K-space Prony’s method for generating the basis functions of multi-Gaussian beam models

The expansion coefficients of a multi-Gaussian ultrasonic beam model are obtained by a new approach that applies Prony´s method in a K-space domain. This method allows the fitting of the Gaussian beam directly at the face of the transducer with very high computational efficiency. It is demonstrated that the K-space Prony’s method can be used to accurately model the transducer field of planar and focused piston transducers, as well as probes that do not act as pistons. The choice of parameters appearing in the method and their influence on performance are discussed.     

An ultrasonic measurement model using a multi-Gaussian beam model for a rectangular transducer

To date, ultrasonic measurement models have primarily treated systems where circular transducers are used. Recently, however, a highly efficient ultrasonic beam model for a rectangular transducer has also become available where the transducer is represented as a superposition of a relatively few Gaussian beams. Thus, using the multi-Gaussian beams, we developed ultrasonic measurement models for systems where a rectangular transducer is employed. In this paper, we describe the developed models including the beam model, the efficiency factor for a rectangular transducer and far-field scattering models for some standard scatterers. Furthermore, the accuracy of the proposed model is verified by the comparison of the model-based predictions to the experimental measurements.     

Optimum and standard beam widths for numerical modeling of interface scattering problems

Gaussian beams provide a useful insonifying field for surface or interface scattering problems such as encountered in electromagnetics, acoustics and seismology. Gaussian beams have these advantages: (i) They give a finite size for the scattering region on the interface. (ii) The incident energy is restricted to a small range of grazing angles. (iii) They do not have side lobes. (iv) They have a convenient mathematical expression. The major disadvantages are: (i) Insonification of an interface is nonuniform. The scattered field will depend on the location of the scatterers within the beam. (ii) The beams spread, so that propagation becomes an integral component of the scattering problem. A standard beam parameterization is proposed which keeps propagation effects uniform among various models so that the effects of scattering only can be compared. In continuous wave problems, for a given angle of incidence and incident amplitude threshold, there will be an optimum Gaussian beam which keeps the insonified area as small as possible. For numerical solutions of pulse beams, these standard parameters provide an estimate of the smallest truncated domain necessary for a physically meaningful result.     

Off-axis flat-topped multi-Gaussian beam and its propagation through paraxial optical system

Off-axis flat-topped multi-Gaussian beam is proposed as an extension of flat-topped multi-Gaussian beam. The electric field of off-axis flat-topped multi-Gaussian beam is expressed as a superposition of a series of off-axis Gaussian beams. Propagation formulae for off-axis flat-topped multi-Gaussian beam through aligned and misaligned optical system are derived. As a numerical example, propagation properties of off-axis flat-topped multi-Gaussian beam in free space and through a misaligned thin lens are discussed.     

Nonparaxial multi-Gaussian beam models and measurement models for phased array transducers

A nonparaxial multi-Gaussian beam model is proposed in order to overcome the limitation that paraxial Gaussian beam models lose accuracy in simulating the beam steering behavior of phased array transducers. Using this nonparaxial multi-Gaussian beam model, the focusing and steering sound fields generated by an ultrasonic linear phased array transducer are calculated and compared with the corresponding results obtained by paraxial multi-Gaussian beam model and more exact Rayleigh-Sommerfeld integral model. In addition, with help of this novel nonparaxial method, an ultrasonic measurement model is provided to investigate the sensitivity of linear phased array transducers versus steering angles. Also the comparisons of model predictions with experimental results are presented to certify the accuracy of this provided measurement model.     

Some extensions of the Gaussian beam expansion: radiation fields of the rectangular and the elliptical transducer

A straightforward extension of Gaussian beam expansion is presented for calculation of the Fresnel field integral [J. J. Wen and M. A. Breazeale, J. Acoust. Soc. Am. 83, 1752-1756 (1988)]. The source distribution function is expanded into the superposition of a series of two-dimensional Gaussian functions. The corresponding radiation field is expressed as the superposition of these two-dimensional Gaussian beams and is then reduced to the computation of these simple functions. This treatment overcomes the limit that the shape of source is of circular axial-symmetry. The numerical examples are presented for the field of the (uniform) elliptical and the rectangular piston transducers and agree well with the results given by complicated computation.     

