Axis Of Wave Propagation Research Articles

Unravelling anisotropic nonlinear shear elasticity in muscles: Towards a non-invasive assessment of stress in living organisms

Acoustoelasticity theory describes propagation of shear waves in uniaxially stressed medium and allows the retrieval of nonlinear elastic coefficients of tissues. In transverse isotropic medium such as muscles the theory leads to 9 different configurations of propagating shear waves (stress axis vs. fibers axis vs. shear wave polarization axis vs. shear wave propagation axis). In this work we propose to use 4 configurations to quantify these nonlinear parameters ex vivo and in vivo. Ex vivo experiments combining ultrasound shear wave elastography and mechanical testing were conducted on iliopsoas pig muscles to quantify three third-order nonlinear coefficients A, H and K that are possibly linked to the architectural structure of muscles. In vivo experiments were performed with human volunteers on biceps brachii during a stretching exercise on an ergometer. A combination of the third order nonlinear elastic parameters was assessed. The knowledge of this nonlinear elastic parameters paves the way to quantify in vivo the local forces produced by muscle during exercise, contraction or movements.

A Broadband Radial Power Combiner Using a Dipole Antenna-Based TM Mode Transducer

A TM01 mode transducer based on dipole antenna is proposed to design a broadband and low-loss radial power combiner at Ka-band (26.5–40 GHz). It is an essential component in the radial power combiners to convert the electromagnetic modes between rectangular and circular waveguides. The latter feeds the cylindrical cavity in TM01 mode of which the fields exhibit a circular symmetry. The proposed TM01 mode transducer consists of the dipole antenna, microstrip, and probe on a dielectric substrate. It is an in-line mode transducer. In other words, the rectangular and circular waveguides are aligned along the same axis of wave propagation. Therefore, it does not require the waveguide components such as tee junctions, steps, and bends which are normally used in the traditional mode transducers and increase the complexity, size, and loss of entire power combiner. The eight-way radial junction is also designed using a cylindrical cavity, where the rectangular waveguides are placed along the circumference of the cylindrical cavity. The dimensions of each component are determined based on the full-wave electromagnetic simulations. The designed eight-way radial power combiner consisting of the TM01 mode transducer and radial junction is fabricated in four-split blocks by mechanical machining. In the measurements, the proposed power combiner exhibits a broadband and low-loss performance under a compact size while maintaining the magnitude and phase balances between the eight ports.

Optical trapping of a perfect electromagnetic conductor (PEMC) sphere exhibiting rotary polarization using nonparaxial focused Gaussian single-beam tweezers

A perfect electromagnetic conductor (PEMC) sphere illuminated by linearly-polarized plane progressive waves is known to experience a positive/repulsive force regardless of the sphere size. The present analysis shows that the situation changes when a Rayleigh (small) PEMC sphere is located along the axis of wave propagation of a linearly-polarized nonparaxial focused Gaussian beam. A negative longitudinal force arises as the sphere is translated beyond the center of the focus in the diverging region of the beam along the axis of wave propagation. Mathematical series related to the co-polarized and cross-polarized force components are derived. An exact expression for the on-axis beam-shape coefficients (BSCs) representing the incident nonparaxial focused Gaussian beam is obtained stemming from the complex source-point (CSP) method. The BSCs are compared to the standard solution obtained using the principle of localization. The case of plane progressive waves is recovered for a highly collimated nonparaxial focused Gaussian beam. In addition, the scattering asymmetry parameter is derived. Computations for the longitudinal radiation force efficiency, the dimensionless scattering asymmetry parameter, and the co-polarized and cross-polarized components are presented and discussed. In the Rayleigh regime, the results for the PEMC sphere show that the co-polarized component of the radiation force efficiency is negative beyond the center of the focal spot, while it is positive in the converging region of the beam. Trapping occurs when the longitudinal force vanishes. The cross-polarized radiation force efficiency is always positive, and counteracts the pulling force. Moreover, the scattering asymmetry parameter and its cross-polarized component are always negative while its co-polarized component is positive. Computations for the force efficiency for a radially-polarized nonparaxial focused Gaussian beam are also performed and compared to those obtained using a linearly-polarized focused field. Although the linearly-polarized focused beam induces larger pulling longitudinal force, improved spatial confinement with radial polarization is achieved.

