An expression is derived for the radiation force on a sphere placed on the axis of an ideal acoustic Bessel beam propagating in an inviscid fluid The expression uses the partial-wave coefficients found in the analysis of the scattering when the sphere is placed in a plane wave traveling in the same external fluid The Bessel beam is characterized by the cone angle β of its plane wave components where β=0 gives the limiting case of an ordinary plane wave Examples are found for fluid spheres where the radiation force reverses in direction so the force is opposite the direction of the beam propagation Negative axial forces are found to be correlated with conditions giving reduced backscattering by the beam This condition may also be helpful in the design of acoustic tweezers for biophysical applications Other potential applications include the manipulation of objects in microgravity Islands in the (ka,β) parameter plane having a negative radiation force are calculated for the case of a hexane drop in w

Axial radiation force of a bessel beam on a sphere and direction reversal of the force.

The exact scattering by a sphere centered on a Bessel beam is expressed as a partial wave series involving the scattering angle relative to the beam axis and the conical angle of the wave vector components of the Bessel beam. The sphere is assumed to have isotropic material properties so that the nth partial wave amplitude for plane wave scattering is proportional to a known partial-wave coefficient. The scattered partial waves in the Bessel beam case are also proportional to the same partial-wave coefficient but now the weighting factor depends on the properties of the Bessel beam. When the wavenumber-radius product ka is large, for rigid or soft spheres the scattering is peaked in the backward and forward directions along the beam axis as well as in the direction of the conical angle. These properties are geometrically explained and some symmetry properties are noted. The formulation is also suitable for elastic and fluid spheres. A partial wave expansion of the Bessel beam is noted.

Scattering of a Bessel beam by a sphere

We report zero-th and high-order acoustic Bessel beams with broad depth-of-field generated using acoustic holograms. While the transverse field distribution of Bessel beams generated using traditional passive methods is correctly described by a Bessel function, these methods present a common drawback: the axial distribution of the field is not constant, as required for ideal Bessel beams. In this work, we experimentally, numerically and theoretically report acoustic truncated Bessel beams of flat-intensity along their axis in the ultrasound regime using phase-only holograms. In particular, the beams present a uniform field distribution showing an elongated focal length of about 40 wavelengths, while the transverse width of the beam remains smaller than 0.7 wavelengths. The proposed acoustic holograms were compared with 3D-printed fraxicons, a blazed version of axicons. The performance of both phase-only holograms and fraxicons is studied and we found that both lenses produce Bessel beams in a wide range of frequencies. In addition, high-order Bessel beam were generated. We report first order Bessel beams that show a clear phase dislocation along their axis and a vortex with single topological charge. The proposed method may have potential applications in ultrasonic imaging, biomedical ultrasound and particle manipulation applications using passive lenses.

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Generating Bessel beams with broad depth-of-field by using phase-only acoustic holograms.

Time-reversed acoustics (TRA) has been developed in the last few years as a powerful tool for several applications, based on the theoretical properties emerging from the time reversal invariance of the wave equation. TRA is expected to be a good basis for the development of imaging techniques in the field of nondestructive evaluation. For this purpose, however, data processing is necessary to discriminate between images due to defects (in general nonlinear scatterers) and images due to linear inclusions, boundaries, etc. We propose here an approach based on the filtering of the time signals. The image of the scatterer is obtained through numerical simulations of the back propagation in a fictitious reference specimen. We validate the approach using the inversion of synthetic data. We also estimate the robustness of the procedure in the presence of constraints that can occur in any experimental procedure.

Efficiency of time-reversed acoustics for nonlinear damage detection in solids

The nonlinear parameter of ultrasound B/A has shown to be a useful diagnostic parameter, reflecting medium content, structure, and temperature. Despite its recognized values, B/A is not yet used as a diagnostic tool in the clinic due to the limitations of current measurement and imaging techniques. This review presents an extensive and comprehensive overview of the techniques developed for B/A measurement of liquid and liquid-like media (e.g., tissue), identifying the methods that are most promising from a clinical perspective. This work summarizes the progress made in the field and the typical challenges on the way to B/A estimation. Limitations and problems with the current techniques are identified, suggesting directions that may lead to further improvement. Since the basic theory of the physics behind the measurement strategies is presented, it is also suited for a reader who is new to nonlinear ultrasound.

/pdf/a-review-on-b-a-measurement-methods-with-a-clinical-3lk4zz9kww.pdf

A review on B/A measurement methods with a clinical perspective

Numerical simulations based on the nonlinear parabolic wave equation are used to investigate time reversal of sound beams radiated by unfocused and focused sources. Emphasis is placed on nonlinear propagation distortion in the time-reversed beam, and specifically its effect on field reconstruction. Distortion of this kind, due to amplification during time reversal, has been observed in recent experiments [A. P. Brysev et al., Acoust. Phys. 44, 641–650 (1998)]. Effects of diffraction introduced by time-reversal mirrors with finite apertures are also considered. It is shown that even in the presence of shock formation, the ability of time reversal to retarget most of the energy on the source or focal region of the incident beam is quite robust.

Time-reversed sound beams of finite amplitude.

Second-harmonic generation in a Bessel beam is investigated analytically, with emphasis on the effect of absorption. It is shown that absorption has a strong influence on the far-field beam profile. Numerical results are presented for higher harmonics and for waveform distortion in a Bessel beam that forms a shock.

Bessel beams of finite amplitude in absorbing fluids

Nonlinear propagation of a quasi-plane conjugate ultrasonic beam

Nonlinear propagation of phase-conjugate, focused, ultrasound beams is studied. Measurements are presented of harmonic amplitudes along the axis and in the focal plane of the conjugate beam, and of the waveform and spectrum at the focus. A maximum peak pressure of 3.9 MPa was recorded in the conjugate beam. The measurements are compared with simulations based on the KZK equation, and satisfactory agreement is obtained.

K. B. Cunningham

Papers

Time-reversed sound beams of finite amplitude.

Bessel beams of finite amplitude in absorbing fluids

Nonlinear propagation of a quasi-plane conjugate ultrasonic beam

Nonlinear propagation of phase-conjugate focused sound beams in water