The complex Jacobi iterative method for non-paraxial beam propagation in nonlinear optical waveguides

The recently introduced beam propagation method using complex Jacobi iteration adapted for modeling of non-paraxial beam propagation in nonlinear optical waveguides is presented in this paper. The beam propagation equation is based on our recently proposed modified Padé(1,1) approximant operator. The resulting approach is very efficient and well-suited for large structures with long propagation paths.     

Three-dimensional coupled-mode model and characteristics of low-frequency sound propagation in ocean waveguide with seamount topography

Large-scale topography, such as a seamount, substantially impacts low-frequency sound propagation in an ocean waveguide, limiting the application of low-frequency acoustic detecting techniques. A three-dimensional (3D) coupled-mode model is developed to calculate the acoustic field in an ocean waveguide with seamount topography and analyze the 3D effect. In this model, a correction is introduced in the bottom boundary, theoretically making the acoustic field satisfy the energy conservation. Furthermore, a large azimuth angle calculation range is obtained by using the operator theory and higher-order Padé approximation. Additionally, the model has advantages related to the coupling mode and parabolic equation theory. The couplings corresponding to the effects of range-dependent environment are fully considered, and the numerical implementation is kept feasible. After verifying the accuracy and reliability of the model, low-frequency sound propagation characteristics in the seamount environment are analyzed. The results indicate lateral variability in bathymetry can lead to out-of-plane effects such as the horizontal refraction phenomenon, while the coupling effect tends to restore the abnormal sound field and produces acoustic field diffraction behind the seamount. This model effectively considers the effects of the horizontal refraction and coupling, which are proportional to the scale of the seamount.     

海洋波导中目标声辐射场的计算方法

针对海洋波导中目标声辐射场的计算问题,提出了一种基于波叠加法并在近、远场采用不同水声传播模型的建模方法,可以将近、远场作为一个统一的系统进行高效地分析。该方法通过给定的已知表面振动速度的结构计算出目标内部虚拟点声源的源强,再配合在相应的水声环境中点声源传播模型的Green函数计算出结构外的声辐射场。以Green函数为纽带,在求源强和计算近场声辐射场时采用镜像虚源法,而在计算远场声辐射场时采用简正波法。通过该方法得到的有限水深波导中声速剖面为正梯度、负梯度、负跃层的3种情况下的脉动球、刚体摆动球的声辐射场计算结果与COMSOL的有限元计算结果进行对比,结果表明了该方法在提高计算效率的同时保证了计算精度。      

Non-paraxial Split-step Finite-difference Method for Beam Propagation

A method based on symmetrized splitting of the propagation operator in the finite difference scheme for non-paraxial beam propagation is presented. The formulation allows the solution of the second order scalar wave equation without having to make the slowly varying envelope and one-way propagation approximations. The method is highly accurate and numerically efficient. Unlike most Padé approximant based methods, it is non-iterative in nature and requires less computation. The method can be used for bi-directional propagation as well.     

一种水平变化波导中声传播问题的耦合模态法

针对介质参数及海底边界水平变化波导中的声传播问题,本文基于多模态导纳法提出一种能量守恒且便于数值稳定求解的耦合模态方法.将声压表示为一组正交完备的本地本征函数之和,对声压满足的Helmholtz方程在本地本征函数上作投影,推导出关于声压模态系数的二阶耦合模态方程组.耦合矩阵直观描述水平变化因素对模态耦合的贡献.为避免直接求解二阶耦合模态方程组可能遇到的数值发散问题,将其重构为两个耦合的一阶演化方程组,引入导纳矩阵并使用Magnus数值积分方法获得稳定的声场解.利用该耦合模态方法数值计算水平变化波导中的声场,并与COMSOL参考解比较,结果表明该耦合模态理论能够精确求解水平变化波导中的点源及分布源传播问题.     

