A spiral wave front beacon for underwater navigation: basic concept and modeling

A spiral wave front source produces an acoustic field that has a phase that is proportional to the azimuthal angle about the source. The concept of a spiral wave front beacon is developed by combining this source with a reference source that has a phase that is constant with the angle. The phase difference between these sources contains information about the receiver's azimuthal angle relative to the beacon and can be used for underwater navigation. To produce the spiral wave front, two sources are considered: a "physical-spiral" source, which produces the appropriate phase by physically deforming the active element of the source into a spiral, and a "phased-spiral" source, which uses an array of active elements, each driven with the appropriate phase, to produce the spiral wave front. Using finite element techniques, the fields produced by these sources are examined in the context of the spiral wave front beacon, and the advantages of each source are discussed.     

Restless rays, steady wave fronts

Observations of underwater acoustic fields with vertical line arrays and numerical simulations of long-range sound propagation in an ocean perturbed by internal gravity waves indicate that acoustic wave fronts are much more stable than the rays comprising these wave fronts. This paper provides a theoretical explanation of the phenomenon of wave front stability in a medium with weak sound-speed perturbations. It is shown analytically that at propagation ranges that are large compared to the correlation length of the sound-speed perturbations but smaller than ranges at which ray chaos develops, end points of rays launched from a point source and having a given travel time are scattered primarily along the wave front corresponding to the same travel time in the unperturbed environment. The ratio of root mean square displacements of the ray end points along and across the unperturbed wave front increases with range as the ratio of ray length to correlation length of environmental perturbations. An intuitive physical explanation of the theoretical results is proposed. The relative stability of wave fronts compared to rays is shown to follow from Fermat's principle and dimensional considerations.     

Numerical simulation of electromagnetic acoustic transducers using distributed point source method

In spite of many advances in analytical and numerical modeling techniques for solving different engineering problems, an efficient solution technique for wave propagation modeling of an electromagnetic acoustic transducer (EMAT) system is still missing. Distributed point source method (DPSM) is a newly developed semi-analytical technique developed since 2000 by Placko and Kundu (2007) [12] that is very powerful and straightforward for solving various engineering problems, including acoustic and electromagnetic modeling problems. In this study DPSM has been employed to model the Lorentz type EMAT with a meander line and flat spiral type coil. The problem of wave propagation has been solved and eddy currents and Lorentz forces have been calculated. The displacement field has been obtained as well. While modeling the Lorentz force the effect of dynamic magnetic field has been considered that most current analyses ignore. Results from this analysis have been compared with the finite element method (FEM) based predictions. It should be noted that with the current state of knowledge this problem can be solved only by FEM.     

A spiral wave front beacon for underwater navigation: transducer prototypes and testing

Transducers for acoustic beacons which can produce outgoing signals with wave fronts whose horizontal cross sections are circular or spiral are studied experimentally. A remote hydrophone is used to determine its aspect relative to the transducers by comparing the phase of the circular signal to the phase of the spiral signal. The transducers for a "physical-spiral" beacon are made by forming a strip of 1-3 piezocomposite transducer material around either a circular or spiral backing. A "phased-spiral" beacon is made from an array of transducer elements which can be driven either in phase or staggered out of phase so as to produce signals with either a circular or spiral wave front. Measurements are made to study outgoing signals and their usefulness in determining aspect angle. Vertical beam width is also examined and phase corrections applied when the hydrophone is out of the horizontal plane of the beacon. While numerical simulations indicate that the discontinuity in the physical-spiral beacon introduces errors into the measured phase, damping observed at the ends of the piezocomposite material is a more significant source of error. This damping is also reflected in laser Doppler vibrometer measurements of the transducer's surface velocity.     

