Experimental study of the formation of nonlinear acoustic waves in focused beams

The shock wave formation in focused beams produced by spherical hydroacoustic transducers with different apertures and an operating frequency of 3 MHz, as well as in weakly divergent high-intensity beams of the same frequency, is studied experimentally. The profiles of the received signals are analyzed for different receiving points in the acoustic beam and for different combinations of nonlinear and diffraction effects. It is found that the distortion of the initial waveform (i.e., of the compression and rarefaction phases) is asymmetric. The asymmetry of the wave profile in a focused beam is more pronounced than that in a quasi-plane wave while the asymmetric distortion of the high-frequency carrier causes an asymmetric distortion of the pulse envelope. The angular characteristics of the difference-frequency waves produced by parametric sound radiators are compared using both focused and weakly divergent beams of pump waves. The experiments also show that the appearance of a bubbly phase screen in the region before the point of the shock formation either shifts this point to greater distances or makes the discontinuity formation impossible. Results illustrating the changes that occur in the shock wave characteristics when the bubbly phase screen is placed in the region of the fully developed shock are presented.     

Modeling of pulsed finite-amplitude focused sound beams in time domain.

A time-domain numerical model is presented for simulating the finite-amplitude focused acoustic pulse propagation in a dissipative and nonlinear medium with a symmetrical source geometry. In this method, the main effects responsible in finite-amplitude wave propagation, i.e., diffraction, nonlinearity, and absorption, are taken into account. These effects are treated independently using the method of fractional steps with a second-order operator-splitting algorithm. In this method, the acoustic beam propagates, plane-by-plane, from the surface of a highly focused radiator up to its focus. The results of calculations in an ideal (linear and nondissipative) medium show the validity of the model for simulating the effect of diffraction in highly focused pulse propagation. For real media, very good agreement was obtained in the shape of the theoretical and experimental pressure-time waveforms. A discrepancy in the amplitudes was observed with a maximum of around 20%, which can be explained by existing sources of error in our measurements and on the assumptions inherent in our theoretical model. The model has certain advantages over other time-domain methods previously reported in that it: (1) allows for arbitrary absorption and dispersion, and (2) makes use of full diffraction formulation. The latter point is particularly important for studying intense sources with high focusing gains.     

Interaction of pulsed laser beams in quadratic nonlinear media

A theory of three-wave cascade interaction of pulsed laser beams in quadratic nonlinear media is developed with regard to diffraction and dispersion. The space-time trajectories of signal motion in a medium with an inhomogeneity induced by high-power low-frequency pumping are analyzed. It is shown that total signal reflection from a moving localized inhomogeneity can be implemented. This reflection is accompanied by a change in the frequency, velocity, and propagation direction of the signal wave.     

Nonlinear pulsed ultrasound beams radiated by rectangular focused diagnostic transducers

A numerical model for simulating nonlinear pulsed beams radiated by rectangular focused transducers, which are typical of diagnostic ultrasound systems, is presented. The model is based on a KZK-type nonlinear evolution equation generalized to an arbitrary frequency-dependent absorption. The method of fractional steps with an operator-splitting procedure is employed in the combined frequency-time domain algorithm. The diffraction is described using the implicit backward finite-difference scheme and the alternate direction implicit method. An analytic solution in the time domain is employed for the nonlinearity operator. The absorption and dispersion of the sound speed are also described using an analytic solution but in the frequency domain. Numerical solutions are obtained for the nonlinear acoustic field in a homogeneous tissue-like medium obeying a linear frequency law of absorption and in a thermoviscous fluid with a quadratic frequency law of absorption. The model is applied to study the spatial distributions of the fundamental and second harmonics for a typical diagnostic ultrasound source. The nonlinear distortion of pulses and their spectra due to the propagation in tissues are presented. A better understanding of nonlinear propagation in tissue may lead to improvements in nonlinear imaging and in specific tissue harmonic imaging. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 4, pp. 560–570. This article was translated by the authors.     

Moment theory of self-trapped laser beams with nonlinear saturation

The moment theory of the quasi-optical equation is used to obtain simple analytical expressions for the relation between beam radius and power of stationary self-trapped light beams in passive nonlinear media with saturation of the index of refraction. In addition, the stability of these self-trapped beams is determined.     

Spectral behavior of pulsed Bessel beams focused by a dispersive lens

Starting from the Huygens–Fresnel diffraction integral, the analytical expression for the power spectrum of pulsed Bessel beams focused by a dispersive aperture lens is derived and used to study the spectral anomalies of pulsed Bessel beams in the focused field. Numerical calculation results are given to illustrate the dependence of spectral anomalous behavior on the pulse parameters, truncation parameter and material dispersion of the lens. It is shown that near the phase singularities the spectral anomalies may take place. The potential applications of spectral anomalies of ultrashort pulsed beams in information encoding and information transmission are considered.     