沉积物中声速和衰减系数的宽带测量方法

海底沉积物作为海洋波导声传播的下边界普遍存在于大洋中,获知其特性对于准确的声传播和混响建模是十分必要的。为了能够快速而准确地测量沉积物中的声速和衰减系数,提出一种基于脉冲压缩技术的测量方法,对接收信号进行压缩来提取透射波,根据不同厚度样品的透射波来计算沉积物中的声速和衰减系数。该方法不仅可以克服实验过程中经常遇到的多途干扰,而且测量过程简单,可以同时获得测量频带内所有频点的声速和衰减系数,即实现了对声速和衰减系数的宽带测量。在实验室环境条件下,90~170kHz的测量频带内,测得沙样品中的声速为1710~1713m/s,衰减系数在56~70dB/m之间。通过窄带和宽带测量结果的比较可以看出,声速的宽带测量结果与窄带测量结果吻合得较好,而衰减系数在频带后半部分存在较大的起伏。      

采用小生境遗传算法反演浅海声速剖面研究*

针对浅海声速剖面反演问题,采用小生境遗传算法,结合声线搜索的最快本征声线匹配反演,实现浅海负跃层条件下的声速剖面估计。利用经验正交函数对声速剖面的多参数不确定性降维,依据声场计算模型获取的最快特征声线传播时延与观测声传播时长进行匹配,采用小生境遗传优化算法,获取最优经验正交函数估计,实现声速剖面反演。按上述方法反演处理浅海声传播实验数据,结果表明,该方法针能够有效反演浅海声速剖面,并且显著优于传统遗传算法反演结果。     

The contribution of a lateral wave in simulating low-frequency sound fields in an irregular waveguide with a liquid bottom

A further development of a previously proposed approach to calculating the sound field in an arbitrarily irregular ocean is presented. The approach is based on solving the first-order causal mode equations, which are equivalent to the boundary-value problem for acoustic wave equations in terms of the cross-section method. For the mode functions depending on the horizontal coordinate, additional terms are introduced in the cross-section equations to allow for the multilayer structure of the medium. A numerical solution to the causal equations is sought using the fundamental matrix equation. For the modes of the discrete spectrum and two fixed low frequencies, calculations are performed for an irregular two-layer waveguide model with fluid sediments, which is close to the actual conditions of low-frequency sound propagation in the coastal zone of the oceanic shelf. The calculated propagation loss curves are used as an example for comparison with results that can be obtained for the given waveguide model with the use of adiabatic and one-way propagation approximations.     

Simulation of low-frequency sound propagation in an irregular shallow-water waveguide with a fluid bottom

A further development of a previously proposed approach to calculating the sound field in an arbitrarily irregular ocean is presented. The approach is based on solving the first-order causal mode equations, which are equivalent to the boundary-value problem for acoustic wave equations in terms of the cross-section method. For the mode functions depending on the horizontal coordinate, additional terms are introduced in the cross-section equations to allow for the multilayer structure of the medium. A numerical solution to the causal equations is sought using the fundamental matrix equation. For the modes of the discrete spectrum and two fixed low frequencies, calculations are performed for an irregular two-layer waveguide model with fluid sediments, which is close to the actual conditions of low-frequency sound propagation in the coastal zone of the oceanic shelf. The calculated propagation loss curves are used as an example for comparison with results that can be obtained for the given waveguide model with the use of adiabatic and one-way propagation approximations.     

Computer modeling of sound fields in the ocean with fine-structured inhomogeneities

The results of a computer modeling of sound propagation in the ocean with fine-structured inhomogeneities are presented. The modeling was performed using a wave code based on the wide-angle approximation, which allows one to estimate the effects of sound field perturbations. These effects include the insonification of the geometric shadow zones and the abnormal attenuation of low-frequency sound in the course of its propagation in an oceanic waveguide. Calculations clearly demonstrate that the fine-structured inhomogeneities of the sound velocity considerably affect the sound propagation in the ocean.     

匹配垂直质点振速的浅海地声参数反演

海底声学参数对海洋波导中的声场特性研究和相关应用具有重要意义。针对一次夏季黄海声传播实验,分析了浅海负跃层环境下垂直质点振速的传播特性和简正波结构,说明当声源和接收器均位于负跃层下时,除海底附近外的大部分深度上垂直质点振速能量较高,且与声压相比,号数高的简正波对垂直质点振速的贡献更大,利用垂直质点振速进行匹配场反演能获得更高的海底参数敏感性。分析了海底吸收系数对垂直质点振速匹配场反演的影响,结果表明只有当进行匹配场反演时设置的海底吸收系数接近真实值时,才能获得准确的海底声速、密度和海深反演结果。利用实验中矢量水听器获取的垂直质点振速信号进行匹配场反演,将海底吸收系数在变化范围内取不同值对海底声速、密度和平均海深进行全局搜索,根据代价函数值最大确定了海底声速、密度及平均海深的反演结果,并利用不同距离上的声压传播损失反演出不同频率下的海底吸收系数。根据反演得到的海底声学参数计算声压传播损失,与实验中声压水听器测量结果符合较好。     