平板式螺旋相位板的设计与应用

传统的螺旋相位板是一种利用沿方位角方向介质材料高度递增实现对光束相位调控产生涡旋光束的光学器件,由于这种特殊的几何结构特征使其不能通过相位板的叠加而调控出射光束所携带的角量子数.本文基于坐标变换方法将介质材料沿方位角方向折射率不变而高度递增的传统螺旋相位板变换为一种介质材料沿方位角方向高度不变而折射率递增的平板式螺旋相位板.通过理论分析与数值模拟,发现本文所设计的平板式螺旋相位板不仅与传统螺旋相位板一样能够产生高质量的涡旋光束,而且平板式螺旋相位板的高度和涡旋光束携带的角量子数可以根据介质材料的折射率选取而任意调节.为了实际应用的需要,可以通过叠加多层平板式螺旋相位板以获得不同角量子数的涡旋光束.这种平板式螺旋相位板在光传输、光通信等领域具有广阔的潜在应用价值.     

Transitions between orbits of resonance attractors for spiral waves

Spiral waves rotating in a thin layer of the light-sensitive Belousov-Zhabotinsky reaction can be controlled by the application of short light pulses at instants corresponding to the passage of a wave front through a measuring point. It is shown that such a feedback results in a drift of the spiral wave core along a discrete set of stable circular orbits centered at the measuring point, in good quantitative agreement with the theory of the resonance attractor recently developed. Variations of parameters in the feedback loop initiate transitions between orbits of different size. Thus a spiral wave drift can be induced along a snail-shaped trajectory with permanently growing distance from the measuring point.     

Excitable wave patterns in a spatially extended nonlinear optical cavity

We show that finite external excitation can lead to a traveling wave in an excitable passive optical system with one-dimensional space geometry. We have studied the excitable behavior of this system in parallel with that of its diffusive counterpart and show the effects of optical phase on the traveling-wave solution and its velocity. In two-dimensional space we observe numerically rotating optical spiral waves evolving from a truncated planar wave front.     

Time-reversal imaging of objects near rough surfaces based on surface flattening transform

This paper considers the imaging of objects located close to rough surfaces such as ocean or terrain. If transmitters and receivers are also located close to rough surfaces, incident wave is no longer a plane wave nor a spherical wave in free space and it is necessary to consider Green’s functions with the point source located close to the surface, similar to the Sommerfeld dipole problem. This paper considers the near-surface imaging by making use of time-reversal imaging and surface flattening transform. Surface flattening transform converts the rough surface problem into flat surface with inhomogeneous random medium. Mutual coherence function is obtained and used to obtain imaging of point target near rough surface, making use of the multi-static data matrix, time-reversal matrix, the eigenvectors, and the steering matrix. Numerical examples are given. An important point is that integration of stochastic wave propagation and signal processing is necessary to obtain imaging through complex clutter environment. Surface flattening transform is related to the transformation electromagnetics which attracted much interest because of cloaking possibilities. This paper includes some discussions on the relations between surface flattening and transformation electromagnetics.     

Beyond the Kuramoto-Zel’dovich theory: Steadily rotating concave spiral waves and their relation to the echo phenomenon

In numerical experiments with the Fitzhugh-Nagumo set of reaction-diffusion equations describing two-dimensional excitable media, unusual solutions are found that correspond to a concave spiral wave steadily rotating round a circular obstacle in a finite-size medium. Such a wave arises in the region of parameters corresponding to the solitonlike regime (see text); it appears due to the interaction between the peripheral areas of a “seed” spiral wave with a convex front and the echo waves incoming from the outer boundaries of a medium. The solutions obtained are in contradiction with intuition and represent a numerical counterexample to the known theories that forbid steadily moving excitation waves with concave fronts. Nevertheless, a concave spiral wave is a stable object; being transformed to the usual spiral wave with a convex front by suppressing echo at the outer boundaries of the medium, it is again recovered upon restoring the echo conditions. In addition to the single-arm spiral concave wave, solutions are obtained that describe multiarm waves of this type; for this reason, the concave fronts of these waves are a coarse property.     

基于螺旋相位调制的非相干全息点扩散函数研究

分析了菲涅耳非相干相关全息(Fresnel incoherent correlation holography,FINCH)系统中纯相位空间光调制器(spatial light modulator,SLM)加载螺旋相位掩模时的点扩散函数.以氙灯为照明光源搭建了FINCH系统,电荷耦合器记录的点源全息图与点扩散函数模拟结果一致.采用该系统分别在SLM上加载双透镜掩模和螺旋相位调制双透镜掩模两种情况下对分辨率板和非染色洋葱细胞成像,给出了成像对比结果.结果表明:采用螺旋相位调制的FINCH系统可以在几乎不牺牲分辨率的情况下提高图像的边缘对比度;同样,对相位物体也可以实现图像的边缘提取和识别.该方法在实时监测活细胞的分裂、形变等方面具有重要应用前景.     

