Partial-wave Series Expansion Research Articles

Optical radiation force and torque of light-sheets on a cylindrical particle near an infinite boundary

This work aims to extend the previous studies on the optical radiation force and torque for a cylindrical dielectric particle to the case near an infinite boundary. Without loss of generality, the two-dimensional cylindrical object is assumed to have an arbitrary shape and be immersed in any light-sheet beam of arbitrary wave front. The partial-wave series expansion method in cylindrical coordinates and the method of images are utilized to derive the exact expressions for the axial and transverse radiation force and torque functions, which are dependent on the beam shape coefficients of the incident light-sheet and the scattering coefficients characterized by the boundary conditions at the surface. Numerical computations are performed for a circular cylindrical particle illuminated by a two-dimensional plane wave and a two-dimensional Gauss beam, respectively, with particular emphases on the size parameter, the refractive index, the particle-boundary distance, the beam waist and the offset shifts. The radiation force will increase in magnitude and reverse its direction under selected conditions. When the absorptive cylindrical particle is shifted off-axially with respect to the beam axis, it will be rotated counterclockwise or clockwise by the radiation torque. The results obtained in this work have potential applications in non-contact particle manipulation and transportation using optical tweezers.

Curved photonic nanojet generated by a rotating cylinder.

The curved photonic nanojet (CPNJ) produced due to the interaction between a dielectric circular cylinder rotating at a stable angular velocity and a plane wave is investigated. Based on this model, the optical Magnus effect of a dielectric circular cylinder is verified. And the analytical expression of both internal and external electric field are given based on the instantaneous rest-frame theory and the partial-wave series expansion method in cylindrical coordinates. The influence of the size parameter, the relative refractive index, and the rotating dimensionless parameter on the CPNJ are analyzed and discussed in numerical results. The "photonic nanojet curved" effect is highlighted, which can be used to generate the off-axis photonic nanojet (PNJ) controlling particles by adjusting the angular velocity of the dielectric cylinder. The results of this manuscript have promising application prospects in optical tweezers, particle manipulation, and optical trapping. Moreover, it also provides theoretical support for the particle spinning and generation of the off-axis CPNJ.

Acoustic radiation torque of a cylindrical quasi-Gauss beam on a viscoelastic cylindrical shell near an impedance boundary

This work presents a comprehensive analytical formalism to calculate the acoustic radiation torque acting on a viscoelastic cylindrical shell near an impedance boundary, which is exerted by a cylindrical quasi-Gauss beam with an arbitrary incident angle propagating in an ideal fluid. An analytical expression in finite series form for the acoustic radiation torque is derived by applying the partial-wave series expansion method, the image theory and the translational addition theorem. Numerical computations for a viscoelastic cylindrical polyethylene shell immersed in water are provided, with particular emphasis on the effects of the reflecting coefficient of the interface, the shell-boundary distance, the position of the shell, the incident angle and the beam waist. Changing the relative thickness and the interior fluid medium are also considered. It is shown that the cylindrical shell can be rotated counter-clockwise or clockwise, depending on the beam frequency, the shell size, the reflecting coefficient and the incident angle. The periodical oscillation of acoustic radiation torque is also observed as the shell moves away from the boundary. The results of this study can improve our understanding of the acoustic radiation torque behaviors for viscoelastic particles near the boundary, which is commonly encountered in biomedical ultrasound and fluid dynamics.

Optical Magnus effect in the photophoresis of a spinning absorptive dielectric circular cylinder.

When a stationary absorptive dielectric cylinder suspended in a gas (such as air) is illuminated by an axisymmetric wave field (such as plane waves), the transverse (T) photophoretic asymmetry factor (PAF) vanishes as required by geometrical symmetry [Appl. Opt.60, 7937 (2021) APOPAI0003-693510.1364/AO.435306]. Counter-intuitively, when the cylinder possesses an initial angular velocity Ω0 with a sufficiently small acceleration and spins around its main axis in the illuminating field of axisymmetric plane waves, it is shown here that the T-PAF (which is directly proportional to the T-photophoretic force vector component) is quantifiable, in analogy with the Magnus effect in hydrodynamics where a force perpendicular to the axis of the cylinder and to the propagation direction arises. Based upon the instantaneous rest-frame theory and the partial-wave series expansion method in cylindrical coordinates, the internal electric field of the spinning absorptive dielectric cylinder is determined and utilized to compute both the longitudinal (L) and T-PAFs. Particular emphases are given on the size parameter of the cylinder, its angular rotation, the light absorption inside its core material and the polarization (TM or TE) of the incident plane waves. The dimensionless intensity function (DIF) is also computed, which reveals quantitative information on the heated portions within the internal absorptive core material of the cylinder. Numerical computations illustrate the analysis and explicate the behaviors of the DIF and the L- and T-PAFs, which predict the emergence of the forward, neutral, and reverse optical/electromagnetic Magnus effect in the photophoresis of an absorptive dielectric cylinder and related applications in spin optics, optical tweezers, optical manipulation of elongated objects, and radiative transfer research.

