1,701 research outputs found
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
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