Dynamic acoustic tractor beams II: Oscillatory powers, cross sections, and energy efficiencies of a spherical non-viscous liquid droplet

A previous work on dynamic acoustic tractor beams [Mitri, J. Appl. Phys. 117, 094903 (2015)] demonstrated the feasibility of pulling a liquid sphere toward a finite circular piezo-disk transducer and vibrating it around an equilibrium position at the beat frequency of two interfering waves driven at slightly different frequencies. The analysis is extended here to investigate the oscillatory phenomenon from the standpoint of energy conservation applied to scattering. Expressions for dynamic scattering, extinction and absorption powers, and their related cross sections and energy efficiencies are formally defined and derived based on the partial-wave series expansion method in spherical coordinates and the short-term time averaging (STTA) procedure. A circular flat piston transducer insonifying a spherical liquid hexane droplet (with arbitrary radius) centered on the axis of wave propagation is considered. Numerical predictions for dynamic extinction and scattering energy efficiencies illustrate the theory. A percentage error criterion related to extinction and scattering energy efficiencies is defined. Computations are also performed to quantify the numerical inaccuracy introduced by the difference-frequency component of the STTA. This criterion must be always utilized as a benchmark tool to validate dynamic radiation force computations. The results show that the percent error (induced by the difference-frequency component of the STTA process) increases as the dimensionless difference-frequency Δka increases. The present analysis is of some importance to validate dynamic radiation force numerical computations from the standpoint of energy conservation, used in the design and optimization of dynamic/oscillatory acoustic tractor beams and single-beam tweezers.

Ultrasonic focusing with mesoscale polymer cuboid

In this paper, we demonstrate that, contrary to what the Geometrical Optics laws dictate, a flat polymer mesoscale cuboid immersed in water with no need of negative refraction can focus sound. Two main polymers were considered and lens parameters compared: PMMA and Rexolite®. It was concluded that Rexolite® is preferable for acoustic jet formation. The nature of the formation of the foci along the longitudinal axis, that is to say along the wave propagation axis, is numerically and experimentally demonstrated. In addition, the conditions under which a cubic particles lens of this type forms a single localized region with a sub-diffraction transverse size (approximately 0.44 wavelength) are determined. The comparisons of the acoustic wave pressures and the focal distance between the Finite Element Method based numerical results and the experimental results show fair agreement.

Leveraging the arrangement of multiple, critically constrained inclusions in resonant metamaterials for control of broadband vibroacoustic energy

In many applications, unwanted vibroacoustic energies are broadband and concentrated at low frequencies, which presents a challenge for resonance-based dampers and lightweight materials to abate such energies. Recent studies have shown that utilizing the elastic stability limit in elastomeric inclusions can lead to a theoretically unbounded increase in macroscopic damping properties. Additionally, by embedding multiple, distributed masses within poroelastic media, the ability of the media to suppress acoustic energy is increased beyond the inherent attenuation characteristics of the foam itself. To understand the interaction between these two phenomena, this research experimentally characterizes the influences of strategically arranging multiple, critically constrained inclusions to tailor the vibroacoustic damping properties of poroelastic, resonant metamaterials. It is found that that such metamaterials are more effective when two adjacent inclusions are more widely spaced in the axis of wave propagation and in different planes orthogonal to the plane wave. The evidence also suggests that inclusions aligned in the axes normal to the wavefront direction especially promote vibroacoustic energy absorption. Arrangements of multiple inclusions are demonstrated to be robust, in that non-ideal, inclusion designs lead to metamaterials that remain effective to attenuate broadband energy. Moreover, these engineered inclusions are compared to traditional solid inclusions, and are shown to have similar or greater energy suppression while using around 40% less mass.