Born approximation of acoustic radiation force and torque for an arbitrary particle in a zero-order standing Bessel beam

The calculation of acoustic radiation force and acoustic radiation torque is an important basis for the precise manipulation of particles. It is difficult to directly apply the partial-wave series expansion method based on the classical acoustic scattering theory to the study of complicated models, while pure numerical methods are not conducive to the parametric analyses of the system. Based on the basic principle of Born approximation, the expressions of acoustic radiation force and torque acting on an arbitrary particle located in the center of a zero-order Bessel standing wave field are derived at low frequencies. On this basis, the numerical simulations are systematically performed by taking spherical, spheroidal and cylindrical particles as examples. The effects of inhomogeneity on the acoustic radiation force and torque are also investigated. The simulation results show that the Born approximation method has a high accuracy in the low frequency range. As the frequency increases and the impedance matching between the particle and the fluid becomes worse, the accuracy of Born approximation will gradually decrease. An acoustic radiation torque caused by asymmetry will be exerted on spheroidal and cylindrical particles obliquely positioned in a zero-order Bessel standing wave field. When the particle size is much smaller than the wavelength, the acoustic radiation force is nearly independent of the particle shape, but this is not the case for acoustic radiation torque. Finally, viscous effect of the surrounding fluid is introduced and the expression of acoustic radiation force is corrected accordingly. The study is expected to provide a theoretical guide for the precise manipulation of small particles using standing wave acoustic tweezers in biomedicine and material sciences.

Longitudinal and transverse PAFs for an absorptive magneto-dielectric circular cylinder in light-sheets of arbitrary wavefronts and polarization.

Based upon the expression of the heat source function in photophoresis, generalized mathematical expressions for the longitudinal (L) and transverse (T) photophoretic asymmetry factors (PAFs) for a light-absorptive magneto-dielectric circular cylinder of arbitrary relative permittivity and permeability, illuminated by an arbitrarily shaped polarized light-sheet, are derived and computed. The L- and T-PAFs are directly proportional to the L and T components of the photophoretic force vector, respectively, induced by light absorption inside the particle, and their sign predicts the behavior of the force (pulling/attractive or pushing/repulsive). The partial-wave series expansion method in cylindrical coordinates is used, and the obtained mathematical expressions for the L- and T-PAFs depend on the beam-shape coefficients and the internal coefficients of the cylinder. Numerical examples illustrate the theory for TE and TM polarized plane waves, and nonparaxial Airy light-sheets with particular emphasis on absorption inside the cylinder and varying the Airy light-sheet parameters. The generalized expressions presented here are applicable to any light-sheet of an arbitrary wavefront, and offer additional quantitative observables for the analysis of the photophoretic force in applications in electromagnetic scattering, optical light-sheet tweezers, particle manipulation, radiative transfer, and other research fields.

Recursive algorithm for solving the axial acoustic radiation force exerted on rigid spheres at the focus of acoustic vortex beams

The trapping capability of focused acoustic vortex (FAV) beams along the radial and axial directions has significant potential in biomedical applications. However, analyses based on the acoustic gradient force are only applicable to tiny particles when acoustic scattering is neglected, and the ideal Bessel beams are still difficult to implement in experiments. In the present work, the axial acoustic radiation force (A-ARF) exerted on objects at the focus for FAV beams is calculated based on an annular spherical transducer with a continuous phase spiral. Through a partial wave series expansion, a recursive algorithm based on acoustic scattering is proposed to calculate the acoustic field for FAV beams with arbitrary order. The A-ARF distributions exerted on rigid spheres with respect to k0a (the product of the wave number and the sphere radius) are simulated. The results demonstrate that the A-ARF created by on-axis acoustic reflection is mainly manifested as a pushing force for FAV beams of all orders. The pulling force produced by off-axis scattering is more likely to be exerted on spheres with a smaller k0a in higher-order FAV beams constructed by narrower transducers. The A-ARF generated by a ring-array of sectorial transducers with more than 16 sources can be estimated from the equivalent result produced by the continuous model. The favorable results demonstrate the validity of the recursive algorithm for solving the A-ARF of FAV beams and the feasibility of experimental ring-arrays of spherical sources, suggesting the potential for the application of dual-directional object manipulation in biomedical fields.

