Leaky modes in optical waveguides

Solutions of the scalar wave equation are presented giving, explicitly, the excitation and subsequent attenuation of leaky modes in optical waveguides.     

套管井声场合成波形及其时频特征分析

数值计算了点声源激励下套管井声场的声压波形。计算模型包括了实际中所有的三类岩石及两个界面的各种胶结情况,声源频率采用实际的测井频率。对合成波形进行了基于Wigner-Ville分布的时频分析。计算和分析结果说明,波列中的套管波、伪瑞利波在一、二界面不同的胶结情况下有明显的变化规律。二界面未胶结时,套管波模式的时频分布随管外水泥层厚度的变化而变化。它们与地层体波成分的特征可作为管外水泥胶结质量评价的重要依据;而中速地层时地层体波能量最强,有利于胶结质量评价。     

套管井中偏心对声场的影响分析*

目前在油田的实际应用中,声幅-变密度水泥胶结测井(CBL/VDL)在套管井的水泥胶结质量评价中发挥重要作用。但是,在一些大斜度井或者水平井中,往往由于仪器或者套管的重量等原因导致套管井中出现偏心现象,这给利用声波测井资料进行水泥胶结质量评价带来一些难题。为此,本文建立了套管偏心和仪器偏心两种情况下的三维声学模型,利用柱坐标系下的三维交错网格有限差分算法数值模拟了两种偏心情况下的声波传播情况,并着重研究了偏心率的变化对套管井中声场波形特征,尤其是套管波及地层波特征的影响。另外,模拟了具有不同外径尺寸的套管和偏心率的组合情况下的声场传播情况,在此基础上研究了偏心率的大小对声场特征的影响规律。本文的研究结果表明,套管偏心和仪器偏心均会给声场波形特征带来影响,且随着偏心率的增加而增大;相比较而言,仪器偏心对套管波的影响更大。     

Leaky modes and directed modes in confined one-dimensional photonic crystal

Directed modes and leaky modes in a confined one-dimensional photonic crystal are analytically described. The dispersion relation of these modes is written as the transverse resonance condition of Floquet-Bloch waves, taking into account phase shifts at interfaces with adjacent media.     

Leaky modes of channel waveguides with uniaxial anisotropy

An exact numerical method for analyzing the propagation properties of leaky modes of inhomogeneous channel optical waveguides with a complex uniaxial diagonal permittivity tensor is developed. The method is based on solving the system of integro-differential equations formulated with respect to transversal components of the magnetic field and the longitudinal component of the electric field. Some results of investigation of leaky modes of diffused channel waveguides in LiNbO₃ and LiTaO₃ crystals are given.     

Leaky modes in twisted microstructured optical fibers

The purpose of this paper is to investigate the effect of a twist on the losses of leaky modes in microstructured optical fibers (MOF). A helicoidal system of coordinates is introduced to define the structure and to set up the problem. These coordinates, albeit non-orthogonal, preserve the translational invariance in a way that allows a two-dimensional finite element model similar to that of classical straight waveguides. The Perfectly Matched Layer (PML) technique is used to compute the leaky modes in the fibers. Helicoidal coordinates and PML are unified under the point of view of geometrical transformations which allows the design of 'twisted PML' that provides the right tool to determine the leaky modes in the twisted structures.     

套管井超声导波成像系统开发与工程应用研究

针对现有套管井检测与评价技术存在的缺陷,开展了进一步的导波成像方法与技术开发研究。对套管壁A0导波模式频散与泄漏衰减特性,以及泄漏衰减特性与管外粘结材料特性阻抗的关系进行了分析。在此基础上进行了不同粘结载荷钢板模型A0模泄漏衰减等特性以及脉冲回波厚度共振波特性的实验测试。结果显示,结合A0模式的衰减与管外粘结材料特性阻抗的测试结果,可有效定征管外粘结材料特性,进一步确定和成像管外环形空间水力联通特性。以此为基础,开发了耐温和耐压宽带超声换能器,以及检测与成像系统。通过模型井和实际井的测试,获得良好效果。     

Acoustic mode waves and individual arrivals excited by a dipole source in fluid-filled boreholes

An approach of separating individual wave arrivals for a dipole logging is presented. The branch points are treated as a type of logarithm and the Riemann surface structure of the multivalued function is studied, that is, the displacement potential within the borehole. Based on the theoretical analysis, the complex poles contributing to the wave field on various Riemann sheets are investigated in detail for the case of a fast formation. It is shown that poles on Riemann sheet (0,0) are real and form branches of modes with dispersion. Mathematically, it is demonstrated that the flexural mode has no cutoff frequency, which is different from the traditional point of view. Poles on other relevant Riemann sheets are complex and form many branches on the complex frequency-wavenumber plane. Further investigation on the pole and branch cut contributions indicates that the vertical branch cut integration method has limitations in separating wave arrivals. By properly taking into account the complex poles on various Riemann sheets together with branch cut integrations, wave arrivals are separated from the full waveforms effectively for both the fast and slow formation models. Specially, there are complex poles on Riemann sheet (0,−1) in the vicinity of the compressional branch cut for a slow formation with a large Poisson’s ratio, which have small imaginary parts and contribute a lot to the p-wave arrival. Supported by the National Natural Science Foundation of China (Grant No. 10534040)     

Leaky modes and their contributions to the compressional head wave in a borehole excited by a dipole source

A method of studying the contributions of leaky modes to the wave field is presented based on the analysis of the Riemann surface structure of the characteristic function, and the sensitivities of con- tributions to various factors of interest are examimed. Numerical results show that their contributions to the compressional head wave are related to the distributions of complex poles on (-1, -1) and (0, -1) Riemann sheets on the frequency-wavenumber (ω - k) plane. For fast formations, their contributions ar...     