Electromagnetic wave beam propagation through a chiral slab

A general scheme for investigating the electromagnetic wave beam reflection by and transmission through a chiral slab is proposed. The electromagnetic wave beams within different regions are described by appropriate cylindrical vector wave function expansions, and their expansion coefficients are determined by using the boundary conditions and projection method. Under illumination by a fundamental Gaussian beam, a Hermite–Gaussian beam and a doughnut mode beam, numerical results of the normalized field intensity distributions are provided and discussed briefly.     

矩形表面波探头声场的高斯声束叠加法

利用矩形压电晶片和有机玻璃楔块折射可激励出超声表面波,广泛用于固体近表面缺陷检测和材料特性测量.由于描述表面波三维声场的理论方法还鲜有报道,因而主要采用简化的表面波二维声场模型来定量分析这类问题.高斯声束模型近些年被广泛应用于解决超声体波传播的各种复杂问题,然而,目前还没有将其扩展应用到超声表面波的声场的计算中.通过结合表面波格林方程和矩形换能器的高斯声束模型,推导出基于高斯声束叠加的表面波三维声场解析解.进一步,将该方法与点源叠加的数值解进行了分析比较,计算结果表明表面波声场的高斯声束叠加方法在具有较好计算精度的同时,还具有更快的计算效率.     

环形光束锥形衍射出射光场偏振特性及光场调控

环形光束的锥形衍射效应对于微粒的操控具有重要的应用价值.本文建立了环状高斯光束的锥形衍射模型,并基于Berry理论给出了线偏振态下环形光束锥形衍射出射光场的计算公式.理论仿真了环状光锥形衍射出射光场的偏振特性,得出环光锥形衍射出射光场的内、外亮环具有相互正交的偏振分布特性.搭建了线偏振态下环状高斯光锥形衍射的实验系统,实验验证了出射光场的偏振特性.针对环形光束锥形衍射出射光场具备的偏振特性,设计了一种组合偏振片,理论和实验研究了该组合偏振片对环光锥形衍射出射光场的调控.结果表明,随着组合偏振片方位角的变化,锥形衍射出射光场的内、外环强度发生周期性的变化.     

Extension of the mode method for viscoelastic media and focused ultrasonic beams

In the present study viscoelasticity is introduced in the mode model and the orthogonality condition is adapted for viscous media. The expansion of convergent acoustic Gaussian beams in terms of radiation modes for viscoelastic media is studied as well. The effects on the reflected and transmitted profiles of acoustic beams incident from an ideal liquid onto a viscoelastic plate are shown and physically explained. It is shown that focusing the incident beam can suppress divergence effects and gives the possibility to measure shear wave attenuation coefficients.     

Diffraction phenomena in the field of a circular piezoelectric transducer viewed in the time domain

Transient diffraction phenomena in the field of a piston transducer have been explained theoretically in terms of the direct and edge wave contributions to the piston response. Previous experimental studies by other workers have verified this concept for single cycles of 4 MHz radiation. Faster transients are difficult to study using thin piezoelectric transducers due to transducer resonance. Thick piezoelectric transducers of very low resonant frequency can be used to generate and receive step function acoustic transients with rise times of 20 ns or less and the problems of transducer resonance can be avoided. Experimental results are presented which show that when such a step function is propagated between two thick transducers the time course of the received wave can be explained in terms of the direct wave/edge wave model in conjunction with the theory of transient reverberations in piezoelectric elements.     

贝塞尔-高斯涡旋光束相干合成研究

基于相干合成技术,提出了对特定离散空间分布的高斯光束阵列加载离散涡旋相位生成二阶贝塞尔-高斯(Bessel-Gaussian,BG)涡旋光束的方案.利用干涉法、桶中功率和相关系数对合成BG涡旋光束的拓扑荷、光束质量进行了定量评价及参数优化.结果表明:基于相干合成技术能够产生特定的目标BG涡旋光束,阵列子光束紧密排布时合成BG光束的光束质量更高.该方法的提出对于其他涡旋光束的产生或者涡旋光束功率的提高具有一定的参考意义.     