Longitudinal and transverse optical scattering asymmetry parameters for a dielectric cylinder in light-sheets of arbitrary wavefronts and polarization.

The asymmetry parameter is an important quantity used in radiative transfer modeling and scattering. This parameter specifies the amount of energy scattered by the particle along the direction of the incident illuminating field. However, a rigorous and complete analysis of the energetic scattering requires determining the energy scattered in the lateral direction as well. As such, the present work introduces generalized expressions for the scattering asymmetry parameters for a dielectric cylinder in arbitrary-shaped light-sheets, both along and perpendicular to the direction of the incident radiation. Both longitudinal and transverse scattering asymmetry parameters are defined, and their generalized expressions are obtained based on the (spatial) average cosine and sine of the scattering angle θ and the expression of the scattering cross section (or energy efficiency). The partial-wave series expansion method in cylindrical coordinates is used, and the resulting mathematical expressions depend on the beam-shaped coefficients and the scattering coefficients of the dielectric cylinder. Numerical results for arbitrary-shaped light-sheets illuminating a dielectric cylinder cross section located arbitrarily in space are presented and discussed. The longitudinal and transverse scattering asymmetry parameters defined here offer additional quantitative (quadratic) observables for the analysis of the energetic scattering in applications in electromagnetic scattering, optical light-sheet tweezers, radiative transfer computations, and remote sensing, to name a few examples.

Acoustic radiation torque on an off-axis elliptical cylinder in Gauss beams

As one of the nonlinear effects of acoustic waves, the time-averaged acoustic radiation torque expression is derived from the transfer of angular momentum from the incident beam to the object. In recent years, the acoustic radiation torque has received substantial attention since it is the underlying principle of well-controlled particle rotations and spins, which provides a new degree of freedom in particle manipulation and acousto-fluidic applications in addition to the translational displacement caused by the acoustic radiation force. Cylindrical particles, such as fibers, carbon nanotubes and other surface acoustic wave devices, are commonly encountered in various applications. The acoustic scattering coefficients for an elliptical cylinder arbitrarily located at the field of Gauss beam in two-dimensions are computed based on the partial-wave series expansion method and the Graf’s additional theorem for cylindrical functions to obtain the off-axis beam shape coefficients. It is worth mentioning that both the rigid and non-rigid cylinders are considered in this work, which requires different boundary conditions at the cylinder surface. Moreover, the closed-form expression of the acoustic radiation torque in this case is derived. On this basis, several numerical simulations are performed with particular emphasis on the off-axis distance, the incident angle and the beam waist. The simulated results show that both the positive and negative acoustic radiation torque can exist under certain conditions, which means that 1) the elliptical cylinder can be rotated in either the clockwise or the counterclockwise direction, 2) rigid elliptical cylinders are more likely to experience a strong acoustic radiation torque than non-rigid elliptical cylinders at low frequencies, 3) the incident wave field with a specific frequency can excite a different resonance scattering mode for a non-rigid elliptical cylinder, therefore the acoustic radiation torque peak is more related to the beam frequency than to the elliptical cylinder’s location in the field, and 4) increasing the beam width can enlarge the scattering cross section area, and thus enhancing the acoustic radiation torque on the elliptical cylinder. The results in this study are expected to provide a theoretical guide for the controllable rotation of a particle and the viscosity inversion of fluid by using the acoustic radiation torque. The exact formalism presented here by using the multipole expansion method, which is valid for any frequency range, can be used to validate other approaches by using purely numerical methods.

Acoustic radiation force on a cylindrical particle near a planar rigid boundary II. – Viscous fluid cylinder example and inherent radiation torque

