Vector spherical quasi-Gaussian vortex beams

Model equations for describing and efficiently computing the radiation profiles of tightly spherically-focused higher-order electromagnetic beams of vortex nature are derived stemming from a vectorial analysis with the complex-source-point method. This solution, termed as a high-order quasi-Gaussian (qG) vortex beam, exactly satisfies the vector Helmholtz and Maxwell's equations. It is characterized by a nonzero integer degree and order (n,m), respectively, an arbitrary waist w0, a diffraction convergence length known as the Rayleigh range zR, and an azimuthal phase dependency in the form of a complex exponential corresponding to a vortex beam. An attractive feature of the high-order solution is the rigorous description of strongly focused (or strongly divergent) vortex wave-fields without the need of neither the higher-order corrections nor the numerically intensive methods. Closed-form expressions and computational results illustrate the analysis and some properties of the high-order qG vortex beams based on the axial and transverse polarization schemes of the vector potentials with emphasis on the beam waist.Comment: 8 pages, 6 figure

Partial-Wave Series Expansion and Angular Spectrum Decomposition Formalisms for Acoustical Beams

Complex weights factors (CWFs) that fully define the incident beam independent of the presence of a scatterer, may be represented mathematically by either a partial-wave series expansion (PWSE) of multipoles, or the method of angular spectrum decomposition (ASD) of plane waves. Once the mathematical expression for the CWFs of the incident waves is known, evaluation of the arbitrary scattering, radiation force, and torque components on an object in 3D, using the Generalized Theories of Resonance Scattering (GTRS), Radiation Force (GTRF) and Radiation Torque (GTRT), becomes feasible. The aim of this Letter is to establish the connection between these two approaches in the framework of the GTRS, GTRF and GTRT in spherical coordinates for various acoustical applications. The advantage of using the ASD approach is also discussed for specific beams with particular properties

Local cross-sections and energy efficiencies in the multiple optical scattering by two conducting particles

In this work, exact mathematical expansions for the intrinsic electromagnetic (EM) or optical cross-sections (i.e., extinction, scattering and absorption) for a pair of perfectly conducting circular cylinders in a homogeneous medium are derived. The incident illuminating field is an axially-polarized electric field composed of plane travelling waves with an arbitrary angle of incidence in the polar plane. The formalism is based on the multipole modal expansion method in cylindrical coordinates and the translational addition theorem applicable to any range of frequencies. An effective EM field, incident on the probed cylinder, is defined first, which includes the initial and re-scattered field from the second cylinder. Subsequently, it is used jointly with the scattered field to derive the mathematical expressions for the intrinsic/local cross-sections based on integrating their corresponding time-averaged intensities over the surface of the probed object by applying the Poynting theorem. Numerical computations for the intrinsic extinction (or scattering) energy efficiencies for a pair of conducting circular cylinders with different radii in a homogeneous medium are considered. Emphasis is given on varying the interparticle distance, the angle of incidence, and the dimensionless sizes of the cylinders. The results computed a priori can be useful in the full characterization of a multiple scattering system of many particles, in conjunction with experimental data for the extrinsic cross-sections.Comment: 14 pages, 8 figure

Near-Field Acoustic Resonance Scattering of a Finite Bessel Beam by an Elastic Sphere

The near-field acoustic scattering from a sphere centered on the axis of a finite Bessel acoustic beam is derived stemming from the Rayleigh-Sommerfeld diffraction surface integral and the addition theorems for the spherical wave and Legendre functions. The beam emerges from a finite circular disk vibrating according to one of its radial modes corresponding to the fundamental solution of a Bessel beam J0. The incident pressure field's expression is derived analytically as a partial-wave series expansion taking into account the finite size and the distance from the center of the disk transducer. Initially, the scattered pressure by a rigid sphere is evaluated, and backscattering pressure moduli plots as well as 3-D directivity patterns for an elastic PMMA sphere centered on a finite Bessel beam with appropriate tuning of its half-cone angle, reveal possible resonance suppression of the sphere only in the zone near the Bessel transducer. Moreover, the analysis is extended to derive the mean spatial incident and scattered pressures at the surface of a rigid circular receiver of infinitesimal thickness. The transducer, sphere and receiver are assumed to be coaxial. Some applications can result from the present analysis since all physically realizable Bessel beam sources radiate finite sound beams as opposed to waves of infinite extent.Comment: IEEE Trans. UFFC 201

Edge-induced radiation force and torque on a cylindrically-radiating active acoustic source near a rigid corner-space