一种水平变化可穿透波导中声传播问题的耦合简正波方法

通过利用标准简正波程序KRAKEN计算本地简正波解及耦合矩阵, 进一步发展了求解水平变化波导中声场的全局矩阵耦合简正波方法(Luo et al., "A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides," Sci. China-Phys. Mech. Astron. 55, 572 (2012)), 使得该方法可以处理具有可穿透海底及随深度变化声速剖面等实际问题, 并提供声场的完全双向解. 本文还给出了双层波导中耦合矩阵的解析表达式, 并利用其验证了本方法中耦合矩阵数值算法的精度. 最后, 利用改善后的全局矩阵耦合简正波模型(DGMCM)计算了美国声学学会(ASA)提出的可穿透楔形波导标准问题, 将所得数值解与参考解比较, 结果表明DGMCM方法可以精确处理水平变化波导中声传播实际问题. 关键词： 耦合简正波理论 全局矩阵方法 可穿透楔形波导     

Acoustic-gravity waves in atmospheric and oceanic waveguides

A theory of guided propagation of sound in layered, moving fluids is extended to include acoustic-gravity waves (AGWs) in waveguides with piecewise continuous parameters. The orthogonality of AGW normal modes is established in moving and motionless media. A perturbation theory is developed to quantify the relative significance of the gravity and fluid compressibility as well as sensitivity of the normal modes to variations in sound speed, flow velocity, and density profiles and in boundary conditions. Phase and group speeds of the normal modes are found to have certain universal properties which are valid for waveguides with arbitrary stratification. The Lamb wave is shown to be the only AGW normal mode that can propagate without dispersion in a layered medium.     

Stability and a fast calculation method of travel speed of pulse peak in convergence zone

A long-range sound propagation experiment was conducted in the West Pacific Ocean in summer 2013.The signals received by a towed array indicate that the travel speed of pulse peak(TSPP)in the convergence zones is stable.Therefore,an equivalent sound speed can be used at all ranges in the convergence zones.A fast calculation method based on the beam-displace-ment ray-mode(BDRM)theory and convergence zone theory is proposed to calculate this equivalent sound speed.The computation speed of this proposed method is over 1000 times faster than that of the conventional calculation method based on the normal mode theory,with the computation error less than 0.4%compared with the experimental result.Also,the effect of frequency and sound speed profile on the TSPP is studied with the conventional and fast calculation methods,showing that the TSPP is almost independent of the frequency and sound speed profile in the ocean surface layer.     

Sound propagation in inhomogeneous waveguides with sound-speed profiles using the multimodal admittance method

The multimodal admittance method and its improvement are presented to deal with various aspects in underwater acoustics, mostly for the sound propagation in inhomogeneous waveguides with sound-speed profiles, arbitrary-shaped liquid-like scatterers, and range-dependent environments. In all cases, the propagation problem governed by the Helmholtz equation is transformed into initial value problems of two coupled first-order evolution equations with respect to the modal components of field quantities(sound pressure and its derivative), by projecting the Helmholtz equation on a constructed orthogonal and complete local basis. The admittance matrix, which is the modal representation of Direchlet-to-Neumann operator, is introduced to compute the first-order evolution equations with no numerical instability caused by evanescent modes. The fourth-order Magnus scheme is used for the numerical integration of differential equations in the numerical implementation. The numerical experiments of sound field in underwater inhomogeneous waveguides generated by point sources are performed. Besides, the numerical results computed by simulation software COMSOL Multiphysics are given to validate the correction of the multimodal admittance method. It is shown that the multimodal admittance method is an efficient and stable numerical method to solve the wave propagation problem in inhomogeneous underwater waveguides with sound-speed profiles, liquid-like scatterers, and range-dependent environments. The extension of the method to more complicated waveguides such as horizontally stratified waveguides is available.     