ObjectiveThis study extends the scope of a previous analysis on the time-averaged acoustic radiation force on a rigid (sound impenetrable) cylinder near a flat boundary [F.G. Mitri, J. Phys. Commun. 2 (2018) 045019] to the case of a viscous compressible fluid (sound penetrable) particle, and determine the time-averaged acoustic radiation torque as well. Motivation and noveltyPrevious analytical formalisms did not consider the case of a sound penetrable cylindrical particle insonified at an arbitrary angle of incidence (in the polar plane) near a reflecting boundary. This work fills this gap, and provides exact expressions and computations for the acoustic radiation force and torque components. MethodThe partial-wave series expansion method, in conjunction with the method of images and the translational addition theorem of cylindrical wave functions are used to derive the analytical expressions for the longitudinal and transverse acoustic radiation force components. Moreover, the emergence of a radiation torque that causes the particle to rotate around its center of mass is computed using an exact partial-wave series expression. Results, key conclusion and some perspectivesAttractive (pulling), repulsive (pushing) and neutral (zero) forces arise depending on the particle-boundary distance, the cylinder size parameter as well as the angle of incidence (in the polar plane) of the insonifying waves. Emphasis is also given on the emergence of an acoustic radiation torque (that vanishes for a rigid or non-viscous circular cylinder). Computations for the axial radiation torque efficiency anticipate the generation of positive radiation torque, its reversal, in addition to a zero efficiency, leading, respectively, to counter-clockwise, clockwise or lack of particle rotation as the angle of the incident waves deviates from normal incidence with respect to the boundary surface. The extension to the case of an elliptical/oval cylinder near a boundary is mentioned, and replies to some misleading and obtuse comments on the paper [F.G. Mitri, Phys. Fluids 28 (2016) 077104] are provided.

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.

Optical cross-sections and energy efficiencies of a cylindrical material exhibiting circular dichroism in arbitrary-shaped monochromatic light-sheets

Optical scattering, extinction and absorption cross-sections are derived for a cylindrical material exhibiting rotary polarization. A structured light-sheet of arbitrary shape illuminates the cylindrical particle of arbitrary geometrical cross-section. The partial-wave series expansion method in cylindrical coordinates is used and Poynting’s theorem is applied. Exact mathematical series expansions are obtained without any approximations. They demonstrate that the optical cross-sections are not the mere sum of linearly polarized components. Additional terms contributing to the series arise from the cross-interaction of the linearly polarized modes (known also as mode conversion TM ⇆ TE) in the scattering field. Numerical examples for the scattering or extinction energy efficiencies of a left-handed circularly polarized Airy light sheet illustrate the analysis for a circular perfect electromagnetic conductor cylinder in air. The results clearly demonstrate the contribution of mode conversion for a cylinder exhibiting circular dichroism. Under some specific conditions determined by the incident light-sheet characteristics and cylinder size, mode conversion can be zero, or it can contribute in the enhancement or reduction of the scattering.

Radiation force and torque on an elliptical cylinder illuminated by a TE-polarized non-paraxial focused Gaussian light sheet with arbitrary incidence.

Predicting and computing the optical radiation force and torque experienced by an elliptical cylinder illuminated by a structured finite light-sheet beam in two dimensions (2D) remains a challenge from the standpoint of light-matter interactions in electromagnetic (EM) optics, tweezers, laser trapping, and scattering theory. In this work, the partial-wave series expansion method in cylindrical coordinates (which utilizes standard Bessel and Hankel wave functions) is proposed, verified, and validated. Exact expressions for the longitudinal and transverse radiation force components (per length) as well as the axial radiation torque component (per length) are derived analytically without any approximations. The example of a TE-polarized non-paraxial focused Gaussian light sheet illuminating a perfect electrically conducting (PEC) elliptical cylinder is considered. The scattering coefficients of the elliptical cylinder are determined by imposing the Neumann boundary condition and numerically solving a linear system of equations by matrix inversion. The structural functions are determined using a single numerical angular integration procedure to enforce the orthogonality and thus validity of the solution, making the proposed method semi-analytical. Calculations are performed for the non-dimensional longitudinal and transverse radiation force efficiencies (or functions) as well as the axial radiation torque efficiency. Emphases are given to varying the ellipticity of the cylindrical particle, its non-dimensional size, the non-paraxial beam waist (i.e., focusing), and the angle of incidence in the polar plane. Suitable convergence plots confirm the validity of the partial-wave series method to evaluate accurately the radiation force and torque with no limitation to a particular frequency range or particle size. The results are mostly relevant in understanding the fundamentals of the optical/EM radiation force and torque theories for structured focused light sheets and related applications dealing with the interactions of EM waves with elongated tubular particles with elliptical surfaces in particle manipulation and other areas. The analogy with the acoustical counterpart is also noted, which shows the universal character of the radiation force and torque phenomena.

Induced radiation force of an optical line source on a cylinder material exhibiting circular dichroism.

