Anderson localization and saturable nonlinearity in one-dimensional disordered lattices

We investigate numerically the propagation and the Anderson localization of plane waves in a one-dimensional lattice chain, where disorder and saturable nonlinearity are simultaneously present. Using a calculation scheme for solving the stationary discrete non-linear Schrödinger equation in the fixed input case, the disorder-averaged logarithmic transmittance and the localization length are calculated in a numerically precise manner. The localization length is found to be a non-monotonic function of the incident wave intensity, acquiring a minimum value at a certain finite intensity, due to saturation effects. For low incident intensities where the saturation effect is ineffective, the enhancement of localization due to Kerr-type nonlinearity occurs in a way similar to the case without saturation. For sufficiently high incident intensities, we find that the localization length is an increasing function of the incident wave intensity, which implies that localization is suppressed for stronger input intensities, and ultimately approaches a saturation value. This feature is associated with the fact that the non-linear system is reduced to an effectively linear one, when either the incident wave intensity or the saturation parameter is sufficiently large. The non-linear saturation effect is found to be stronger and more pronounced when the energy of the incident wave is larger. We also calculate the variance of the inverse localization length and find that it also shows a non-monotonic behaviour.     

失谐压电周期结构中波动的局部化

针对压电周期结构中弹性波的局部化问题进行了研究。采用传递矩阵方法推导了结构中相邻单胞间的传递矩阵,采用W o lf方法给出了结构中局部化因子的表达式,给出了数值算例,并分析了压电材料各参数对局部化因子的影响。分析表明,对于不同的压电材料,结构中的频带性质和局部化程度有很大不同,可以通过调整结构的材料特性来改变弹性波的局部化程度,从而改变波动在结构中的传播特性。     

Left-handed metamaterials based on only modified circular electric resonators

Abstract

The novel design of a single-sided left-handed metamaterial (LHM) based only on modified circular electric resonators (MCERs) is presented experimentally and numerically in this letter. A capacitive gap is introduced in the middle arm of the electric resonator. Through adjusting the geometrical dimensions properly, the two frequency bands corresponding to negative permittivity and permeability overlap, which is validated by the parametric retrieval algorithm and equivalent circuit analysis. Furthermore, a dual-band LHM is achieved by combining two kinds of MCERs within the same unit cell. Compared to previous composite structures, the MCERs have the advantages of simple pattern, flexible design and fabricating three-dimensional LHMs readily.     

左右手材料构成的双层结构的转移矩阵

推导出了由左右手材料构成的双层结构的转移矩阵.利用这个转移矩阵,推导出了由左右手材料交替构成的一维光子晶体的色散关系.     

Light transport in quasi-one-dimensional disordered waveguides composed of locally two-dimensional random square lattices

We present numerical studies on the light transport properties which are tuned by the disorder strength in quasi-one-dimensional disordered waveguides consisting of periodically arranged scatterers with random dielectric constant. The transport mean free path is found to be inversely proportional to the square of the relative fluctuation of the dielectric constant as in the 1D and 2D cases but the proportionality coefficient is between those of 1D and 2D. The transport properties of light through a sample with a fixed size can be tuned from ballistic to localized regime as well, and a generalized scaling function is introduced to determine the light transport status in such a sample. The calculation of the energy density profile of the most transmitted eigenchannel clearly exhibits the transition of transport behaviour from diffusion to localization.     

Extreme narrow photonic bands and strong photonic localization produced by 2D defect two-segment-connected quadrangular waveguide networks

In this paper, we investigate the properties of optical transmission and photonic localization of two-dimensional (2D) defect two-segment-connected quadrangular waveguide networks (DTSCQWNs) and find that many groups of extreme narrow photonic bands are created in the middle of the transmission spectra. The electromagnetic (EM) waves in DTSCQWNs with the frequencies of extreme narrow photonic bands can produce strong photonic localizations by adjusting defect broken degree. On the other hand, we obtain the formula of extreme narrow photonic bands’ frequencies dependent on defect broken degree and the formula of the largest intensity of photonic localization dependent on defect broken degree, respectively. It may possess potential application for designing all-optical devices based on strong photonic localizations. Additionally, we propose a so-called defecton mode to study the splitting rules of extreme narrow photonic bands, where decomposition-decimation method is expanded from the field of electronic energy spectra to that of optical transmission spectra.     

