Imaging through an inhomogeneous layer with an acoustic antenna array

A method is proposed for obtaining images through a layer of an inhomogeneous medium by using an antenna array scanning in angle or space. The method is based on the wave front inversion, which allows one to form an undisturbed sound field on the object of location in an inhomogeneous medium. This property makes it possible to suppress the effect of the thin inhomogeneous layer on the signals observed at the array output. The technique consists in a mutual processing of two received signals, one of which is obtained by locating the objects through the inhomogeneous medium and the other is obtained by locating the same objects, in the same medium, by the front-inverted wave. The mutual processing procedure consists in using the first received signal to form a filter for the second signal. The method is tested by a numerical simulation.     

Time reversal of speckle noise

Focusing a wave in an unknown inhomogeneous medium is an open problem in wave physics. This work presents an iterative method able to focus in pulse-echo mode in an inhomogeneous medium containing a random distribution of scatterers. By performing a coherent summation of the random echoes backscattered from a set of points surrounding the desired focus, a virtual bright pointlike reflector is generated. A time-reversal method enables an iterative convergence towards the optimal wave field focusing at the location of this virtual scatterer. Thanks to this iterative time-reversal process, it is possible to focus at any arbitrary point in the heterogeneous medium even in the absence of pointlike source. An experimental demonstration is given for the correction of strongly distorted images in the field of medical ultrasound imaging. This concept enables envisioning many other applications in wave physics.     

Enhanced Deflection of Light Ray by Atomic Ensemble on Coherent Population Oscillation

In recent experiments [e.g., Nature Physics 2 (2006) 332], the enhancedlight deflection in an atomic ensemble due to inhomogeneous fields is demonstrated by the electromagnetically induced transparency (EIT) based mechanism. In this paper, we explore a different mechanism for the similar phenomenon of the enhanced light deflection. This mechanism is based on the coherent population oscillation, which leads to the hole burning in the absorption spectrum. The medium causing the deflection of probe light is an ensemble of two-level atoms manipulated by a strong controlled field on the two photon resonances. In the large detuning condition, the response of the medium to the pump field and signal field is obtained with steady state approximation. And it is found that after the probe field travels across the medium, the signal ray bends due to the spatial-dependent profile of thecontrol beam.     

Focused antenna array in a strongly inhomogeneous medium

A focused acoustic antenna array is considered in a strongly inhomogeneous stationary medium. An opportunity is indicated to determine the coordinates of a number of objects by active location. It is assumed that, in insonifying the objects by a wave with an arbitrary wave front, they scatter spherical waves and are sufficiently separated in distance and angle to be resolved by the same array in a homogeneous medium. The procedure of determining the coordinates of the objects involves a wave front inversion for distinguishing between the signals from different objects. The coordinates are determined by estimating the parameters for each individual object. The parameter estimation procedure is shown to provide a high efficiency of extracting the argument of a complex signal. The results of the numerical modeling and solution of the problem are presented.     

Distortion of waves with profile discontinuities in the medium with a periodic transverse inhomogeneity distribution

For the purpose of describing the joint influence of nonlinear effects and refractive inhomogeneities on the evolution of intense acoustic waves, a model of the medium the local velocity of sound of which is periodic in the transverse direction and decreases in the propagation direction, which generalizes the known models of the layered medium and of the infinitesimally thin phase screen, is proposed. An exact solution is found for the wave with arbitrary initial conditions: time profile and transverse profile. The spatial wave structure in the inhomogeneous medium is calculated; it is shown that narrow high-amplitude regions are formed and the rate of nonlinear effect accumulation changes. It is shown that the amplitude of the wave at long distances from the source may differ little from its initial value due to compensation for the effects of nonlinear attenuation and of focusing by inhomogeneities. Possibilities of amplification of intense waves depending on the proportion between parameters of the wave and those of the inhomogeneous medium are studied.     

Oscillatory disturbance in force calibration of optical tweezers

In the calibration of the optical trap stiffness, it is found that there appears an attenuating oscillation as an oscillatory disturbance added to the trapped bead movement, when the scanner is driven by a triangular wave input.An equivalent oscillator model is put forward to explain the mechanism of the oscillatory disturbance. Both the measurements and calculations show that the attenuating oscillation comes from the oscillation of the scanner and the triangular wave drive causes this additional oscillation of the scanner. Furthermore, the analysis indicates that the oscillatory disturbance will become stronger, when the stiffness of the trap increases or the natural frequency of the scanner decreases. We adopt another driving way, i.e. a sinusoidal wave input is used instead of the triangular wave input. Our experiment has verified that in this case the oscillatory disturbance is eliminated completely.     