Radiation force and torque of light-sheets

The aim of this work is to provide exact analytical closed-form expressions for the longitudinal and transverse optical radiation force and axial spin torque components, for a 2D surface cross-section with arbitrary shape in the field of light-sheet beams of arbitrary wavefront. Generalized partial-wave series expressions for the longitudinal and transverse optical radiation forces and torque are derived based on the multipole expansion in cylindrical wave functions, stemming from series expansions for the incident and scattered electromagnetic fields. The incident light-sheet wavefields are expressed using generalized series involving the beam-shape coefficients (BSCs), and the scattered fields are given in terms of series involving the scattering coefficients of the object. Numerical illustrative examples on a dielectric absorptive circular cylindrical cross-section are provided for different wavefronts, ranging from plane waves, as well as non-paraxial scalar Airy and Gaussian light-sheet beams. The BSCs are derived based on the angular spectrum decomposition method, which provides adequate means to evaluate the radiation force and torque components when the cylinder cross-section is centered on the beam, or shifted off-axially with respect to the incident axis of wave propagation. In essence, the present theoretical analysis provides a complete formalism in the framework of the generalized Lorenz–Mie theory in 2D based upon exact closed-form series expressions to compute the optical force and torque components induced by 2D light-sheets of arbitrary wavefronts, illuminating a scatterer with an arbitrary geometrical cross-section (in 2D). Possible applications are in particle transport and rotation.

Axial acoustic radiation force on rigid oblate and prolate spheroids in Bessel vortex beams of progressive, standing and quasi-standing waves

The analysis using the partial-wave series expansion (PWSE) method in spherical coordinates is extended to evaluate the acoustic radiation force experienced by rigid oblate and prolate spheroids centered on the axis of wave propagation of high-order Bessel vortex beams composed of progressive, standing and quasi-standing waves, respectively. A coupled system of linear equations is derived after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid, and solved numerically by matrix inversion after performing a single numerical integration procedure. The system of linear equations depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated but converging PWSEs in the least-squares sense. Numerical results for the radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface, are computed with particular emphasis on the amplitude ratio describing the transition from the progressive to the pure standing waves cases, the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle and order of the Bessel vortex beam, as well as the dimensionless size parameter. A generalized expression for the radiation force function is derived for cases encompassing the progressive, standing and quasi-standing waves of Bessel vortex beams. This expression can be reduced to other types of beams/waves such as the zeroth-order Bessel non-vortex beam or the infinite plane wave case by appropriate selection of the beam parameters. The results for progressive waves reveal a tractor beam behavior, characterized by the emergence of an attractive pulling force acting in opposite direction of wave propagation. Moreover, the transition to the quasi-standing and pure standing wave cases shows the acoustical tweezers behavior in dual-beam Bessel vortex beams. Applications in acoustic levitation, particle manipulation and acousto-fluidics would benefit from the results of the present investigation.

Optical pulling force on a magneto-dielectric Rayleigh sphere in Bessel tractor polarized beams

The optical radiation force induced by Bessel (vortex) beams on a magneto-dielectric subwavelength sphere is investigated with particular emphasis on the beam polarization and order l (or topological charge). The analysis is focused on identifying the regions and some of the conditions to achieve retrograde motion of the sphere centered on the axis of wave propagation of the incident beam, or shifted off-axially. Exact non-paraxial analytical solutions are established, and computations for linear, circular, radial, azimuthal and mixed polarizations of the individual plane wave components forming the Bessel (vortex) beams by means of the angular spectrum decomposition method (ASDM) illustrate the theory with particular emphasis on the tractor (i.e. reversal) behavior of the force. This effect results in the pulling of the magneto-dielectric sphere against the forward linear momentum density flux associated with the incoming waves. Should some conditions related to the choice of the beam parameters as well as the permittivity and permeability of the sphere be met, the optical force vanishes and reverses sign. Moreover, the beam polarization is shown to affect differently the axial negative pulling force for either the zeroth- or the first-order Bessel beam. When the sphere is centered on the beam′s axis, the axial force component is always negative for the zeroth-order Bessel beam except for the radial and azimuthal polarization configurations. Nonetheless, for the first-order Bessel beam, the axial force is negative for the radial polarization case only. Additional tractor beam effects arise when the sphere departs from the center of the beam. It is also demonstrated that the tractor beam effect arises from the force component originating from the cross-interaction between the electric and magnetic dipoles. Potential applications are in particle manipulation, optical levitation, tractor beam tweezers, and other emergent technologies using polarized Bessel beams on a small (Rayleigh) magneto-dielectric particle.

