周期背景下怪波的激发和调制

为了研究怪波在周期背景中的激发和演化情况,以含有周期外势的自聚焦非线性薛定谔方程为模型,采用快速分步傅里叶算法,讨论了在两种周期势(实势和复势)的情况下,怪波的激发和演化情况.研究表明:在两种周期势背景下都能通过平面波加微扰来激发怪波;在实周期背景下,通过改变周期势的振幅和周期能够产生不同的光学现象;在复周期背景下,通过同样的初始波能够激发一种超大怪波,而且实部振幅对怪波具有能量耗散和减速作用,虚部振幅对怪波具有能量增益和加速作用,选择合适的实部振幅与虚部振幅可以产生强度不同的大怪波.研究结果有助于在光晶格中捕获和调节怪波,以及获得高功率波.     

水波在周期性钻孔底部结构中的传播及其能带

采用平面波展开法计算了浅水表面波在底部按周期性钻孔结构下的能带,找到了完全带隙的出现.通过考虑方形孔按正方晶格排列、圆形孔按正方晶格和六角晶格排列等三种钻孔模型,发现带隙的数量、宽度、频率、位置与孔的面积、形状、方位角及其排列晶格等都有关.且这些规律与光子/声子晶体的情况相类似. 关键词： 周期性 水波 能带 带隙     

苯的“自由电子模型”的能级和波函数

通过解Mathieu方程得出了“自由电子模型”的能级和波函数 ,其解比用微扰法得出的结果更精确。结果表明 ,微扰势只使那些级数为n =3k(k =1,2 ,3… )的能级发生分裂 ,简并消除     

纳米晶体线的热膨胀性质

将原子间相互作用势的非谐项作为微扰,运用声子数表象中的晶格原子振动位移和晶格振动哈密顿公式,推导了纳米晶体线的热膨胀系数公式,并进行了数值计算.研究结果表明,纳米晶体线越细,其热膨胀系数越大.     

不同晶格光子晶体异质结的界面传导模

利用平面波展开方法与超原胞方法研究了两种不同晶格的光子晶体异质结的界面态. 这两种异质结都是在纯电介质背景上放置空气散射子. 一种异质结由正方形格子上放置正方形散射子和三角形格子上放置六角形散射子组成（SSTH异质结）. 另一种由长方格子上放置长方形散射子和三角形格子上放置圆形散射子组成（RRTC异质结）. 对于SSTH异质结，当沿着界面作晶格的横向拉开或者侧向滑移，都可产生界面态. 而对于RRTC异质结，无需从界面做晶格拉开或者侧向滑移就可产生界面传导模，这个结果有别于其他纯电介质光子晶体异质结的性质. 关键词： 光子晶体 异质结 传导模 超原胞     

晶体电子在外场作用下的Bloch振荡和散射对电流的影响

通过对晶体周期势场中电子在直流外场作用下的Ｂｉｏｃｈ振荡的分析，指出晶体在外场作用下的电流是由于电子受到散射的结果；没有散射作用，电子在外场作用下的运动为Ｂｌｏｃｈ振荡，不产生电流。     

半径位置微扰对于不同光子晶体波导结构的影响

本文理论上分析了不同程度的位置半径微扰分别对于二维三角晶格不同空气孔形状的光子晶体波导结构透射率性能的影响。主要关注三个区域,低频带隙边缘,高频带隙边缘以及导模交叉点;三种空气孔形状,圆形,方形,椭圆形。仿真结果显示微扰对于交叉点影响最为严重。随着微扰程度变大,高低频边缘平坦的透射率区域逐渐变窄。相同形状相同微扰程度下,透射率对位置微扰更加敏感。不同形状比较发现,慢光区域正方空气孔对于位置微扰更稳健,圆形空气孔对于半径微扰更稳健。这对于光子晶体制作和实验过程中不可避免的位置和半径的随机微扰具有理论指导意义。     