Effective medium method of slightly compressible elastic media permeated with air-filled bubbles

An effective medium method is developed for the slightly compressible elastic media permeated with air-filled bubbles, according to the nonlinear oscillation of the bubble, which happens when compressional wave travels through the porous media. The effective Lame coefficients of the porous medium and the nonlinear elastic wave equation are deduced, based on the fact that the micro-unit of the effective medium should have the same stress and strain as the micro-unit of the porous media. The linearized properties obtained by this method are in good agreement with the results of Gaunaurd’s classic theory [Gaunaurd G.C. and überall H., J. Acoust. Soc. Am., 1978, 63: 1699–1711]. Furthermore, the nonlinear coefficient, which is an important property of the porous media, can also be acquired by this method. __________ Translated from Acta Acustica, 2006 (in Chinese) (in press)     

Influence of Magnetic-Field and Plasma-Density Inhomogeneities on the Propagation and Amplification of Radio Waves in the Solar Corona

We analyze the maser generation of millisecond spikes of the solar radio emission at the cyclotron resonance of a fast extraordinary wave in an inhomogeneous medium. It is shown that the magnetic-field inhomogeneity with parameters typical of the solar corona drastically reduces the time of electromagnetic-wave amplification, which is explained by the fact that these waves leave the resonance region in the wave-vector space. As a result, an unstable electron distribution can be formed. The efficient generation of radiation becomes possible only in such local regions where the influence of the magnetic-field inhomogeneity is compensated by small-scale inhomogeneities of the plasma density with typical scales ranging from tens to hundreds of kilometers. Taking the effect of inhomogeneous medium into account allows us to explain spatial and temporal characteristics of the spikes.     

Gap solitons in an extended anti-directional coupler

A nonlinear solitary wave in an inhomogeneous medium formed by two tunnel-coupled waveguides is considered. One of the waveguides is manufactured from an ordinary dielectric, while the second has negative refraction. The results from numerical simulations demonstrate the high stability of gap solitons with respect to collisions. It is discovered that for low relative velocities of two colliding solitons, a longlived coupled state of these solitons can be formed.     

Pulse signal detection in a focal area of a convergent wave front

Diffraction effects, taking place during nonlinear transformations in inhomogeneous acoustic fields, are experimentally investigated. The case of a convergent spherical wave front propagating in a uniform nonlinear medium, detection of an acoustic field in a focus, and receiving of the detected signal in the region of the initial wave front aperture are considered. A spherical piezoceramic transducer is used in the experiments as a focusing device. Broad-angle “nonlinear scattering” signals have been recorded at the experimental facility where a pulsed mode of focused transducer operation in water is implemented. The dependence of the amplitude of the signal, detected in the focal area, and its shape on the scattering direction, as well as on the distance between the focus and the receiving point, are studied.     

Statistical characteristics of an intense wave behind a two-dimensional phase screen

An analysis of the parameters of nonlinear waves transmitted through a layer of a randomly inhomogeneous medium is carried out. The layer is modeled by a two-dimensional phase screen. Passing through the screen plane, the wave acquires a random phase shift. The wave front becomes distorted, and randomly located regions of ray convergence and divergence are formed, in which the nonlinear evolution of the wave alters profoundly. The problem is solved in the approximation of geometrical acoustics. The ray pattern of a plane wave transmitted through the regular screen is constructed. The solution that describes the spatial structure of the field and the evolution of an arbitrary temporal wave profile behind the screen is obtained. Statistical characteristics of the discontinuity amplitude are calculated for different distances from the screen. A random modulation is shown to result in a faster (in comparison with the case of a homogeneous medium) nonlinear attenuation of the wave and in the smoothing of the shock profile. The distribution function of the wave field parameters becomes broader because of random focusing effects.     