Acoustic radiation force and spin torque on a viscoelastic cylinder in a quasi-Gaussian cylindrically-focused beam with arbitrary incidence in a non-viscous fluid

The axial and transverse acoustic radiation force components for a viscoelastic phenolic polymer circular cylinder placed arbitrarily in the field of a zeroth-order quasi-Gaussian focused beam in 2D are computed, based on the partial-wave series expansion (PWSE) method and Graf’s addition theorem for the cylindrical wave functions to compute the off-axial beam-shape coefficients. Moreover, the analysis is extended to derive the expression for the acoustic spin radiation torque experienced by the cylinder when the beam is shifted off-axially with respect to the axis of wave propagation. The emergence of the acoustic spin radiation torque experienced by the circular cylinder is a consequence of acoustic attenuation inside its absorptive material. Depending on the direction of the shift, the spin torque is negative or positive, causing the rotation of the cylinder in the polar plane in either the clockwise or the anticlockwise direction, respectively. Moreover, for a fixed position of the cylinder in the off-axial configuration, a spin torque reversal is predicted due to the variation of absorption of both the longitudinal and shear waves. The effect of increasing the surrounding fluid’s density is also investigated, which has a substantial effect on the radiation force and spin torque plots. Numerical results are performed with particular emphasis on the properties of the incident beam, the amount of the shift from the center of the cylinder as well as the properties of the surrounding fluid. The analytical formalism allows evaluating the axial and transverse radiation force components and radiation torque for any 2D beam that is generally an exact solution of the Helmholtz equation. The sought applications are in controlled rotation of a particle and its manipulation using “acoustical sheets” (i.e., finite beams in 2D).

Annular spherically focused ring transducers for improved single-beam acoustical tweezers

The use of ultrasonic transducers with a central hollow is suggested for improved single-beam acoustical tweezers applications. Within the framework of the Fresnel-Kirchhoff parabolic approximation, a closed-form partial-wave series expansion (PWSE) for the incident velocity potential (or pressure) field is derived for an annular spherically focused ring (asfr) with uniform vibration across its surface in spherical coordinates. The Rayleigh-Sommerfeld diffraction integral and the addition theorems for the Legendre and spherical wave functions are used to obtain the PWSE assuming a weakly focused beam (with a focusing angle α ≤ 20°). The PWSE allows evaluating the incident field from the finite asfr in 3D. Moreover, the obtained solution allows computing efficiently the acoustic scattering and radiation force on a sphere centered on the beam's axis of wave propagation. The analytical solution is valid for wavelengths largely exceeding the radius of the asfr and when the viscosity of the surrounding fluid can be neglected. Numerical predictions for the beam-forming, scattering, and axial time-averaged radiation force are performed with particular emphasis on the asfr thickness, the axial distance separating the sphere from the center of the transducer, the (non-dimensional) size of the transducer, as well as the sphere's elastic properties without restriction to the long- (i.e., Rayleigh) or the short-wavelength (i.e., ray acoustics) regimes. Potential applications of the present solution are in beam-forming design, particle tweezing, and manipulation due to negative forces using ultrasonic asfr transducers.

