Gap deformation and classical wave localization in disordered two-dimensional photonic band gap materials

By using two ab initio numerical methods we study the effects that disorder has on the spectral gaps and on wave localization in two-dimensional photonic band gap materials. We find that there are basically two different responses depending on the lattice realization (solid dielectric cylinders in air or vise versa), the wave polarization, and the particular form under which disorder is introduced. Two different pictures for the photonic states are employed, the ``nearly free'' photon and the ``strongly localized'' photon. These originate from the two different mechanisms responsible for the formation of the spectral gaps, ie. multiple scattering and single scatterer resonances, and they qualitatively explain our results.Comment: Accepted for publication in Phys. Rev.

Robustness of One-Dimensional Photonic Bandgaps Under Random Variations of Geometrical Parameters

The supercell method is used to study the variation of the photonic bandgaps in one-dimensional photonic crystals under random perturbations to thicknesses of the layers. The results of both plane wave and analytical band structure and density of states calculations are presented along with the transmission cofficient as the level of randomness and the supercell size is increased. It is found that higher bandgaps disappear first as the randomness is gradually increased. The lowest bandgap is found to persist up to a randomness level of 55 percent.Comment: Submitted to Physical Review B on April 8 200

Viscoelastic response of sonic band-gap materials

A brief report is presented on the effect of viscoelastic losses in a high density contrast sonic band-gap material of close-packed rubber spheres in air. The scattering properties of such a material are computed with an on-shell multiple scattering method, properties which are compared with the lossless case. The existence of an appreciable omnidirectional gap in the transmission spectrum, when losses are present, is also reported.Comment: 5 pages, 4 figures, submitted to PR

Scattering of elastic waves by periodic arrays of spherical bodies

We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres, characterized by Lam\'e coefficients which may be complex and frequency dependent, arranged periodically in a host medium with different mass density and Lam\'e coefficients. We view the crystal as a sequence of planes of spheres, parallel to and having the two dimensional periodicity of a given crystallographic plane, and obtain the complex band structure of the infinite crystal associated with this plane. The method allows one to calculate, also, the transmission, reflection, and absorption coefficients for an elastic wave (longitudinal or transverse) incident, at any angle, on a slab of the crystal of finite thickness. We demonstrate the efficiency of the method by applying it to a specific example.Comment: 19 pages, 5 figures, Phys. Rev. B (in press

Acoustic properties of colloidal crystals

We present a systematic study of the frequency band structure of acoustic waves in crystals consisting of nonoverlapping solid spheres in a fluid. We consider colloidal crystals consisting of polystyrene spheres in water, and an opal consisting of close-packed silica spheres in air. The opal exhibits an omnidirectional frequency gap of considerable width; the colloidal crystals do not. The physical origin of the bands are discussed for each case in some detail. We present also results on the transmittance of finite slabs of the above crystals.Comment: 7 pages, 9 figures, prb approve

Defect structures in metallic photonic crystals

Cataloged from PDF version of article.We have investigated metallic photonic crystals built around a layer‐by‐layer geometry. Two different crystal structures (face‐centered‐tetragonal and tetragonal) were built and their properties were compared. We obtained rejection rates of 7–8 dB per layer from both metallic crystals. Defect modes created by removing rods resulted in high peak transmission (80%), and high quality factors (1740). Our measurements were in good agreement with theoretical simulations. © 1996 American Institute of Physic

Quasimetallic silicon micromachined photonic crystals

Cataloged from PDF version of article.We report on fabrication of a layer-by-layer photonic crystal using highly doped silicon wafers processed by semiconductor micromachining techniques. The crystals, built using (100) silicon wafers, resulted in an upper stop band edge at 100 GHz. The transmission and defect characteristics of these structures were found to be analogous to metallic photonic crystals. We also investigated the effect of doping concentration on the defect characteristics. The experimental results agree well with predictions of the transfer matrix method simulations. (C) 2001 American Institute of Physics

Exceptionally directional sources with photonic-bandgap crystals

Cataloged from PDF version of article.Three-dimensional photonic-bandgap crystals are used to design and fabricate uniquely directional sources and receivers. By utilizing the resonances of a Fabry-Perot cavity formed with photonic-bandgap crystals, we were able to create exceptionally directional sources by placing the sources within such a cavity. Very good agreement between finite-difference time-domain calculations and the experiment is obtained. Radiation patterns with half-power beam widths of less than 12 degrees were obtained. (C) 2001 Optical Society of America

Laser-micromachined Millimeter-wave Photonic band gap cavity structures

Cataloged from PDF version of article.We have used laser-micromachined alumina substrates to build a three-dimensional photonic band-gap crystal. The rod-based structure has a three-dimensional full photonic band gap between 90 and 100 GHz. The high resistivity of alumina results in a typical attenuation rate of 15 dB per unit cell within the band gap. By removing material, we have built defects which can be used as millimeter-wave cavity structures. The resulting quality ~Q! factors of the millimeter-wave cavity structures were as high as 1000 with a peak transmission of 10 dB below the incident signal. © 1995 American Institute of Physics

Tight-binding parameterization for photonic band gap materials

The ideas of the linear combination of atomic orbitals (LCAO) method, well known from the study of electrons, is extended to the classical wave case. The Mie resonances of the isolated scatterer in the classical wave case, are analogous to the localized eigenstates in the electronic case. The matrix elements of the two-dimensional tight-binding (TB) Hamiltonian are obtained by fitting to ab initio results. The transferability of the TB model is tested by reproducing accurately the band structure of different 2D lattices, with and without defects, thus proving that the obtained TB parameters can be used to study other properties of the photonic band gap materials.Comment: 4 pages, 3 postscript figures, sumbitted to Phys. rev. Let