The wave flow effect on a plane boundary between vacuum and an optical medium with a quasi-zero refractive index

A boundary problem in which a plane electromagnetic wave is reflected and refracted at a plane boundary of a semi-infinite optical medium with a quasi-zero refractive index has been solved. Such a medium has a random refractive index taking values in an interval from zero to some finite value less than unity. It means that the concept of a sharp interface between two media loses its meaning, the boundary of the medium becomes inhomogeneous, and laws of reflection and refraction of light become non-Fresnelian. Formulas for non-Fresnelian amplitudes of reflection and refraction have been derived. It is shown that a surface wave arises near the boundary of a medium with a quasi-zero refractive index. The wave propagates both on the inside and outside of the boundary.     

On the theory of multiple scattering of sound waves by spherical particles in liquid and elastic media

Two independent systems of equations are derived for describing the scalar and vector potentials of the sound field in a liquid or elastic medium containing discrete inhomogeneities. One of the systems determines the sound field as the sum of the fields scattered by the particles according to the law of scattering by a single particle with the oscillation amplitudes governed by the properties of the inhomogeneous medium. The other system determines the sound field as the sum of the scattered fields formed in the inhomogeneous medium with the oscillation amplitudes of a particle in a homogeneous medium. Expressions relating the fields that occur in a medium consisting of N particles to the fields in a medium consisting of N − 1 particles are proposed. These expressions may simplify and diversify the methods used for computer simulation of sound fields with the aim to verify the calculations. The results of the study are valid for any particle concentrations under the condition that the scattering by a single particle is determined by its monopole, dipole, and rotary oscillations.     

Localized and extended states in a disordered trap

We study Anderson localization in a disordered potential combined with an inhomogeneous trap. We show that the spectrum displays both localized and extended states, which coexist at intermediate energies. In the region of coexistence, we find that the extended states result from confinement by the trap and are weakly affected by the disorder. Conversely, the localized states correspond to eigenstates of the disordered potential, which are only affected by the trap via an inhomogeneous energy shift. These results are relevant to disordered quantum gases and we propose a realistic scheme to observe the coexistence of localized and extended states in these systems.     

Time reversal and the inverse filter

To focus ultrasonic waves in an unknown inhomogeneous medium using a phased array, one has to calculate the optimal set of signals to be applied on the transducers of the array. In the case of time-reversal mirrors, one assumes that a source is available at the focus, providing the Green's function of this point. In this paper, the robustness of this time-reversal method is investigated when loss of information breaks the time-reversal invariance. It arises in dissipative media or when the field radiated by the source is not entirely measured by the limited aperture of a time-reversal mirror. However, in both cases, linearity and reciprocity relations ensure time reversal to achieve a spatiotemporal matched filtering. Nevertheless, though it provides robustness to this method, no constraints are imposed on the field out of the focus and sidelobes may appear. Another approach consists of measuring the Green's functions associated to the focus but also to neighboring points. Thus, the whole information characterizing the medium is known and the inverse source problem can be solved. A matrix formalism of the propagation operator is introduced to compare the time-reversal and inverse filter techniques. Moreover, experiments investigated in various media are presented to illustrate this comparison.     

Spherical focusing of acoustic pulses in a liquid

Nonlinear processes accompanying the focusing of a microsecond acoustic pulse produced by an electromagnetic source shaped as a spherical segment are investigated. The processes are considered to be far from the boundaries of a liquid, in the absence of cavitation. Detailed measurements of the pressure field by a fiber-optic sensor and high-speed photography of the shock front are performed. The pressure field is found to be determined by the nonlinear effects that occur in the course of the propagation of the initial converging compression wave and an edge rarefaction wave. The peak pressure amplitudes at the focus are 75 and ?42 MPa for the compression and rarefaction waves, respectively, at the maximum voltage of the pulse generator in use. The measured length of the compression wave front is equal to the response time of the sensor (8 ns). The pressure amplitude is shown to be limited by the irregularity of the propagation of a shock wave in the form of Mach’s disk. At the focus, the pressure gradient across the radiator axis reaches 0.5 atm/μm, while the diameter of the focal spot is 2.5±0.2 mm. The focus of the edge rarefaction wave formed due to diffraction is located closer to the radiator than the focus of the compression wave, which may facilitate the study of the biological effect of cavitation independently of the shear motion of the medium.     