Acoustic radiation force on a rigid elliptical cylinder in plane (quasi)standing waves

The acoustic radiation force on a 2D elliptical (non-circular) cylinder centered on the axis of wave propagation of plane quasi-standing and standing waves is derived, based on the partial-wave series expansion (PWSE) method in cylindrical coordinates. A non-dimensional acoustic radiation force function, which is the radiation force per unit length, per characteristic energy density and per unit cross-sectional surface of the ellipse, is defined in terms of the scattering coefficients that are determined by applying the Neumann boundary condition for an immovable surface. A system of linear equations involving a single numerical integration procedure is solved by matrix inversion. Numerical simulations showing the transition from the quasi-standing to the (equi-amplitude) standing wave behaviour are performed with particular emphasis on the aspect ratio a/b, where a and b are the ellipse semi-axes, as well as the dimensionless size parameter kb (where k is the wavenumber), without the restriction to a particular range of frequencies. It is found that at high kb values > 1, the radiation force per length with broadside incidence is larger, whereas the opposite situation occurs in the long-wavelength limit (i.e., kb < 1). The results are particularly relevant in acoustic levitation of elliptical cylinders, the acoustic stabilization of liquid columns in a host medium, acousto-fluidics devices, and other particle dynamics applications to name a few. Moreover, the formalism presented here may be effectively applied to compute the acoustic radiation force on other 2D surfaces of arbitrary shape such as super-ellipses, Chebyshev cylindrical particles, or other non-circular geometries.

Acoustical pulling force on rigid spheroids in single Bessel vortex tractor beams

The theoretical formalism for acoustical Bessel vortex (helicoidal) tractor beams and results presented here are the first to demonstrate the emergence of a pulling force of attraction on non-spherical oblate and prolate rigid spheroidal particles centered on the beam's axis of wave propagation. Numerical predictions for the axial acoustic radiation force illustrate the theory with particular emphasis on the aspect ratio of the spheroid, the half-cone angle and order of the beam, as well as the dimensionless size parameter. It is demonstrated here that the Bessel vortex beam parameters may be tailored in such a way that the spheroid is pulled against the forward linear momentum density flux associated with the incoming waves. Those results potentially suggest the use of Bessel vortex beams in the development of emergent technologies for non-contact remote sampling and particle characterization.

Acoustical tweezers using single spherically focused piston, X-cut, and Gaussian beams

Partial-wave series expansions (PWSEs) satisfying the Helmholtz equation in spherical coordinates are derived for circular spherically focused piston (i.e., apodized by a uniform velocity amplitude normal to its surface), X-cut (i.e., apodized by a velocity amplitude parallel to the axis of wave propagation), and Gaussian (i.e., apodized by a Gaussian distribution of the velocity amplitude) beams. The Rayleigh-Sommerfeld diffraction integral and the addition theorems for the Legendre and spherical wave functions are used to obtain the PWSEs assuming weakly focused beams (with focusing angle α ⩽ 20°) in the Fresnel-Kirchhoff (parabolic) approximation. In contrast with previous analytical models, the derived expressions allow computing the scattering and acoustic radiation force from a sphere of radius a without restriction to either the Rayleigh (a ≪ λ, where λ is the wavelength of the incident radiation) or the ray acoustics (a ≫λ) regimes. The analytical formulations are valid for wavelengths largely exceeding the radius of the focused acoustic radiator, when the viscosity of the surrounding fluid can be neglected, and when the sphere is translated along the axis of wave propagation. Computational results illustrate the analysis with particular emphasis on the sphere's elastic properties and the axial distance to the center of the concave surface, with close connection of the emergence of negative trapping forces. Potential applications are in single-beam acoustical tweezers, acoustic levitation, and particle manipulation.