Efficient beam-propagation method based on Padé approximants in the propagation direction

We propose a novel beam-propagation method (BPM) based on the higher-order Padé approximants in both the transverse and the longitudinal directions. Extending the Padé approximation to the propagation direction and adopting the multistep method increase the programming effort by only a small amount. Compared with the conventional BPM's, this method is more accurate and efficient. The accuracy and the propagation step size are well predicted by a phase analysis.     

Sound propagation and scattering in media with random inhomogeneities of sound speed, density and medium velocity

This review presents both classical and new results of the theory of sound propagation in media with random inhomogeneities of sound speed, density and medium velocity (mainly in the atmosphere and ocean). An equation for a sound wave in a moving inhomogeneous medium is presented, which has a wider range of applicability than those used before. Starting from this equation, the statistical characteristics of the sound field in a moving random medium are calculated using Born-approximation, ray, Rytov and parabolic-equation methods, and the theory of multiple scattering. The results obtained show, in particular, that certain equations previously widely used in the theory of sound propagation in moving random media must now be revised. The theory presented can be used not only to calculate the statistical characteristics of sound waves in the turbulent atmosphere or ocean but also to solve inverse problems and develop new remote-sensing methods. A number of practical problems of sound propagation in moving random media are listed and the further development of this field of acoustics is considered.     

An effective quiescent medium for sound propagating through an inhomogeneous,moving fluid

The idea of similarity between acoustic fields in a moving fluid and in a certain "effective" quiescent medium, first put forward by Lord Rayleigh, proved very helpful in understanding and modeling sound propagation in an atmosphere with winds and in an ocean with currents, as well as in other applications involving flows with small velocity compared to sound speed. Known as effective sound speed approximation, the idea is routinely utilized in the contexts of the ray theory, normal mode representation of the sound field, and the parabolic approximation. Despite the wide use of the concept of effective sound speed in acoustics of moving media, no theoretical justification of Rayleigh's idea was published that would be independent of the chosen representation of the sound field and uniformly apply to distinct propagation regimes. In this paper, we present such a justification by reducing boundary conditions and a wave equation governing sound fields in the inhomogeneous moving fluid with a slow flow to boundary conditions and a wave equation in a quiescent fluid with effective sound speed and density. The derivation provides insight into validity conditions of the concept of effective quiescent fluid. Introduction of effective density in conjunction with effective sound speed is essential to ensure accurate reproduction of acoustic pressure amplitude in the effective medium. Effective parameters depend on sound speed, flow velocity, and density of the moving fluid as well as on sound propagation direction. Conditions are discussed under which the dependence on the propagation direction can be avoided or relaxed.     

变声速弹性沉积层下压缩波与剪切波的耦合影响

针对压缩波声速n²线性分布、剪切波声速平方线性分布的变参数弹性海底沉积层中声场建模问题,建立了关于压缩波与剪切波本征函数的偏微分耦合方程组,基于微扰法,通过逐次微分给出了本征函数的近似解析解.理论分析表明,只有剪切波声速平方的梯度不为零的情况下,沉积层中的压缩波才会与剪切波产生耦合.压缩波与剪切波耦合的影响会带来本征值的变化,其对近场声传播的影响较小,但远距离声传播损失的预报在考虑耦合后与实测数据符合得更好.此外,耦合还会导致沉积层中本征函数及其导数的变化,使得耦合与非耦合情况下沉积层中质点位移场不同.通过与商用声场软件COMSOL计算结果的对比分析检验了本文方法的正确性,且本文方法计算时间远小于COMSOL软件运行时间.     

A New Type of Terahertz Waveguides

A new type of THz waveguides, which employs a solid polyethylene rod as the core and polyethylene tubes in a periodic array of square lattice as the cladding, is proposed. Optical properties of this new THz waveguide, especially in dispersion, confinement loss and single mode property, are investigated in detail with the plane wave expansion method and the beam propagation method. Numerical results demonstrate that the new THz waveguide can reach not only low dispersion but also low confinement loss at single mode propagation. Therefore, the square lattice structure is a better candidate as THz waveguides than the triangular ones.