Amplitude degradation of time-reversed pulses in nonlinear absorbing thermoviscous fluids

The linear wave equation in a lossless medium is time reversible, i.e., every solution p(x, t) has a temporal mirror solution p(x, -t). Analysis shows that time reversal also holds for the lossless nonlinear wave equation. In both cases, time-reversal invariance is violated when losses are present. For nonlinear propagation loses cannot normally be ignored; they are necessary to prevent the occurrence of multivalued waveforms. Further analysis of the nonlinear wave equation shows that amplification of a time-reversed pulse at the array elements also leads to a violation of time reversal even for lossless nonlinear acoustics. Numerical simulations are used to illustrate the effect of nonlinearity on the ability of a time-reversal system to effectively focus on a target in an absorbing fluid medium. We consider both the amplitude and arrival time of retrodirected pulses. The numerical results confirm that both shock generation (with the accompanying absorption) and amplification at the array, adversely affect the ability of a time-reversal system to form strong retrodirective sound fields.     

Vector Diffraction Integrals for Solving Inverse Problems of Radio-Holographic Sensing of the Earth's Surface and Atmosphere

Vector relationships between the fields on a certain surface confining an inhomogeneous three-dimensional volume and the fields inside this volume are obtained by the Stratton–Chu method developed for the case of homogeneous media. The vector relationships allow us to solve the direct and inverse problems of determining the fields inside an inhomogeneous medium given the field on its boundary. The vector equations take into acount the polarization changes of direct and inverse waves propagated in an inhomogeneous medium. In the case of a two-dimensional homogeneous medium, the vector equations reduce to the previously obtained scalar equations used in the approximation of spherical symmetry to describe the process of backward wave propagation during the atmospheric and ionospheric radio-occultation monitoring. It is shown that the Green's function of the scalar wave equation in an inhomogeneous medium should be used as the reference signal for solving the inverse problem of radio-occultation monitoring. This validates the method of focused synthetic aperture previously used for high-accuracy retrieval of the vertical refractive-index profiles in the ionosphere and atmosphere. In this method, the reference-signal phase was determined from a model which describes with sufficient accuracy the radiophysical parameters of a refracting medium in the region of radio-occultation sensing. The obtained equations can be used for the high-accuracy solving of inverse problems of radio-holographic sensing of the Earth's atmosphere and surface by precision signals from radio-navigation satellites.     

Mean-field model for Josephson oscillation in a Bose-Einstein condensate on an one-dimensional optical trap

Using the axially-symmetric time-dependent Gross-Pitaevskii equation we study the phase coherence in a repulsive Bose-Einstein condensate (BEC) trapped by a harmonic and an one-dimensional optical lattice potential to describe the experiment by Cataliotti et al. on atomic Josephson oscillation [Science 293, 843 (2001)]. The phase coherence is maintained after the BEC is set into oscillation by a small displacement of the magnetic trap along the optical lattice. The phase coherence in the presence of oscillating neutral current across an array of Josephson junctions manifests in an interference pattern formed upon free expansion of the BEC. The numerical response of the system to a large displacement of the magnetic trap is a classical transition from a coherent superfluid to an insulator regime and a subsequent destruction of the interference pattern in agreement with the more recent experiment by Cataliotti et al. [New J. Phys. 5, 71 (2003)].Received: 20 March 2003, Published online: 30 July 2003PACS: 03.75.-b Matter waves - 03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices and topological excitations - 03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow     

Instability of oscillations in the flow moving through a random medium as the counterpart of the localization of waves in a passive random medium

This paper deals with waves propagating in a one-dimensional flow moving through a randomly layered medium. The flow velocity is assumed to be greater than the group velocity of the waves in the reference system of the flow. As a result, in the laboratory reference system, all the waves propagate in a single direction. Amplitudes of these waves moving through a randomly inhomogeneous medium are growing exponentially. This effect is analogous to the wave localization phenomenon in a randomly inhomogeneous passive medium. The only difference is that the wave propagation in a passive medium is described by the boundary value problem, while all the oscillations in a medium with flow propagate in a single direction and hence the corresponding problem is formulated in the form of the initial value Cauchy problem. In the former case exponentially decreasing solutions are realized in the direction of the wave incidence, while in the latter case (as in the case of parametric resonances) the exponentially increasing solutions are realized.