The effect of disorder on the wave propagation in one-dimensional periodic optical systems

The influence of disorder on the transmission through periodic waveguides is studied. Using a canonical form of the transfer matrix, we investigate the dependence of the Lyapunov exponent γ on the frequency ν and magnitude of the disorder σ. It is shown that in the bulk of the bands γ?～?σ², while near the band edges it has order γ?～?σ^2/3. This dependence is illustrated by numerical simulations.     

On the enhancement of the nonlinear frequency transformation in periodic media

It is theoretically shown that an enhancement of the nonlinear frequency transformation in a periodic medium occurs under definite conditions if it is accompanied by light diffraction in this medium. The enhancement of the phase-matched frequency transformation occurs if the harmonic frequency ω approaches the stop band frequency ω_e. In the nondepleted pump approximation the corresponding increase of the harmonic intensity is proportional to ω_e(ω?ω_e)^?1 and is restricted by a quantity proportional to the fourth power of the sample thickness. The formulas for the enhancement of second harmonic generation are presented.     

On Asymptotic Expansions and Scales of Spectral Universality in Band Random Matrix Ensembles

 We consider real random symmetric N × N matrices H of the band-type form with characteristic length b. The matrix entries are independent Gaussian random variables and have the variance proportional to , where u(t) vanishes at infinity. We study the resolvent in the limit and obtain the explicit expression for the leading term of the first correlation function of the normalized trace . We examine on the local scale and show that its asymptotic behavior is determined by the rate of decay of u(t). In particular, if u(t) decays exponentially, then . This expression is universal in the sense that the particular form of u determines the value of C > 0 only. Our results agree with those detected in both numerical and theoretical physics studies of spectra of band random matrices. Received: 8 April 2000 / Accepted: 7 June 2002 Published online: 21 October 2002 RID="*" ID="*" Present address: Département de Mathématiques, Université de Versailles Saint-Quentin, 78035 Versailles, France.     

Light propagation in photonic crystal with gain: Applicability of the negative loss approximation

The applicability of the concept of permittivity with Im ?_gain < 0 to describe the light propagation in a metamaterial system with gain is discussed using the example of a 1D photonic crystal containing gain layers. It is shown that this approach is in agreement with the principle of causality, unless lasing is present. Though the lasing process itself requires nonlinear analysis, the lasing threshold can be determined by linear (negative loss) approximation. Connecting the onset of lasing with the passage of the transfer function pole into the upper half-plane of the complex frequency, we show that (i) if the pump frequency lies in a pass band then an increase in the number N of elementary cells will sooner or later lead to lasing; (ii) if the frequency of the pump lies in the band gap, then lasing at band gap frequencies may occur in a sample with a low N before the band gap has been formed. Nevertheless, lasing will be necessarily suppressed by a further increase in N. In any case, for sufficiently large number of layers due to a finite line width of ?_gain(ω), lasing appears in the pass band even if the pump frequency is in the band gap.     

Suppression of Noise Effects in Color Correction by Spectral Sensitivities of Image Sensors

The accurate transformation of device responses to tristimulus values is important at an early stage in color management and this transformation is usually called color correction. In this paper it is shown that the influence of noise on color correction can be suppressed if the square of the singular values by the singular value decomposition (SVD) of a sensor matrix represented by surface reflectance, SLVA^1/2, is larger than the noise variance, where S is the M × N matrix of M channel spectral sensitivities, L is the N × N diagonal matrix for an recording illuminant, V is the N × N matrix which is composed of eigenvectors of an autocorrelation matrix for spectral reflectance of samples, A is the N × N diagonal matrix with eigenvalues of the autocorrelation matrix along the diagonal and N is the number of the dimension, respectively. A method to suppress the influence of noise on color correction by spectral sensitivities of sensors is presented for the first time.     

Effect of pinning fields on the spin wave band gaps in comblike structures

We consider, in the frame of the long-wavelength Heisenberg model, the effect of a pinning field on the spin wave band gaps and transmission spectra of one-dimensional comb-like structures. Using a Greens function method, we obtained closed-form expressions for the band structure and the transmission coefficients for an arbitrary value of the number N of sites (Nof resonators) in the comb-like structure. We report the opening-up of stop bands inside the pass-bands due to the effect of the pinning field at the ends of the resonators of the comb. These structures, composed of one-dimensional ferromagnetic materials, may exhibit large gaps where the propagation of spin waves is forbidden. The width and frequency position of these gaps depends on the strength of the pinning field.Received: 17 October 2003, Published online: 9 April 2004PACS: 75.30.Gw Magnetic anisotropy - 75.30.Ds Spin waves - 75.75. + a Magnetic properties of nanostructures     