Study of Rayleigh type surface wave in the initial stressed irregular bottom of ocean due to point source

Rayleigh type surface wave propagation in the irregular bottom of ocean model which is the interface of homogeneous liquid layer over laying an irregular boundary of homogeneous orthotropic half space under initial stresses has been discussed in this paper. Three different dispersion equations are obtained in the form of simple equation using and not using Perturbation technique. Some special cases have been considered. The effect of irregularity, initial stressed, point source, and depth of liquid layer on the propagation of Rayleigh waves has been analyzed and results of numerical discussion have been presented graphically for three different dispersion equations. Mainly the graphs are shown the variation of phase velocity with wave number in different cases.     

液体中激光等离子体冲击波波前传播特性研究及测试

将空气中球对称冲击波衰减波前传播公式推广到非完全中心对称情况，根据对光学阴影法对激光等离子体冲击波波前测试数据的计算分析，提出液体中点源激光等离子体冲击波旋转椭球面波前传播公式.并且用声学方法对水中和酒精中的激光等离子体冲击波波前进行实验测试，结果表明测试结果与计算公式相吻合. 关键词： 激光 等离子体冲击波 旋转椭球面     

General solution of cumulative second harmonic by Lamb wave propagation in a solid plate

A straightforward approach has been developed for the general solution of cumulative second harmonic by Lamb wave propagation in a solid plate. The present analyses of second-harmonic generation by Lamb waves focus on the cases where the phase velocity of the fundamental Lamb wave is exactly or approximately equal to that of the double frequency Lamb wave （DFLW）. Based on the general solution obtained, the numerical analyses show that the cumulative second-harmonic fields are associated with the position of excitation source and the difference between the phase velocity of the fundamental Lamb wave and that of the dominant DFLW component.     

Simulation of anisoplanatism of adaptive optical system in inhomogeneous turbulent atmosphere

The goal of this study was to analyse anisoplanatism of adaptive optics under an inhomogeneous turbulent atmosphere over a pupil of finite size. By means of a numerical model with layers of turbulence software was proposed by which point spread function (PSF), optical transfer function (OTF) as well as system isoplanatic angle can be calculated. Atmospheric turbulence was simulated with the aid of a set of moving random phase screens with arbitrary statistics. Both reference and target are assumed to be the point light sources. To simulate atmospheric turbulence we applied the concept of a number of moving random phase screens with Kolmogorov spectrum. In my investigation I used the model of the Shack-Hartmann wave front sensor and the ideal model of a wave front adaptive mirror that is assumed to reproduce a given number of Zernike polynomials without time delays. The designed software allows calculation of instantaneous and average values of phase correction errors at different angles between a reference beacon and target source. Simulations can be made with a broad range of parameters of an adaptive system and atmospheric turbulence. The system of the model allows changing of the control algorithm of phase correction. Both common phase conjugation and weighted phase conjugation algorithm have been tested. This program is capable of calculating the effects of beam diffraction during propagation in the atmosphere.     

光栅刻划机直线度误差补偿的研究

中阶梯光栅是一种特殊的衍射光栅, 它以高的衍射级次和大的衍射角来工作, 具有高分辨率、全波闪耀等特性。已广泛应用于高端光谱仪器之中,极大地促进了航天航空、天文、医疗、军事、环境等尖端科技的发展。但是专业的刻划系统需要定制,价格昂贵。使用已成熟的超精密加工设备来加工中阶梯光栅,可以大大降低中阶梯光栅母版的制备成本。超精密单点金刚石车床制备中阶梯光栅时,系统直线度不好,存在较大的累积误差,导致中阶梯光栅衍射波前较差,达不到制备要求。为了减小超精密单点金刚石车床固有的直线度误差,对超精密单点金刚石车床进行了误差补偿。首先,以累积误差曲线为依据进行第一次补偿。实验结果表明,当补偿系数为0.75～0.85时,此时衍射波前的PV(峰谷值)值在约400 nm,一次直线度补偿效果到达极限。然后,以闪耀级的衍射波前曲线为依据进行第二次直线度补偿,二次补偿后的衍射波前PV值为约83 nm。补偿后的结果表明衍射波前得到大幅改善,有利于提高所制备光栅的质量,在光栅实际刻划中具有指导作用。     