Spectral anomalies of pulsed Hermite-cosh-Gaussian beams focused by an aperture lens

The spectral behaviors of pulsed Hermite-cosh-Gaussian (HChG) beams focused by an aperture lens are studied. The propagation equation for the power spectra of pulsed HChG beams focused by an aperture lens is derived and used to study the spectral anomalies of pulsed HChG beams in the focused field. Numerical results are given to illustrate the dependence of spectral anomalies behavior on the pulse parameter and truncation parameter. The potential applications of spectral anomalies of ultrashort pulsed beams in information encoding and information transmission are considered.     

Kerr非线性介质中聚焦像散高斯光束的传输特性

当高功率激光通过Kerr非线性介质传输时,Kerr效应会严重影响激光的传输特性.实际应用中常遇到像散光束.迄今为止,像散光束传输特性的研究大都局限于在线性介质中的传输,而在非线性介质中传输的研究较少,且还未涉及像散激光束通过含光学系统的Kerr非线性介质传输变换的研究.本文主要研究Kerr效应对聚焦光束像散特性和焦移特...     

Material property estimation in thin plates using focused,synthetic-aperture acoustic beams

The method developed here exploits the wide angular range of focused acoustic probes and the large synthetic aperture of scanned transducers to permit a rapid and reliable estimation of material properties in thin plates. It is found in several tests with various materials that estimates of elastic behavior using this method agree with contact measurements to within less than 5%. The method utilizes transmission (or reflection) coefficient reconstruction for an infinite thin plate, across a wide range of frequency and wave number, from which elastic property estimates are made. Data collected over a large synthetic acoustic aperture are processed with temporal and spatial Fourier transforms applied to change the acquired data from the coordinate and time domains to the wave number and frequency domains. Extrinsic real-beam effects on the data are accounted for with a complex transducer point analysis. Transmission measurements yield reconstructed data extending to the mode cutoffs, permitting easy and nearly unambiguous estimation of a subset of the elastic stiffnesses. For anisotropic plates, elastic stiffnesses are estimated with an inversion procedure that uses only limited data carefully selected from different portions of the measured scattering coefficient. Estimates are made by reconstructing in a stepwise fashion, based on sensitivity studies, where only one stiffness is estimated from the data at any one time, restricting the optimization to a robust one-dimensional search.     

部分空间相干和部分光谱相干厄米-高斯脉冲光束的焦场的相干特性

从部分相干光的传输理论出发,采用傅里叶变换法,推导出聚焦部分空间相干部分光谱相干厄米一高斯脉冲光束的光谱和光谱相干度的解析表达式,并用以研究了聚焦场的相干特性．研究结果表明,聚焦光束的光谱相干度与空间相关长度、时间相干长度和光束阶数有关．时间相干长度的减小将引起光谱相干度的减小,但光谱相干度的空间分布特性不受影响．随着光束阶数的增大,光谱相干度会出现振荡,且光束阶数越大,空间相关长度越小,振荡越明显．     

Lie algebraic analysis for the nonlinear transportof intense pulsed beams in electrostatics lenses

The Lie algebraic method is applied to the analysis of the nonlinear transport of an intense pulsed beam in cylindrically symmetrical electrostatic lenses, and particle orbits in a six-dimensional phase space (x, p_x, y, p_y, τ, p_τ) are obtained in the second order approximation. They can also be acquired in the third or higher order approximation if needed. In the analysis, we divide the electrostatic lenses into several segments. Each segment is considered as a uniform accelerating field, and each dividing point is treated as a thin lens. The particle distribution in a three-dimensional ellipsoid is of Gaussian type.     

Modeling the propagation of nonlinear three-dimensional acoustic beams in inhomogeneous media

A three-dimensional model of the forward propagation of nonlinear sound beams in inhomogeneous media, a generalized Khokhlov-Zabolotskaya-Kuznetsov equation, is described. The Texas time-domain code (which accounts for paraxial diffraction, nonlinearity, thermoviscous absorption, and absorption and dispersion associated with multiple relaxation processes) was extended to solve for the propagation of nonlinear beams for the case where all medium properties vary in space. The code was validated with measurements of the nonlinear acoustic field generated by a phased array transducer operating at 2.5 MHz in water. A nonuniform layer of gel was employed to create an inhomogeneous medium. There was good agreement between the code and measurements in capturing the shift in the pressure distribution of both the fundamental and second harmonic due to the gel layer. The results indicate that the numerical tool described here is appropriate for propagation of nonlinear sound beams through weakly inhomogeneous media.     