Propagation of acoustic waves in a fluid-filled pipe with periodic elastic Helmholtz resonators

Helmholtz resonators are widely used to reduce noise in a fluid-filled pipe system. It is a challenge to obtain lowfrequency and broadband attenuation with a small sized cavity. In this paper, the propagation of acoustic waves in a fluid-filled pipe system with periodic elastic Helmholtz resonators is studied theoretically. The resonance frequency and sound transmission loss of one unit are analyzed to validate the correctness of simplified acoustic impedance. The band structure of infinite periodic cells and sound transmission loss of finite periodic cells are calculated by the transfer matrix method and finite element software. The effects of several parameters on band gap and sound transmission loss are probed.Further, the negative bulk modulus of periodic cells with elastic Helmholtz resonators is analyzed. Numerical results show that the acoustic propagation properties in the periodic pipe, such as low frequency, broadband sound transmission, can be improved.     

退火对含氮氟非晶碳膜结构及光学带隙的影响

采用射频等离子体增强化学气相沉积法,在不同条件下制备了含氮氟非晶碳膜,着重考察了退火温度对膜结构和光学带隙的影响. 研究发现：在350℃时,膜仍很稳定,当退火温度达到400℃时,其内各化学键的相对含量发生很大的改变. 膜的光学带隙随着退火温度的升高而增大,红外和拉曼光谱分析显示其原因是：退火使得膜内F的相对浓度降低,sp²相对含量升高,导致σ-σ^*带边态密度降低. 关键词： 含氮氟非晶碳膜 退火 光学带隙     

Analytical representation of the density derivative of the Percus–Yevick hard-sphere radial distribution function

ABSTRACT

Explicit analytical expressions are presented for the density derivative, ?g_HS(R; ρ)/?ρ, of the Percus–Yevick approximation to the hard-sphere radial distribution function for R ≤ 6σ, where σ is the hard-sphere diameter and ρ = (N/V)σ³ is the reduced density, where N is the number of particles and V is the volume. A FORTRAN program is provided for the implementation of these for R ≤ 6σ, which includes code for the calculation of g_HS(R; ρ) itself over this range. We also present and incorporate within the program code convenient analytical expressions for the numerical extrapolation of both quantities past R = 6σ. Our expressions are numerically tested against exact results.     

Current noise and long time tails in biased disordered random walks

We calculate the mean velocity and the velocity correlation function for a random walk with a uniform bias on a disordered chain. We find a new long time tail in the velocity correlation function due to the combined effects of the bias and of the disorder in the site variables. This long time tail persists to a low-frequency cutoff inversely proportional to the square of the bias. By associating the velocity correlation function with the spectrum of current fluctuations, we calculate the excess low-frequency current noise associated with this long time tail. The spectrum of current fluctuations goes as(I ²/N)f ^–1/2, whereI is the DC current,N is the number of charge carriers, andf is the frequency. The possible connection to 1/f noise is discussed. The calculation is done by a perturbation expansion in the strength of the disorder, but is shown to be exact to all orders for weak enough bias.Supported by a fellowship of the German Academic Exchange Service (DAAD).Supported by the National Science Foundation through Grant No. DMR-8108328 and through the Cornell Materials Science Center.     

Wigner Random Matrices with Non-Symmetrically Distributed Entries

We show that the spectral radius of an N× N random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from above by 2 σ + o(N−6/11+ε), where σ² is the variance of the matrix entries and ε is an arbitrary small positive number. Our bound improves the earlier results by Z. Füredi and J. Komlós (1981), and Van Vu (2005).     

High-resolution infrared spectrum of the ν2 + ν3 band of 14N16O2

The ν₂ + ν₃ band of ¹⁴N¹⁶O₂ has been recorded with resolution of 0.028 cm^?1. Ground state and upper state rotational constants have been obtained. The band center obtained, ν₀ = 2355.1517 ± 0.0011 cm^?1 (error cited is 3σ), has been combined with the band centers recently determined for ν₃ and ν₂ to calculate X₂₃ = ?11.348 ± 0.020 cm^?1 where the uncertainty cited is based on reasonable estimates of the absolute frequency error.     