Resonance scattering and radiation force calculations for an elastic cylinder using the translational addition theorem for cylindrical wave functions

The standard Resonance Scattering Theory (RST) of plane waves is extended for the case of any two-dimensional (2D) arbitrarily-shaped monochromatic beam incident upon an elastic cylinder with arbitrary location using an exact methodology based on Graf’s translational addition theorem for the cylindrical wave functions. The analysis is exact as it does not require numerical integration procedures. The formulation is valid for any cylinder of finite size and material that is immersed in a nonviscous fluid. Partial-wave series expansions (PWSEs) for the incident, internal and scattered linear pressure fields are derived, and the analysis is further extended to obtain generalized expressions for the on-axis and off-axis acoustic radiation force components. The wave-fields are expressed using generalized PWSEs involving the beam-shape coefficients (BSCs) and the scattering coefficients of the cylinder. The off-axial BSCs are expressed analytically in terms of an infinite PWSE with emphasis on the translational offset distance d. Numerical computations are considered for a zeroth-order quasi-Gaussian beam chosen as an example to illustrate the analysis. Acoustic resonance scattering directivity diagrams are calculated by subtracting an appropriate background from the expression of the scattered pressure field. In addition, computations for the radiation force exerted on an elastic cylinder centered on the axis of wave propagation of the beam, and shifted off-axially are analyzed and discussed.

Interaction of an acoustical 2D-beam with an elastic cylinder with arbitrary location in a non-viscous fluid

The classical Resonance Scattering Theory (RST) for plane waves in acoustics is generalized for the case of a 2D arbitrarily-shaped beam incident upon an elastic cylinder with arbitrary location that is immersed in a nonviscous fluid. The formulation is valid for an elastic (or viscoelastic) cylinder (or a cylindrical shell, a layered cylinder/shell, or a multilayered cylindrical shell, etc.) of any size and material. Partial-wave series expansions (PWSEs) for the incident, internal and scattered fields are derived, and numerical examples illustrate the theory. The wave-fields are expressed using a generalized PWSE involving the beam-shape coefficients (BSCs) and the scattering coefficients of the cylinder. When the beam is shifted off the center of the cylinder, the off-axial BSCs are evaluated by performing standard numerical integration. Acoustic resonance scattering directivity diagrams are calculated by subtracting an appropriate background from the expression of the scattered pressure field. The properties related to the arbitrary scattering of a zeroth-order quasi-Gaussian cylindrical beam (chosen as an example) by an elastic brass cylinder centered on the axis of wave propagation of the beam, and shifted off-axially are analyzed and discussed. Moreover, the total and resonance backscattering form function moduli are numerically computed, and the results discussed with emphasis on the contribution of the surface waves circumnavigating the cylinder circular surface to the resonance backscattering. Furthermore, the analysis is extended to derive general expressions for the axial and transverse acoustic radiation force functions for the cylinder in any 2D beam of arbitrary shape. Examples are provided for a zeroth-order quasi Gaussian cylindrical beam with different waist. Potential applications are in underwater and physical acoustics, however, ongoing research in biomedical ultrasound, non-destructive evaluation, imaging, manufacturing, instrumentation, and acoustic holography to name a few, would benefit from the results of this analysis.

Acoustic radiation force on oblate and prolate spheroids in Bessel beams

A formal theoretical analysis is developed using the partial-wave series expansion (PWSE) method in spherical coordinates, which allows accurate evaluation of the acoustic radiation force (ARF) of a Bessel beam incident upon a rigid oblate or prolate spheroid, centered on its axis of wave propagation. The scattering coefficients for either the oblate or the prolate spheroid are determined based on Neumann’s boundary condition for a rigid immovable surface, and used to compute the ARF function, which is the radiation force per unit characteristic energy density and surface cross-section of the spheroid. Numerical results are performed with particular emphasis on the waves’ amplitude ratio describing the evolution from progressive (traveling), quasi-standing and pure Bessel standing waves, the half-cone angle β of the beam, and the aspect ratio (i.e. the distance from the center to pole along the symmetry axis a divided by the equatorial radius b) of the spheroid. Unlike the results obtained in the Rayleigh limit (i.e., ka≪1, where k is the wavenumber of the incident illuminating waves), calculations for the ARF functions for progressive, quasi-standing and standing Bessel waves for ka>1, generally reveal larger amplitudes for an oblate rather than a prolate spheroid having the same surface cross-section. Exceptions are also noted for Bessel beams with a large half-cone angle. Potential applications are in acoustic levitation of dense spheroids in air, particle dynamics, and other related research.