固体的光散射讲座第三讲 晶格振动的喇曼散射

晶体的喇曼散射是研究晶体内部结构的一种简单而有效的成熟方法.它对研究材料的结构和结构相变以及各种特殊条件下的晶体状态有着重要的作用.本文先从晶体的对称性出发,讨论晶格振动的分类,并以k=0处的晶格振动为例,介绍晶格振动模的对称类的分类.然后简述晶体喇曼散射的机理以及对晶体喇曼谱的实验研究. 一、晶体的对称性 我们知道,分子具有一定的点对称性,即保持体系中一点位置不变,对体系施以转动、反射或反演等(点)对称操作,体系仍处于与操作前等效的状态.晶体不仅也具有这种点对称性,而且由于其中原子排列的周期性,晶体还具有平移对称…     

一维非厄密光子晶格中分叉可调无衍射光传输

理论计算和数值模拟了一维周期性复式光子晶格中光的分叉无衍射传输现象.当晶格满足退化的SSH模型时,波矢为±π的入射光将分裂为两束完全相同的对称无衍射光,且分叉夹角可通过耦合系数J来调节;在此基础上,通过微扰波导作用引入了调制相位?,当微扰满足宇称时间对称时,只要入射光波矢k与调制相位?之和为±π便能实现任意入射光波的无...     

量子受限效应和对称性效应对硅光子晶体禁带的影响

光子晶体不仅可以用来调控自发辐射, 还可以用来控制光的传输和局域. 采用平面波展开法进行模拟计算, 分析硅背景下的二维正方、三角晶格光子晶体散射基元的形状和空间取向对光子禁带的影响. 计算结果表明: 对称性和量子受限效应之间的竞争是导致光子晶体禁带宽度发生变化的原因.     

Nonlinear scattering in BaTiO3 induced by two orthogonally polarized waves

A new nonlinear scattering effect is described which is induced by the simultaneous action of ordinary and extraordinary waves impigning on a BaTiO₃ crystal in the plane perpendicular to the c-axis. The scattered light of ordinary polarization propagates along a circular cone and the light intensity on this cone is nonuniform. We present a model that describes the experimental observations rather well, including phase matching conditions and the unusual intensity distribution of the scattered light.     

COUPLED WAVES ON A PERIODICALLY SUPPORTED TIMOSHENKO BEAM

A mathematical model is presented for the propagation of structural waves on an infinitely long, periodically supported Timoshenko beam. The wave types that can exist on the beam are bending waves with displacements in the horizontal and vertical directions, compressional waves and torsional waves. These waves are affected by the periodic supports in two ways: their dispersion relation spectra show passing and stopping bands, and coupling of the different wave types tends to occur. The model in this paper could represent a railway track where the beam represents the rail and an appropriately chosen support type represents the pad/sleeper/ballast system of a railway track. Hamilton's principle is used to calculate the Green function matrix of the free Timoshenko beam without supports. The supports are incorporated into the model by combining the Green function matrix with the superposition principle. Bloch's theorem is applied to describe the periodicity of the supports. This leads to polynomials with several solutions for the Bloch wave number. These solutions are obtained numerically for different combinations of wave types. Two support types are examined in detail: mass supports and spring supports. More complex support types, such as mass/spring systems, can be incorporated easily into the model.     

Ponderomotive effects in intense pumping wave action on electron and plasma bunches

Ponderomotive effects that arise when an intense plane pumping wave acts on low-concentration electron and plasma bunches are theoretically studied within the framework of a one-dimensional model. Using the Lagrange variables, an electron (plasma) bunch under the action of a pumping field can be represented as a gas comprising macroparticles with ponderomotive and Coulomb interactions. The ponderomotive force at small interparticle distances is attractive, that is, directed oppositely to the Coulomb force; it cannot, however, completely balance the latter. The constructed model is used to study superradiance, which arises when an intense pumping wave acts on an extended electron bunch. Radiation is then scattered in the form of narrow pulses whose amplitude is proportional to the total number of particles in the bunch. In addition, we describe acceleration of a neutral plasma layer, narrow on the wavelength scale, in the field of an intense wave and radiation field-induced partial contraction of an electron bunch with an incompletely compensated charge.     