Computing the Loewner Driving Process of Random Curves in the Half Plane

We simulate several models of random curves in the half plane and numerically compute the stochastic driving processes that produce the curves through the Loewner equation. Our models include models whose scaling limit is the Schramm-Loewner evolution (SLE) and models for which it is not. We study several tests of whether the driving process is Brownian motion, as it is for SLE. We find that testing only the normality of the process at a fixed time is not effective at determining if the random curves are an SLE. Tests that involve the independence of the increments of Brownian motion are much more effective. We also study the zipper algorithm for numerically computing the driving function of a simple curve. We give an implementation of this algorithm which runs in a time O(N ^1.35) rather than the usual O(N ²), where N is the number of points on the curve.     

Field theory of the random flux model

The random flux model (defined here as a model of lattice fermions hopping under the influence of maximally random link disorder) is analysed field theoretically. It is shown that the long range physics of the model is described by the supersymmetric version of a field theory that has been derived earlier in connection with lattice fermions subject to weak random hopping. More precisely, the field theory relevant for the behaviour of n-point correlation functions is of non-linear σ model type, where the group GL(n|n) is the global invariant manifold. It is argued that the model universally describes the long range physics of random phase fermions and provides further evidence in favour of the existence of delocalised states in the middle of the band in two dimensions. The same formalism is applied to the study of non-Abelian generalisations of the random flux model, i.e. N-component fermions whose hopping is mediated by random U(N) matrices. We discuss some physical applications of these models and argue that, for sufficiently large N, the existence of long range correlations in the band centre (equivalent to metallic behaviour in the Abelian case) can be safely deduced from the RG analysis of the model.     

Elastic wave propagation in a randomly stratified solid medium

Abstract

The mean-field method is used to analyse longitudinal and transverse (both SV- and SH-type) wave propagation in an unbounded randomly stratified solid medium. It is assumed that elastic moduli of the medium are constant while a density is a random function of the cartesian coordinate z. For a case of small density fluctuations, expressions are obtained for z-components of effective propagation vectors of P-, SV- and SH-waves for arbitrary relations between wavelengths and a correlation length of the random inhomogeneities. It is shown, that when the correlation length is small in comparison with the wavelengths, the mean-field attenuation coefficients are proportional to the frequency squared. In this case P- and SV-waves convert into each other. When the correlation length is large in comparison with the wavelengths, the mean-field attenuation coefficients are also proportional to the frequency squared, but in this case P- and SV-waves propagate independently.     

On the transmission of X-ray beams through rough near-surface channels

The transmission of X-rays through a rough narrow channel in a dielectric material is investigated by numerical simulation with regard for diffraction and loss in coherence. It is found that the transmission factor may sharply decrease in channels with periodic deformations. The effect of roughness on the transmission is explained in terms of the statistical theory of X-ray scattering in a rough boundary layer. The mode damping factors β are related to the channel width d as 1/d ³ and are proportional to the roughness amplitude. The explanation for the anomalous propagation through thin Cr/C/Cr channels is given.     

Control of sound and vibration for cylindrical shells by utilizing a periodic structure of functionally graded material

A periodic shell made of functionally graded material (FGM) is proposed in this Letter. Wave propagation and vibration transmission in the FGM periodic shell for different circumferential modes are investigated. By illustrating the dynamical behavior of the periodic FGM shell within the pass/stop band frequency ranges, the mechanism of wave propagation and vibration transmission in the shell are illuminated. Moreover, the suppression characteristics of structure-borne sound in the internal field of the shell, either within the stop or pass band frequency ranges, are studied.     

Dual-band high impedance surface with graphene-based metasurfaces

High impedance surface (HIS) is an electromagnetic band gap (EBG) material that shows magnetic conductor surface properties within its band gap frequencies. The operation bandwidth is corresponding to the frequency range, where the reflection phase varies between +90^∘ and −90^∘. In this paper, a dual-band HIS is investigated based on planar periodic graphene arrays placed on a grounded dielectric substrate. Analytical circuit model of the graphene array together with the transmission line theory is employed to analyze the proposed structure. We demonstrate that the HIS bands can be adjusted by tuning the geometrical parameters of the structure and the Fermi level of graphene. The graphene-based HIS promises future applications in the low-profile, high gain and high efficiency antennas at THz frequencies.     

Universality of a dynamical percolative approach to 1/f γ noise

A dynamical percolative model explaining the universality of 1/ f ^γ noise is reported. Exponents γ ranging from 0 to 2 are obtained under the hypothesis that noise originates from random switching events between two ON-OFF states in elemental parts (switchers) of a physical system. The usual noise behaviour with γ very close to 1 in an arbitrarily wide frequency range is obtained assuming a statistical distribution of switcher relaxation time τ proportional to τ ^-1 , as in McWhorter's model. The impact of these results with respect to recent self-organised criticality models is discussed. Received 6 November 2000 and Received in final form 22 May 2001