双层界面下非近轴近似多元高斯模型的相控阵声场模拟

非近轴近似多元高斯模型克服了近轴近似条件的限制,能保证较大偏转角度下模拟声场的精确度和效率。根据双层介质的瑞利积分模型和单层介质的非近轴近似多元高斯模型,推导出双层介质中基于非近轴近似多元高斯模型的单阵元辐射声场计算模型。并在得到各阵元声束偏转聚焦的延迟时间基础上,累加得到基于非近轴近似高斯模型的超声相控阵横波检测辐射声场计算模型。模拟计算带丙烯酸树脂楔块的超声相控阵探头在钢中横波检测的声束偏转与偏转聚焦辐射声场,并与近轴近似多元高斯模型的横波检测声束的偏转聚焦辐射声场进行比较分析。对比分析结果表明非近轴近似多元高斯模型计算速度更快,用时约为近轴近似多元高斯模型的1/13。此外,非近轴近似高斯模型方法横波检测的聚焦声束覆盖区域更大,能量更集中,更适于远场区域检测。      

Exact partial wave expansion of optical beams with respect to an arbitrary origin

Using an analytical expression for an integral involving Bessel and Legendre functions, we succeed in obtaining the partial wave decomposition of a general optical beam at an arbitrary location relative to the origin. We also showed that solid angle integration will eliminate the radial dependence of the expansion coefficients. The beam shape coefficients obtained are given by an exact expression in terms of single or double integrals. These integrals can be evaluated numerically on a short time scale. We present the results for the case of a linear-polarized Gaussian beam.     

High-aperture binary axicons for the formation of the longitudinal electric field component on the optical axis for linear and circular polarizations of the illuminating beam

Diffraction of uniformly polarized laser beams with vortex phase singularity is theoretically analyzed using the plane wave expansion. It is shown that for a high numerical aperture, an intense longitudinal electric field component is formed on the optical axis in this case. It is numerically demonstrated that an analogous effect is ensured for diffraction of a conventional Gaussian beam from asymmetric binary axicons. The field intensity on the optical axis can be varied either by rotating the optical element or by changing the direction of polarization of radiation.     

Calculation of radiation acoustical fields from phased arrays with nonparaxial multi-Gaussian beam model

A nonparaxial multi-Gaussian beam model based on the rectangular aperture is proposed in order to overcome the limitation of paraxial Gaussian beam model which losing accuracy in off-axis beam fields. With the method, acoustical field generated by an ultrasonic linear phased array transducer is calculated and compared with the corresponding field obtained by Rayleigh-Sommerfeld integral, paraxial multi-Gaussian beam model, and Fraunhoffer approximation method. Simulation examples show that nonparaxial multi-Gaussian beam model is not limited by the paraxial approximation condition and can predict efficiently and accurately the acoustical field radiated by a linear phased array transducer over a wide range of steering angles.     

The simulation of ultrasonic beams with a Gaussian beam equivalent point source model

Point Sources and Gaussian beams are used frequently as fundamental building blocks for developing ultrasonic beam models. Both these models have different weaknesses that limit their effectiveness. Here, we will show that one can develop a Gaussian Beam Equivalent Point Source （GBEPS） model that removes those weaknesses and combines the accuracy and versatility of the point source models with much of the speed and well-behaved nature of Gaussian beam models. We will demonstrate the efficiency and versatility of this new GBEPS model in simulating the beams generated from ultrasonic phased arrays, using as few as one Gaussian beam per element of the array. A single element GBEPS model will be shown to be as accurate as a point source model even when substantial beam focusing or steering is present in the array or where the array beam is transmitted through an interface. At the same time the GBEPS model will be shown to be several orders of magnitude faster than the point source model.     

A generalized approach to beam wave interaction with a dielectric interface

New phenomena have been reported recently in connection with Gaussian beam interaction with a plane dielectric interface, namely, the deterioration of the reflected and refracted beams from shapes predicted by geometric optics, and the generation of higherorder components that cause angular beam deflection. Any bounded, symmetric beam, which is not necessarily Gaussian, can be comprised in terms of an angular spectrum of plane waves. Utilizing such a modal expansion, a model of the interaction process that seems to point out the generality of the phenomena involved for bounded symmetrical beams with any cross-section is presented. The procedure is applied to a Cauchy profile, and analytical results are given. Comparison with previous results obtained for the Gaussian beam and careful examination of the respective spectral functions demonstrate close correspondence between the results. This adds credence to the general approach presented here which can be applied to bounded symmetrical beams of general shape.