material has many interesting wave-manipulating properties. These materials can in principle be realized using man-made composites comprising metallic resonators or chiral inclusions, but metallic components have losses that compromise functionality at high frequencies. It would be highly desirable if we could achieve a zero refractive index using dielectrics alone. Here, we show that by employing accidental degeneracy, dielectric photonic crystals can be designed and fabricated that exhibit Dirac cone dispersion at the centre of the Brillouin zone at a finite frequency. In addition to many interesting properties intrinsic to a Dirac cone dispersion, we can use effective medium theory to relate the photonic crystal to a material with effectively zero permittivity and permeability. We then numerically and experimentally demonstrate in the microwave regime that such dielectric photonic crystals with reasonable dielectric constants manipulate waves as if they had near-zero refractive indices at and near the Dirac point frequency.
806 citations
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.
737 citations
TL;DR: In this article, the authors show that by restricting the geometry of the photonic crystal to two dimensions (in a waveguide configuration), structures with polarization-sensitive photonic band-gaps at still lower wavelengths (in the range 800-900 nm) can be readily fabricated.
Abstract: PHOTONIC crystals are artificial structures having a periodic dielectric structure designed to influence the behaviour of photons in much the same way that the crystal structure of a semiconductor affects the properties of electrons1. In particular, photonic crystals forbid propagation of photons having a certain range of energies (known as a photonic bandgap), a property that could be incorporated in the design of novel optoelectronic devices2. Following the demonstration of a material with a full photonic bandgap at microwave frequencies3, there has been considerable progress in the fabrication of three-dimensional photonic crystals with operational wavelengths as short as 1.5 μm (ref. 4), although the optical properties of such structures are still far from ideal5. Here we show that, by restricting the geometry of the photonic crystal to two dimensions (in a waveguide configuration), structures with polarization-sensitive photonic band-gaps at still lower wavelengths (in the range 800–900 nm) can be readily fabricated. Our approach should permit the straightfor-ward integration of photonic-bandgap structures with other optical and optoelectronic devices.
727 citations
TL;DR: It is shown that complete photonic bandgaps—non-directional and for any polarization—to be realized with small air holes in silicon nitride, glass, and even glass make photonic quasicrystals promising for application in a range of optical devices.
Abstract: Photonic crystals are attracting current interest for a variety of reasons, such as their ability to inhibit the spontaneous emission of light1,2. This and related properties arise from the formation of photonic bandgaps, whereby multiple scattering of photons by lattices of periodically varying refractive indices acts to prevent the propagation of electromagnetic waves having certain wavelengths. One route to forming photonic crystals is to etch two-dimensional periodic lattices of vertical air holes into dielectric slab waveguides3,4,5,6,7. Such structures can show complete photonic bandgaps8,9,10, but only for large-diameter air holes in materials of high refractive index (such as gallium arsenide, n = 3.69), which unfortunately leads to significantly reduced optical transmission when combined with optical fibres of low refractive index. It has been suggested that quasicrystalline (rather than periodic) lattices can also possess photonic bandgaps11,12,13,14. Here we demonstrate this concept experimentally and show that it enables complete photonic bandgaps—non-directional and for any polarization—to be realized with small air holes in silicon nitride (n = 2.02), and even glass (n = 1.45). These properties make photonic quasicrystals promising for application in a range of optical devices14,15,16,17,18.
506 citations
TL;DR: In this paper, a three-dimensional finite-difference time-domain analysis of localized defect modes in an optically thin dielectric slab that is patterned with a two-dimensional array of air holes is presented.
Abstract: We present a three-dimensional finite-difference time-domain analysis of localized defect modes in an optically
thin dielectric slab that is patterned with a two-dimensional array of air holes. The symmetry, quality factor, and radiation pattern of the defect modes and their dependence on the slab thickness are investigated.
481 citations