Thermal and acoustic effects in absorbing liquids under the action of pulsed light beams

We present the results from simulating the impact of pulsed light beams of different spatial structures (Gaussian, Bessel, singular) in absorbing liquids. Profiles of refractive index inhomogeneities excited in a medium are calculated and the kinetics of their relaxation is studied.     

格子玻尔兹曼方法对不同张角聚焦声束的建模

高强度聚焦超声(HIFU)是一种新型的无创治疗肿瘤新技术,其中换能器声场数值计算能够为HIFU治疗提供重要的依据。传统非线性KZK和SBE模型广泛应用于换能器声场数值计算,但依然存在某些不足。我们采用一种介观尺度的新型流体力学方法,即格子Boltzmann方法(LBM),基于2维9离散速度(D2Q9)格子构建了轴对称多弛豫参数LBM模型,并通过调节弛豫参数分析其对模型的影响;利用该模型对两个具有不同张角的球面聚焦换能器的声场进行数值模拟,并与KZK和SBE模型的计算结果进行比较。结果表明LBM模型能够很好地描述超声波的激发和传播机制,从流体力学的角度描述聚焦声场的分布,具有清晰的物理意义,且计算过程不受换能器张角的限制,在换能器声场的理论分析和模拟计算及其在HIFU治疗中的应用有着积极的意义。     

Time-domain modeling of nonlinear distortion of pulsed finite amplitude sound beams

This work aims to validate a time domain numerical model for the nonlinear propagation of a short pulse of finite amplitude sound beam propagation in a tissue-mimicking liquid. The complete evolution equation is simply derived by a superposition of elementary operators corresponding to the 'one effect equation'. Diffraction LD, absorption and dispersion LAD, and nonlinear distortion LNL effects are treated independently using a first order operator-splitting algorithm. Using the method of fractional steps, the normal particle velocity and the acoustical pressure are calculated plane by plane, at each point of a two-dimensional spatial grid, from the surface of the plane circular transducer to a specified distance. The LA operator is a time convolution between the particle velocity and the causal attenuation filter built after the Kramers-Kroning relations. The LNL operator is a time-based transformation obtained by following an implicit Poisson analytic solution. The LD operator is the usual Rayleigh integral. We present a comparison between theoretical and experimental temporal pressure waveform and axial pressure curves for fundamental (2.25 MHz), second, third and fourth harmonics, obtained after spectral analysis.     

Principles of obtaining and processing of acoustic signals in linear and nonlinear tomographs

Physical, mathematical, and engineering problems related to creating two fundamentally different types of tomographs (so-called linear and nonlinear tomographs) are considered. The tomographs under development are designed for diagnosing pathological tumors of soft biological tissues at early stages of their growth.     

Using degenerate parametric interaction of intense acoustic beams to amplify weak signals

The paper considers the degenerate parametric interaction of an intense acoustic pumping beam and a weak signal beam at the subharmonic. The use of a special emitter system with independent signal emission at the harmonic and subharmonic made it possible to study the features of nonlinear interaction both for different amplitude levels and arbitrary phase relations of the fields at these frequencies. Just as predicted in the theory, the experiment showed that signal amplification at the subharmonic hardly occurs at all. It is shown that the use of odd field harmonics, which are absent for a zero amplitude of the signal wave, makes it possible to substantially increase the efficiency of isolating a weak signal wave. The interaction of beams for large and small acoustic Reynolds numbers of the signal wave is studied.     

Spectral and spatiotemporal properties of Bessel–Gauss pulsed beams focused by a dispersive aperture lens

The spectral and spatiotemporal properties of Bessel–Gauss pulsed beams focused by a dispersive aperture lens are studied, where the dispersion of the first, second, and higher orders is taken into consideration. It is shown that the spectral switches take place at the geometrical focal plane, and the dispersion of the first order leads to a shift of the critical position towards the z-axis. The dispersion plays a noticeable role in the spatiotemporal intensity distribution. The dispersion of the first order results in a decrease of the peak intensity, in a shift and a broadening of the pulse form, and the effect becomes more noticeable with increasing waist width. The dispersion of the second order results in a further broadening and a decrease of the peak intensity, and the effect is larger as the thickness of the lens increases. However, the dispersion of the higher order plays a relatively minor role. The results are illustrated by numerical examples and interpreted physically.