Partial-wave series expansions in spherical coordinates for the acoustic field of vortex beams generated from a finite circular aperture.

Stemming from the Rayleigh-Sommerfeld surface integral, the addition theorems for the spherical wave and Legendre functions, and a weighting function describing the behavior of the radial component vp1 of the normal velocity at the surface of a finite circular radiating source, partial-wave series expansions are derived for the incident field of acoustic spiraling (vortex) beams in a spherical coordinate system centered on the axis of wave propagation. Examples for vortex beams, comprising ρ-vortex, zeroth-order and higher order Bessel-Gauss and Bessel, truncated Neumann-Gauss and Hankel- Gauss, Laguerre-Gauss, and other Gaussian-type vortex beams are considered. The mathematical expressions are exact solutions of the Helmholtz equation. The results presented here are particularly useful to accurately evaluate analytically and compute numerically the acoustic scattering and other mechanical effects of finite vortex beams, such as the axial and 3-D acoustic radiation force and torque components on a sphere of any (isotropic, anisotropic, etc.) material (fluid, elastic, viscoelastic, etc.), either centered on the beam's axis of wave propagation, or placed off-axially. Numerical predictions allow optimal design of parameters in applications including but not limited to acoustical tweezers, acousto-fluidics, beamforming design, and imaging, to name a few.

Producing acoustic ‘Frozen Waves’: Simulated experiments with diffraction/attenuation resistant beams in lossy media

The so-called Localized Waves (LW), and the “Frozen Waves” (FW), have raised significant attention in the areas of Optics and Ultrasound, because of their surprising energy localization properties. The LWs resist the effects of diffraction for large distances, and possess an interesting self-reconstruction —self-healing— property (after obstacles with size smaller than the antenna’s); while the FWs, a sub-class of LWs, offer the possibility of arbitrarily modeling the longitudinal field intensity pattern inside a prefixed interval, for instance 0⩽z⩽L, of the wave propagation axis. More specifically, the FWs are localized fields “at rest”, that is, with a static envelope (within which only the carrier wave propagates), and can be endowed moreover with a high transverse localization.In this paper we investigate, by simulated experiments, various cases of generation of ultrasonic FW fields, with the frequency of f0=1MHz in a water-like medium, taking account of the effects of attenuation. We present results of FWs for distances up to L=80mm, in attenuating media with absorption coefficient α in the range 70⩽α⩽170dB/m.Such simulated FW fields are constructed by using a procedure developed by us, via appropriate finite superpositions of monochromatic ultrasonic Bessel beams.We pay due attention to the selection of the FW parameters, constrained by the rather tight restrictions imposed by experimental Acoustics, as well as to some practical implications of the transducer design.The energy localization properties of the Frozen Waves can find application even in many medical apparatus, such as bistouries or acoustic tweezers, as well as for treatment of diseased tissues (in particular, for the destruction of tumor cells, without affecting the surrounding tissues; also for kidney stone shuttering, etc.).

Attraction by sound—examples on the negative acoustic radiation forces of Bessel “tractor” beams on a sphere

Expressions for the axial (i.e. acting along the axis of wave propagation) and transverse (lateral) acoustic radiation forces on a suspended object in an ideal fluid are derived for arbitrary shaped beams. These expressions are obtained from the integration of the radiation stress tensor in the far-field. Numerical examples on non-vortex and vortex Bessel beams on a spherical target are presented. It is demonstrated the existence of both “pushing” and “tractor” behaviors for which the axial force can be oriented, respectively, along the direction of wave propagation or opposite to it. This can be adjusted by choosing specific values of the beam cone angle and the sphere size factor ka (where k is the wavenumber and a is the sphere's radius). Furthermore, by changing the topological charge m of the beam and the position of the sphere, the transverse force may be oriented radially (outward or inward) for m=0 or may exhibit a vortex pattern for m ≥ 1.