Sound modes in a nonequilibrium fluid with acoustic boundary conditions

The sound modes in a plane fluid layer with sound-absorbing walls at different temperatures are evaluated. The eigenvalue problem is solved by means of a singular perturbation theory and the WKB method. The bending of sound, the nonexponential damping, and the roie of the wall admittance are discussed.     

Propagation behaviors of thickness-twist modes in an inhomogeneous piezoelectric plate with two imperfectly bonded interfaces

The thickness-twist modes in an inhomogeneous piezoelectric plate with two imperfectly bonded interfaces are analyzed, and an exact solution is obtained according to the spring-type relation from the equations of the linear theory of piezoelectricity. The frequency shift, the displacement and the stress components are all obtained and plotted. Both theoretical analysis and numerical examples show that the effect of mechanical imperfection is more evident than that of the electrical imperfection on the thickness-twist modes. Results show that the displacement and the stress components all change obviously due to the imperfectly bonded interfaces. The relationship between the frequency shift Δω and the non-dimensional number γ that is related to the imperfect interfaces is linear, which can be used to provide the foundation for a new experimental procedure for measuring the level of the interface bonding.     

套管井体胶结状态对井孔中声传播的影响

从波动方程出发,利用匹配边界条件,木文推导出套管井中由单极子和多极子声源激发的井内声场定解表达式及相应的导波色散方程.利用实轴积分法和快速傅里叶交换数值方法,具体计算了套管井中不同胶结情况时由单极子声源和偶极子声源激发的井轴上不同源距处的全波列波形。结合套管井中的轴对称导波模式,分析了胶结状况对套管井中单极子和偶极子声源激发的声场的影响.研究结果表明:仅利用普通单极子声源或偶极子声源进行套管井测井,难以区分出套管胶结良好、套管与水泥为滑移胶结和自由套管情况三种不同的胶结情况;只有把普通单极子声源测井与偶极子声源测井结合起来,才有可能准确评价套管的胶结情况。     

Zero modes,boundary conditions and anomalies on the lattice and in the continuum

We examine the connection, and occasional lack of it, between zero modes and anomalies in lattice and continuum models. In particular we discuss the index theorem for the polyacetylene problem and for two-dimensional Kogut-Susskind/Kähler-Dirac fermions, paying special attention to boundary effects which may be important in simulations on small lattices.     

Multi-chimera states and transitions in the Leaky Integrate-and-Fire model with nonlocal and hierarchical connectivity

The effects of nonlocal and fractal connectivity are investigated in a network of Leaky Integrate-and-Fire (LIF) elements. The idea of fractal coupling originates from the hierarchical topology of networks formed by neuronal axons, which transmit the electrical signals in the brain. If a number of LIF elements with finite refractory period are nonlocally coupled, multi-chimera states emerge whose multiplicity depends both on the coupling strength and on the refractory period. We provide evidence that the introduction of a hierarchical topology in the coupling induces novel complex spatial and temporal structures, such as nested chimera states and transitions between multi-chimera states with different multiplicities. These results demonstrate new complex patterns, as well as transitions between different multi-chimera states arising from the combination of nonlinear dynamics with the hierarchical coupling.     

带扇形窜槽的套管井声场

首次使用2.5维的有限差分算法对带窜槽的套管井声场进行了数值研究,计算得到了带有不同大小窜槽套管井的声场展开图及井轴上不同源距的接收波列。本文还应用2维谱的方法对带窜槽的套管井声场进行了分析研究。发现窜槽的存在影响了纵波头波的速度,其大小决定纵波头波的幅度。并且只有当窜槽形成角度大于30°时,才能从接收波列中被鉴别。     

对硬币在不同环境下转动的分析

本文推导了硬币在不同环境下的基本运动方程,分析了硬币的绕圈运动问题,并利用其结果讨论了两种特殊的运动模式,最后用计算机模拟的方法进行了验证.     

Normalization of interface optical phonon modes in cylindrical quantum wires with semiconductor-semiconductor and metal-semiconductor boundary conditions

In this work, analytical solutions for the interface longitudinal optical (LO) phonons in cylindrical polar-semiconductor quantum wires are normalized by the standard quantization condition. Two cases are considered: polar-semiconductor quantum wires encapsulated in another polar-semiconductor and polar-semiconductor quantum wires encapsulated in metal. For the case of metal encapsulation it is demonstrated that unwanted inelastic interface LO phonon scattering is eliminated since the interface modes do not satisfy the appropriate boundary conditions.     

椭圆包层光纤场的迭代近似解与漏模损耗计算

试图理论上处理椭圆包层各向异性光纤复杂的折射率分布。数学过程包括折射率分布的级数展开、δ－涵数的导数和积分以及用格林函数求解方程的迭代技术。给出了椭圆包层各向异性光纤漏模损耗的解析表达式。数值结果表明椭圆包层各向异性光纤的漏模损耗比领结型光纤小，比阶跃型各向异性光纤大；偏心率越大越有利于制造单模单偏光纤。