热学超材料研究进展

热学超材料是超材料家族的新成员,从一开始就备受瞩目,尤其近年来得到迅猛发展。本文以热学超材料关键技术为主线,着眼于坐标变换的基本理论和先进超材料的新奇性质,综述了近年来热学超材料的研究进展,重点关注其在热隐身、热防护、热管理和热信息等方面的应用前景。基于热学超材料的研究现状和发展趋势,进行了系统性的分类梳理,分析和归纳了近年来相关研究的内容与特色,给出了未来热学超材料在隐身、热管理、信息等领域的研究展望。

     

Chirped bright and double-kinked quasi-solitons in optical metamaterials with self-steepening nonlinearity

Considering the self-steepening effect in a metamaterial (MM) can significantly change its behaviour. We study the propagation of ultrashort pulses in nonlinear MMs that is governed by a generalized nonlinear Schrö dinger equation with higher order effects such as pseudo-quintic nonlinearity and self-steepening effect. A class of chirped quasi-soliton solutions is obtained in the presence of the self-steepening term, and some of which are derived for the first time. The solutions comprise chirped bright quasi-solitons on a constant and zero background, kink and anti-kink quasi-solitons, and double-kink quasi-solitons. It is found that the nonlinear chirp associated with each of these waves is directly proportional to the intensity and its amplitude can be controlled by selecting the self-steepening and dispersion coefficients. Particular cases of chirp-free quasi-solitons are discussed. The conditions on MM parameters for the formation of these structures are also presented. The obtained results are important to explore much richer localized light pulses in MMs.     

All-optical tunable dual Fano resonance in nonlinear metamaterials in optical communication range

Low-power, ultra-fast all-optical tunable dual Fano resonance was realized in a metamaterial coated with a non-linear nanocomposite layer composed of gold nanoparticle-doped polycrystalline barium strontium titanate and multilayer tungsten disulphide microsheets. A high non-linear refractive index of ?2.148 × 10^?11 m²/W was achieved in the nanocomposite material that originated in the non-linearity enhancement associated with the quantum confinement effect, the local-field enhancement effect, and reinforced interactions between photons and the multilayer tungsten disulphide microsheets. An ultra-low threshold pump intensity of 600 kW/cm² was obtained. An ultra-fast response time of 25.4 ps was maintained because of the fast relaxation dynamics of the bound electrons in the nanoscale polycrystalline barium strontium titanate grains. The large third-order non-linear responses of the metamaterial were confirmed with a high third harmonic generation conversion efficiency of 5.4 × 10^?5. This work may help to pave the way towards realization of ultra-high-speed information processing chips and multifunctional integrated photonic devices based on metamaterials.     

Scaling, localization and anisotropy in fracturing central-force spring lattices with strong disorder

We analyze scaling and localization phenomena in the fracture of a random central-force spring lattice model with strong disorder by means of computer simulation. We investigate the statistical and topological properties of the developing damage pattern and the scaling behaviour of the threshold. Our observations show that from the beginning and up to the point of maximum stress, damage develops in a uniform manner, qualitatively like in a percolating lattice, but numerically different from random percolation. Beyond the maximum-stress point localization and anisotropy come into play, resulting in final crack formation. The fraction of broken bonds at which the lattice fails, as well as the strain corresponding to failure, scale with the lattice size via power laws. The roughness of the final crack scales as a power law of the crack length over three decades of lengthscale.     

左手材料薄板波导中的传导模

推导了左手材料薄板波导中传导模的色散方程,分析了波导中存在传导模与波导材料和包敷材料参数取值范围之间的关系.数值算例证实了这些关系.     

Stable diffraction-management soliton in a periodic structure with alternating left-handed and right-handed media

In this paper, we first derive a modified two-dimensional non-linear Schrödinger equation including high-order diffraction (HOD) suitable for the propagation of optical beam near the low-diffraction regime in Kerr non-linear media with spatial dispersion. Then, we apply our derived physical model to a designed two-dimensional configuration filled with alternate layers of a left-handed material (LHM) and a right-handed media by employing the mean-field theory. It is found that the periodic structure including LHM may experience diminished, cancelled, and even reversed diffraction behaviours through engineering the relative thickness between both media. In particular, the variational method analytically predicts that close to the zero-diffraction regime, such periodic structure can support stable diffraction-management solitons whose beamwidth and peak amplitude evolve periodically with the help of HOD effect. Numerical simulation based on the split-step Fourier method confirms the analytical results.     

Disordered animal multilayer reflectors and the localization of light

Multilayer optical reflectors constructed from ‘stacks’ of alternating layers of high and low refractive index dielectric materials are present in many animals. For example, stacks of guanine crystals with cytoplasm gaps occur within the skin and scales of fish, and stacks of protein platelets with cytoplasm gaps occur within the iridophores of cephalopods. Common to all these animal multilayer reflectors are different degrees of random variation in the thicknesses of the individual layers in the stack, ranging from highly periodic structures to strongly disordered systems. However, previous discussions of the optical effects of such thickness disorder have been made without quantitative reference to the propagation of light within the reflector. Here, we demonstrate that Anderson localization provides a general theoretical framework to explain the common coherent interference and optical properties of these biological reflectors. Firstly, we illustrate how the localization length enables the spectral properties of the reflections from more weakly disordered ‘coloured’ and more strongly disordered ‘silvery’ reflectors to be explained by the same physical process. Secondly, we show how the polarization properties of reflection can be controlled within guanine–cytoplasm reflectors, with an interplay of birefringence and thickness disorder explaining the origin of broadband polarization-insensitive reflectivity.     