This work examines the physical effect of the edge-induced acoustic radiation force and torque on an acoustically radiating circular source, located near a rigid corner. Assuming harmonic (linear) radiating waves of the source, vibrating in monopole or dipole radiation modes near a rigid corner-space in a non-viscous fluid, the modal series expansion method in cylindrical coordinates, the classical method of images and the translational addition theorem are applied to obtain the mathematical expressions for the radiation force and torque components in exact closed-form partial-wave series. Computational results illustrate the theory, and examine some of the conditions where the radiation force and torque components vanish, which has the potential to achieve total motion suppression (i.e., translation or rotation). Furthermore, depending on the size parameter of the source and the distances from the rigid corner space, these physical observables take positive or negative values, anticipating the prediction of pulling/pushing motions toward the corner space, and possible spinning of the source clockwise or counter-clockwise. The present analysis and its results are useful in some applications related to the manipulation of an active carrier or ultrasound contrast agents near a corner space or chamber walls at a right angle.Comment: 7 pages, 8 figure

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 weighing function describing the behavior of the radial component 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 \rho-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 3D acoustic radiation force and torque components on a sphere of any (isotropic, anisotropic etc.) material (fluid, elastic, viscoelastic etc.). Numerical predictions allow optimal design of parameters in applications including but not limited to acoustical tweezers, acousto-fluidics, beam-forming design and imaging to name a few.Comment: Accepted, in press in IEEE Transactions on UFFC 201

Reply to: Comment on "Radiation forces and torque on a rigid elliptical cylinder in acoustical plane progressive and (quasi)standing waves with arbitrary incidence, arXiv:1603.03446" [Phys. Fluids 28, 077104 (2016)]

The aim of this communication is to correct inaccurate statements presented in a Commentary on the paper titled: "Radiation forces and torque on a rigid elliptical cylinder in acoustical plane progressive and (quasi)standing waves with arbitrary incidence" [Phys. Fluids 28, 077104 (2016)].Comment: 3 page

Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid

Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure (\theta = \pi) in the near-field and the backscattering form function in the far-field for both prolate and oblate spheroids are presented and discussed, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle of the Bessel beam \beta, and the dimensionless frequency. The plots display periodic oscillations (versus the dimensionless frequency) due to the interference of specularly reflected waves in the backscattering direction with circumferential Franz' waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3D directivity patterns illustrate the near and far-field axisymmetric scattering. Investigations in underwater acoustics, particle levitation, scattering, and the detection of submerged elongated objects and other related applications utilizing Bessel waves would benefit from the results of the present study.Comment: 10 pages, 7 figures, Correcting some minor typos and citations for reference

Validity of the linear viscoelastic model for a polymer cylinder with ultrasonic hysteresis-type absorption in a nonviscous fluid

A necessary condition for the validity of the linear viscoelastic model for a (passive) polymeric cylinder with an ultrasonic hysteresis-type absorption submerged in a non-viscous fluid requires that the absorption efficiency is positive (Qabs > 0) satisfying the law of the conservation of energy. This condition imposes restrictions on the values attributed to the normalized absorption coefficients for the compressional and shear-wave wavenumbers for each partial-wave mode n. The forbidden values produce negative axial radiation force, absorption and extinction efficiencies, as well as an enhancement of the scattering efficiency, not in agreement with the conservation of energy law. Numerical results for the radiation force, extinction, absorption and scattering efficiencies are performed for three viscoelastic (VE) polymer cylinders immersed in a non-viscous host liquid (i.e. water) with particular emphasis on the shear-wave absorption coefficient of the cylinder, the dimensionless size parameter and the partial-wave mode number n. Mathematical constraints are established for the non-dimensional absorption coefficients of the longitudinal and shear waves for a cylinder (i.e. 2D case) and a sphere (i.e. 3D case) in terms of the sound velocities in the VE material. The analysis suggests that the domain of validity for any viscoelastic model describing acoustic attenuation inside a lossy cylinder (or sphere) in a non-viscous fluid must be verified based upon the optical theorem

Negative optical spin torque wrench of a nondiffracting non-paraxial fractional Bessel vortex beam

An absorptive Rayleigh dielectric sphere in a non-diffracting non-paraxial fractional Bessel vortex beam experiences a spin torque. The axial and transverse radiation spin torque components are evaluated in the dipole approximation using the radiative correction of the electric field. Particular emphasis is given on the polarization as well as changing the topological charge and the beam's half-cone angle. When the beam order is zero, the axial spin torque component vanishes. However, when the beam order becomes a real positive number, the vortex beam induces left-handed (negative) axial spin torque as the sphere shifts off-axially from the center of the beam. The results show that a non-diffracting non-paraxial fractional Bessel vortex beam is capable to induce a spin reversal of an absorptive Rayleigh sphere placed arbitrarily in its path. Potential applications are yet to be explored in particle manipulation, rotation in optical tweezers, optical tractor beams, the design of optically-engineered metamaterials to name a few areas.Comment: 5 pages, Accepted for publication in the Journal of Quantitative Spectroscopy and Radiative Transfer (2016