Parametric scattering of high-frequency elastic waves by a small spherical cavity oscillating under the action of a Rayleigh wave

Scattering of high-frequency transverse and longitudinal plane waves incident on a spherical cavity located at a small depth under the surface of a half-space is considered. The cavity oscillates as a whole in the field of a low-frequency Rayleigh surface wave, the oscillation vectors of the longitudinal, transverse, and surface waves being coplanar. The cavity radius is assumed to be small compared to the wavelengths of the sounding wave and the pumping surface wave. The scattered compression and shear waves at the combination frequencies ω±Ω are calculated in the dipole approximation. Expressions obtained describe the qualitative behavior of the combination-frequency signal levels produced at the outputs of horizontally and vertically oriented geophones moving over the free surface of the elastic half-space.     

Three-dimensional elastic wave scattering by a layer containing vertical periodic fractures

Elastic wave scattering off a layer containing a single set of vertical periodic fractures is examined using a numerical technique based on the work of Hennion et al. [J. Acoust. Soc. Am. 87, 1861-1870 (1990)]. This technique combines the finite element method and plane wave method to simulate three-dimensional scattering off a two-dimensional fractured layer structure. Each fracture is modeled explicitly, so that the model can simulate both discrete arrivals of scattered waves from individual fractures and multiply scattered waves between the fractures. Using this technique, we examine changes in scattering characteristics of plane elastic waves as a function of wave frequency, angle of incidence, and fracture properties such as fracture stiffness, height, and regular and irregular spacing.     

Electroacoustic waves confined by a moving domain wall superlattice of a ferroelectric crystal

The dispersion properties of electroacoustic wave modes confined by a superlattice of uniformly moving 180° domain walls in a tetragonal ferroelectric crystal are considered. It is shown that the manifold of partial electroacoustic interfacial waves in the lattice is restricted to the first allowed band, the configuration of which in the plane of spectral variables can significantly vary under the action of the moving domain walls.     

Surface excitation of hypersound in piezoelectric crystals by plane electromagnetic waves

The generation of hypersound at a free surface of a piezoelectric crystal by means of an incident plane electromagnetic wave is considered and the corresponding boundary problem is discussed in detail. The formula developed in this paper are quite general and can be applied to any piezoelectric crystal and any face orientation. As an important example, the excitation of sound waves at several quartz faces is treated numerically and the results are presented in diagrams showing directly the power conversion from the plane incident electromagnetic wave into the sound waves as function of the angle of incidence and of polarization directions.     

Approximations for modal coupling in scattered fields from orifices

Previous investigations have used Hankel transforms to establish the velocity potentials of the wave fields resulting from arbitrary angle plane wave impingement on a circular orifice in a rigid, thick wall. The scattered field from the orifice is examined, in particular the modal contributions to the amplitude of its velocity potential. For each m,n mode the amplitude is dependent upon the amplitude of the in-orifice waves and a driving term unique to each m,n mode. In establishing the amplitudes of the in-orifice waves, the effects of modal coupling are also considered. In this work these two components of the scattered wave amplitude are investigated on a modal basis and approximations given for coupling effects. These approximations are then used to calculate the scattered field and the results compared with conventional solutions that use full modal coupling.     

Near-field ultrasound tomography

In this paper, a near-field tomographic solution is introduced to solve the imaging problem of fluid objects assumed to be weakly heterogeneous (Born approximation) and excited by spherical waves. The solution to the forward problem is based on the Huygens-Fresnel principle which describes the scattered field as the result of the interference scheme of all the secondary spherical waves. From the derivation of the scattered field, a new Fourier transform that has been called the elliptical Fourier transform is defined: It differs from the standard Fourier transform in that instead of a plane wave decomposition, a harmonic ellipsoidal wave decomposition is obtained. Based on this spectral analysis, a near-field Radon transform is designed that complements the "far-field tools" published in diffraction tomography literature. Then, assuming that the measuring distance is greater than one wavelength, the feasibility of reconstructing either the impedance or the velocity maps of an acoustical (perfect fluid) model is demonstrated. Numerical simulations were performed which confirmed the validity of the theory presented here; a theory which has many potential applications in future wave theory research.     

The effect of impedance boundary conditions on the potential function of the boundary diffraction wave theory

A novel potential function of the boundary diffraction wave theory is obtained for the impedance surfaces by the asymptotic reduction of the modified theory of physical integrals. The function is expressed in terms of the direction vectors of the incident and scattered rays. The application of the method is performed on the problem of diffraction of plane waves by an impedance half plane for oblique incidence.