Rogue waves generation in a left-handed nonlinear transmission line with series varactor diodes

We investigate the electromagnetic wave behavior and its characterization using collective variables technique. Second-order dispersion, first- and second-order nonlinearities, which strongly act in a left-handed nonlinear transmission line with series varactor diodes, are taken into account. Four frequency ranges have been found. The first one gives the so-called energetic soliton due to a perfect combination of second-order dispersion and first-order nonlinearity. The second frequency range presents a dispersive soliton leading to the collapse of the electromagnetic wave at the third frequency range. But the fourth one shows physical conditions which are able to provoke the appearance of wave trains generation with some particular waves, the rogue waves. Moreover, we demonstrate that the number of rogue waves increases with frequency. The soliton, thereafter, gains a relative stability when second-order nonlinearity comes into play with some specific values in the fourth frequency range. Furthermore, the stability conditions of the electromagnetic wave at high frequencies have been also discussed.     

Novel high gain regimes of spatio-temporal modulational instability for a single-cycle pulse in metamaterials

We derive a generalized expression for the spatio-temporal modulational instability (MI) gain in a metamaterial incorporating linear dispersion terms up to fourth order and nonlinear dispersion terms up to second order and study the influence of the varying input pulse widths and carrier frequency on MI gain. For a single-cycle pulse we have found new regimes of spatio-temporal MI, symmetrically located with respect to the central gain maximum at q?=?0 (q being the transverse spatial frequency of the perturbation). The gain in these new branches of MI is much higher compared to the central branch.     

Effect of disordered magnetic correlations in a layered high-temperature superconductor

Using the Eliashberg equations for superconductivity in a layered high-temperature superconductor and taking into consideration the phonon-mediated electron-electron interaction and the effect of the disordered magnetic correlations, we calculated the expressions for the critical temperature. The phonon and the magnetic kernels have a logarithmic divergence in the lowfrequency limit and the critical temperature differs from the McMillan form. The effect of various parameters on the decrease of the critical temperature has been analyzed. The renormalization functionZ _ph () contains a logarithmic dependence on.     

Transverse intersection of invariant manifolds in perturbed multi-symplectic systems

A multi-symplectic system is a PDE with a Hamiltonian structure in both temporal and spatial variables. This article considers spatially periodic perturbations of symmetric multi-symplectic systems. Due to their structure, unperturbed multi-symplectic systems often have families of solitary waves or front solutions, which together with the additional symmetries lead to large invariant manifolds. Periodic perturbations break the translational symmetry in space and might break some of the other symmetries as well. In this article, periodic perturbations of a translation invariant PDE with a one-dimensional symmetry group are considered. It is assumed that the unperturbed PDE has a three-dimensional invariant manifold associated with a solitary wave or front connection of multi-symplectic relative equilibria. Using the momentum associated with the symmetry group, sufficient conditions for the persistence of invariant manifolds and their transversal intersection are derived. In the equivariant case, invariance of the momentum under the perturbation gives the persistence of the full three-dimensional manifold. In this case, there is also a weaker condition for the persistence of a two-dimensional submanifold with a selected value of the momentum. In the non-equivariant case, the condition leads to the persistence of a one-dimensional submanifold with a seleceted value of the momentum and a selected action of the symmetry group. These results are applicable to general Hamiltonian systems with double zero eigenvalue in the linearization due to continuous symmetry. The conditions are illustrated on the example of the defocussing non-linear Schrödinger equations with perturbations which illustrate the three cases. The perturbations are: an equivariant Hamiltonian perturbation which keeps the momentum level sets invariant; an equivariant damped, driven perturbation; and a perturbation which breaks the rotational symmetry.     

铝合金厚板拉伸过程横向残余应力消减分析

运用Marc有限元软件对厚板预拉伸过程进行模拟分析,获得厚板沿厚度纵、横两个方向应力分布.结合仿真和实验,阐述了拉伸过程中横向应力削减现象,同时,将横向与纵向应力削减效果进行分析,论述了厚板横向残余应力演变的机理.分析认为,高强度残余应力使材料处在高弹性势能状态,在外力触发下有利于破坏晶粒横向平衡,从而改变了晶粒间原有应力平衡状态,实现横向应力逐层削弱.     

管内流体交变流动速度的横向分布研究

基于线性理论分析,考虑流体的可压缩性、速度横向分布的相位延迟,对微扰项使用Fourier变换,给出充分发展、层流交变流动管内速度分布解析解.给出的解析解适用于描述各种小振幅振型的振荡,体现出流体速度横向分布的相位延迟,并验证了交变流动状态下的"环形效应".关于流体速度横向分布的解析解给出了流体在谐振状态下的速度分布函数,与肖家华在热声研究中使用常规摄动分析方法假设微扰项以单一频率振荡条件下得到的解析解一致.分析了可压缩流体和不可压缩流体在理论模型上的区别.