The optical radiation force experienced by a cylinder material of circular cross section exhibiting circular dichroism (known also as rotary polarization) in an electric line source illumination is considered. An exact analytical expression for the radiation force (per length) valid for any frequency range is derived assuming an electric line source radiating cylindrically diverging TM-polarized waves without any approximations. The partial-wave series expansion method in cylindrical coordinates utilizing standard Bessel and Hankel functions is used to derive the electric and magnetic field expressions and a dimensionless radiation force function (or efficiency), which depends on the scattering coefficient of the cylinder as well as the distance from the radiating source. To illustrate the analysis, numerical computations for the dimensionless radiation force function for a perfect electromagnetic conductor (PEMC) cylinder are performed with emphasis on its dimensionless size parameter and source distance, which clearly draw attention to the contribution of the cross-polarized scattered waves (resulting from the rotary polarization effect) to the total force. The numerical predictions demonstrate the possibility to pull a circular-shaped cylinder material with rotary polarization toward the illuminating electric line source with TM-polarized waves using a curved wavefront depending on the PEMC material admittance, distance to the source, and size of the cylinder.

Electromagnetic radiation force on a perfect electromagnetic conductor (PEMC) circular cylinder

Unlike isotropic dielectric objects, the interaction of incident electromagnetic (EM) or optical waves with a material allowing rotary polarization produces coupled polarized internal and scattered fields. The aim of this investigation is to examine theoretically a novel physical effect, which concerns the contributions of the co-polarized and cross-polarized fields to the radiation force (per-length) experienced by an infinitely long perfect electromagnetic conductor (PEMC) cylinder having a circular cross-section and illuminated by TM-polarized plane progressive waves propagating perpendicularly to its axis. The multipole partial-wave series expansion method in cylindrical coordinates is used to derive exact series expansions for the co-polarized and cross-polarized components of the longitudinal radiation force per-length (i.e. acting along the direction of wave propagation). In contrast with the perfect electric or magnetic conductors (PECs or PMCs), or the dielectric cylinder case, numerical illustrative results for the radiation force function (which is the radiation force per unit energy density and cross-sectional surface) clearly demonstrate the contribution of the cross-polarized component of the radiation force for a PEMC cylinder allowing rotary polarization. The results show that the cross-polarized component of the radiation force function can be positive or negative as the dimensionless frequency parameter ka varies (where k is the wavenumber in the medium of wave propagation and a is the radius of the cylinder). Moreover, it vanishes for ka = 0.67946 regardless of the admittance of the PEMC cylinder. Notice that the total force (i.e. the sum of the co-polarized and cross-polarized components) is always repulsive (i.e., positive). It is also verified that the results are in complete agreement with the law of energy conservation applied to scattering. The present analysis generalizes the classical radiation force investigations by introducing extra new terms in the series expansion for the longitudinal radiation force function for cylindrical materials allowing rotary polarization.

The involvement of vaginal microbiome in threatened premature delivery

This investigation shows that an active emitting electromagnetic (EM) Dirichlet source (i.e., with axial polarization of the electric field) in a homogeneous non-dissipative/non-absorptive medium placed near a perfectly conducting boundary can render total invisibility (i.e. zero extinction cross-section or efficiency) in addition to a radiation force cancellation on its surface. Based upon the Poynting theorem, the mathematical expression for the extinction, radiation and amplification cross-sections (or efficiencies) are derived using the partial-wave series expansion method in cylindrical coordinates. Moreover, the analysis is extended to compute the self-induced EM radiation force on the active source, resulting from the waves reflected by the boundary. The numerical results predict the generation of a zero extinction efficiency, achieving total invisibility, in addition to a radiation force cancellation which depend on the source size, the distance from the boundary and the associated EM mode order of the active source. Furthermore, an attractive EM pushing force on the active source directed toward the boundary or a repulsive pulling one pointing away from it can arise accordingly. The numerical predictions and computational results find potential applications in the design and development of EM cloaking devices, invisibility and stealth technologies.

Scattering of an arbitrary order acoustical Bessel beam by a rigid off-axis spheroid.