Adaptive correction of vortex laser beam in a closed-loop system with phase only liquid crystal spatial light modulator

We propose and demonstrate the wave front correction of a vortex laser beam by using dual phase only liquid crystal spatial light modulators (LC-SLMs) and a stochastic parallel gradient descent (SPGD) algorithm. One phase only LC-SLM is used to generate vortex laser beam by loading spiral phase screen onto the wave front of input quasi-Gaussian beam. The other phase only LC-SLM under SPGD controller based on the subzone control method adaptively compensates the wave front of vortex laser beam. Numerical simulation and experimental results show that after correction, vortex doughnut like beam is focused into a beam with airy disk pattern distribution in the far field. The adaptive corrections of vortex laser beam with different optical topological charges are studied. The results show that the optical topological charge has little influence on adaptive correction. The powers in the main lobe of far field intensity distributions of vortex laser beams with different optical topological charges are all greatly improved by adaptive correction. The technique proposed in this paper can be used in optical communication, relay mirror and atmospheric turbulence correction.     

铁冲击相变的分子动力学研究

用分子动力学方法模拟了单晶铁(Fe)在一定初始温度下冲击相变(α相→ε相)的微观过程，结果显示温度会导致冲击相变压力阈值降低.基于此微观过程，对加卸载波系的传播规律进行了相应计算和分析，结果表明在卸载过程中逆相变波(ε相→α相)相对于波前以当地纵波声速传播，而相对波后以亚声速传播，这可由卸载压力-密度曲线给出相应解释；计算了不同初态的卸载压力-密度状态曲线，并给出了逆相变带的分布，其分布规律显示了卸载过程逆相变的滞后现象. 关键词： 分子动力学 多体势 冲击波 相变     

Selection of spiral waves in excitable media with a phase wave at the wave back

Universal relationships between the medium excitability and the angular velocity and the core radius of rigidly rotating spiral waves in excitable media are derived for situations where the wave front is a trigger wave and the wave back is a phase wave. Two universal limits restricting the region of existence of spiral waves in the parameter space are demonstrated. The predictions of the free-boundary approach are in good quantitative agreement with results from numerical reaction-diffusion simulations performed on the Kessler-Levine model.     

Wave Grouping of a Drifting Spiral Wave in the Presence of an External Field

The phenomenon of wave grouping, in which the dense waves and the sparse waves can form groups in front of the spiral tip when the spiral wave is meandering, has been reported in a chemical reaction system recently. We present a method to realize the phenomenon of wave grouping by applying an external field to the system. The numerical simulations are carried out on the basis of the FitzHugh-Nagumo equations.     

Higher mode sound transmission from a point source through a rectangular aperture

This paper considers the higher-order scattered and transmitted wave fields that result when an acoustic wave from a point source impinges at an arbitrary angle on a rectangular aperture in a rigid, thick wall. In this analysis, it is assumed that free field conditions exist on both sides of the aperture. Although the full scattered and transmitted pressure fields contain both modal sum and modal coupling effects, the modal coupling effects of the higher-order modes are ignored such that an approximate analytical solution to the uncoupled analysis can be utilized. Experiments have been undertaken to measure the sound pressure levels in the transmitted field that result when sound from a point source impinges on the opposite side of a rectangular aperture. Measurements were made with the source located at the required position to drive a particular in-aperture higher-order mode. The source was also located at positions that did not directly excite any in-aperture higher-order mode at a cut-on frequency. These results indicate that the approximate analysis developed here gives accurate solutions whether or not any mode of the aperture is driven at cut-on. Thus, the method can be used for any relative location of a source from a rectangular aperture of any dimensions.