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.

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

Nonlocal electrodynamics of two-dimensional wire mesh photonic crystals

We calculate analytically the spectra of plasma waves and electromagnetic waves (EMW) in metallic photonic crystal consisting of the parallel thin infinite metallic cylinders embedded in the dielectric media. The axes of metallic cylinders form a regular square lattice in a plane perpendicular to them. The metal inside the cylinders is assumed to be in the high frequency regime $\omega \tau >> 1$, where $\tau$ is the relaxation time. The proposed analytical theory is based upon small parameters $f << 1$, where $f$ is the volume fraction of the metal, and $kR << 1$, where $k$ is the wave vector and $R$ is the radius of the cylinder. It is shown that there are five different branches of the EMW that cover all frequency range under consideration except one very small omnidirectional gap in the vicinity of the frequency of the surface plasmon. However, at some directions of propagation and polarizations the gap may be much larger. The reflection and refraction of the EMW is also considered. The general theory of refraction is proposed which is complicated by the spatial dispersion of the dielectric constant, and one particular geometry of the incident EMW is considered.Comment: 14 pages, 8 figure

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

The Functional Diversity of the High-Affinity Nitrate Transporter Gene Family in Hexaploid Wheat: Insights from Distinct Expression Profiles

High-affinity nitrate transporters (NRT) are key components for nitrogen (N) acquisition and distribution within plants. However, insights on these transporters in wheat are scarce. This study presents a comprehensive analysis of the NRT2 and NRT3 gene families, where the aim is to shed light on their functionality and to evaluate their responses to N availability. A total of 53 NRT2s and 11 NRT3s were identified in the bread wheat genome, and these were grouped into different clades and homoeologous subgroups. The transcriptional dynamics of the identified NRT2 and NRT3 genes, in response to N starvation and nitrate resupply, were examined by RT-qPCR in the roots and shoots of hydroponically grown wheat plants through a time course experiment. Additionally, the spatial expression patterns of these genes were explored within the plant. The NRT2s of clade 1, TaNRT2.1-2.6, showed a root-specific expression and significant upregulation in response to N starvation, thus emphasizing a role in N acquisition. However, most of the clade 2 NRT2s displayed reduced expression under N-starved conditions. Nitrate resupply after N starvation revealed rapid responsiveness in TaNRT2.1-2.6, while clade 2 genes exhibited gradual induction, primarily in the roots. TaNRT2.18 was highly expressed in above-ground tissues and exhibited distinct nitrate-related response patterns for roots and shoots. The TaNRT3 gene expression closely paralleled the profiles of TaNRT2.1-2.6 in response to nitrate induction. These findings enhance the understanding of NRT2 and NRT3 involvement in nitrogen uptake and utilization, and they could have practical implications for improving nitrogen use efficiency. The study also recommends a standardized nomenclature for wheat NRT2 genes, thereby addressing prior naming inconsistencies

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

What is the right form of the probability distribution of the conductance at the mobility edge?

The probability distribution of the conductance Pc(g) at the Anderson critical point is calculated. It is find that Pc(g) has a dip at small g in agreement with epsilon expansion results. The Pc(g) for the 3d system is quite different from the 2d quantum critical point of the integer quantum Hall effect. The universality or not of these distributions is of central importance to the field of disordered systems.Comment: 1 page, 1 figure submitted to Phys. Rev. Lett. (Comment

Impact of the inherent periodic structure on the effective medium description of left-handed and related meta-materials

We study the frequency dependence of the effective electromagnetic parameters of left-handed and related meta-materials of the split ring resonator and wire type. We show that the reduced translational symmetry (periodic structure) inherent to these meta-materials influences their effective electromagnetic response. To anticipate this periodicity, we formulate a periodic effective medium model which enables us to distinguish the resonant behavior of electromagnetic parameters from effects of the periodicity of the structure. We use this model for the analysis of numerical data for the transmission and reflection of periodic arrays of split ring resonators, thin metallic wires, cut wires as well as the left-handed structures. The present method enables us to identify the origin of the previously observed resonance/anti-resonance coupling as well as the occurrence of negative imaginary parts in the effective permittivities and permeabilities of those materials. Our analysis shows that the periodicity of the structure can be neglected only for the wavelength of the electromagnetic wave larger than 30 space periods of the investigated structure.Comment: 23 pages, 14 figure

Absolute negative refraction and imaging of unpolarized electromagnetic waves by two-dimensional photonic crystals

Absolute negative refraction regions for both polarizations of electromagnetic wave in two-dimensional photonic crystal have been found through both the analysis and the exact numerical simulation. Especially, absolute all-angle negative refraction for both polarizations has also been demonstrated. Thus, the focusing and image of unpolarized light can be realized by a microsuperlens consisting of the two-dimensional photonic crystals. The absorption and compensation for the losses by introducing optical gain in these systems have also been discussed

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