In this study, the authors use the partial-wave series expansion method in the spherical coordinate system and provide a theoretical formula for the off-axis acoustical scattering by rigid prolate and oblate spheroids illuminated by an arbitrary-order Bessel beam to explore the physical characteristics of the off-axis far-field scattering (the axis of the Bessel beam is parallel to the axis of the spheroids). The proposed method is verified and several three-dimensional far-field directivity patterns of rigid spheroids illuminated by zeroth- and first-order Bessel beams are depicted to explore the off-axis scattering. A special emphasis is placed on the geometry size of the prolate and oblate spheroids, the half-cone angle of the Bessel beam, the order of the Bessel beam, and the offset position. Compared with the on-axis scattering, the derivation and calculation of the off-axis scattering takes into account the spherical harmonic function using a numerical integral procedure. In addition, no symmetry was observed in the patterns of the far-field acoustic scattering form function for the zeroth- and higher-order Bessel beams with the off-axis illumination. This investigation provides a tool for the exploration of the complex scattering problems of underwater non-spherical particles under the illumination of the Bessel beam.

Active electromagnetic invisibility cloaking and radiation force cancellation

This investigation shows that an active emitting electromagnetic (EM) Dirichlet source (i.e., with axial polarization of the electric field) in a homogeneous non-dissipative/non-absorptive medium placed near a perfectly conducting boundary can render total invisibility (i.e. zero extinction cross-section or efficiency) in addition to a radiation force cancellation on its surface. Based upon the Poynting theorem, the mathematical expression for the extinction, radiation and amplification cross-sections (or efficiencies) are derived using the partial-wave series expansion method in cylindrical coordinates. Moreover, the analysis is extended to compute the self-induced EM radiation force on the active source, resulting from the waves reflected by the boundary. The numerical results predict the generation of a zero extinction efficiency, achieving total invisibility, in addition to a radiation force cancellation which depend on the source size, the distance from the boundary and the associated EM mode order of the active source. Furthermore, an attractive EM pushing force on the active source directed toward the boundary or a repulsive pulling one pointing away from it can arise accordingly. The numerical predictions and computational results find potential applications in the design and development of EM cloaking devices, invisibility and stealth technologies.

Extrinsic and intrinsic acoustical cross-sections for a viscous fluid particle near a planar rigid boundary: circular cylinder example

The objective of this investigation is to derive closed-form partial-wave series expansions for the extrinsic and intrinsic acoustical scattering, extinction and absorption cross-sections of a fluid viscous cylindrical particle of arbitrary geometrical cross-section, located nearby a flat rigid boundary. Plane progressive waves with arbitrary incidence angle are considered in a non-viscous fluid. The multiple scattering between the particle and the boundary is described using the multipole expansion in cylindrical coordinates, the method of images and the translational addition theorem. The extrinsic cross-sections are determined by integrating the associated power flow densities over a virtual surface of large radius enclosing the object and its image, stemming from far-field expressions of the incident and scattered pressure fields. The expressions for the intrinsic cross-sections are established after defining an effective acoustic field incident on the particle, which includes the primary incident field, the reflected waves from the boundary and the scattered field from the image object. Subsequently, the incident effective field is used with the scattered field from the object to derive closed-form analytical expressions for the intrinsic cross-sections, based on a far-field scattering approach, which does not introduce any approximation in the evaluation of the expressions. The obtained expressions involve the angle of incidence, the expansion coefficients of the scatterer and its image, and the distance from the center of mass of the particle to the boundary. Numerical examples for a viscous fluid circular cylindrical cross-section are considered, and computations illustrate the analysis with particular emphasis on varying the size of the particle, the angle of incidence and the particle-wall distance. The results find potential applications in the quantitative predictions of the acoustical cross-sections from fluid/soft/compressible objects nearby a boundary, such as contrast agents in biomedicine, oceanography, sonochemistry, marine science, and (borehole) geophysical applications to name a few examples.

Acoustic radiation force induced by two Airy–Gaussian beams on a cylindrical particle**Project supported by the National Key R & D Program, China (Grant No. 2016YFF0203000), the National Natural Science Foundation of China (Grant Nos. 11774167 and 61571222), Fundamental Research Funds for the Central Universities, China (Grant No. 020414380001), State Key Laboratory of Acoustics, Chinese Academy of Sciences (Grant No. SKLA201609),

Based on the angular spectrum decomposition and partial-wave series expansion methods, we investigate the radiation force functions of two Airy–Gaussian (AiG) beams on a cylindrical particle and the motion trajectory of the particle. The simulations show that the particle can be pulled or propelled into either the positive or negative transverse direction by turning the phase difference between the two AiG beams appropriately; and the larger the beam widths of the two AiG beams are, the bigger the radiation force can be obtained to control the particle. In addition, the direction of the accelerated particle can be controlled while the dimensionless frequency bandwidth changes. The results indicate that the phase plays an important role in controlling the direction of the particle, which may provide a theoretical basis for the design of acoustical tweezers and the development of drug delivery.