Radiation force of a helicoidal Bessel beam on a sphere.

The partial-wave series for the scattering of an acoustic helicoidal Bessel beam by a sphere centered on the axis of the beam is applied to the calculation of the acoustic radiation force by the beam on the sphere in an inviscid fluid. The term "helicoidal" refers to a type of beam having an axial amplitude null and an azimuthal phase gradient. Such a beam is known as an acoustic vortex and only the case of a vortex having a unit magnitude topological charge is considered. There is no monopole contribution to the radiation force. Radiation force examples are computed for a soft sphere, a fixed rigid sphere, a movable rigid sphere, an aluminum sphere in water, and an acrylic sphere in water. Beam parameters are found for the rigid sphere and the aluminum and acrylic cases in which the radiation force is directed opposite the propagation direction of the beam. Negative radiation forces appear to be associated with relatively weak scattering into the backward hemisphere. Some aspects of the low frequency scattering of plane waves and helicoidal Bessel beams are examined for movable rigid spheres.

[1]  Miceli,et al.  Diffraction-free beams. , 1987, Physical review letters.

[2]  P. Marston.  Scattering of a Bessel beam by a sphere: II. Helicoidal case and spherical shell example. , 2008, The Journal of the Acoustical Society of America.

[3]  K. Dholakia,et al.  Bessel beams: Diffraction in a new light , 2005 .

[4]  Farid G. Mitri,et al.  Acoustic scattering of a high-order Bessel beam by an elastic sphere , 2008 .

[5]  D. Grier.  A revolution in optical manipulation , 2003, Nature.

[6]  F. Mitri.  Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel beam tweezers , 2008 .

[7]  P. Marston,et al.  Equivalence of expressions for the acoustic radiation force on cylinders , 2005 .

[8]  Paul A Dayton,et al.  The magnitude of radiation force on ultrasound contrast agents. , 2002, The Journal of the Acoustical Society of America.

[9]  A. Fetter,et al.  Theoretical mechanics of particles and continua , 1980 .

[10]  Junru Wu,et al.  Acoustic radiation force on a small compressible sphere in a focused beam , 1990 .

[11]  Gregory Goddard,et al.  Ultrasonic particle concentration in a line-driven cylindrical tube. , 2003, The Journal of the Acoustical Society of America.

[12]  Karen Volke-Sepúlveda,et al.  Transfer of angular momentum to matter from acoustical vortices in free space. , 2008, Physical review letters.

[13]  Robert Hickling,et al.  Analysis of Echoes from a Solid Elastic Sphere in Water , 1962 .

[14]  P. Marston.  Negative axial radiation forces on solid spheres and shells in a Bessel beam. , 2007, The Journal of the Acoustical Society of America.

[15]  Régis Marchiano,et al.  Pseudo angular momentum and topological charge conservation for nonlinear acoustical vortices. , 2003, Physical review letters.

[16]  Philip L Marston,et al.  Manipulation of Fluid Objects with Acoustic Radiation Pressure , 2004, Annals of the New York Academy of Sciences.

[17]  Andrea Prosperetti,et al.  Thermal effects and damping mechanisms in the forced radial oscillations of gas bubbles in liquids , 1977 .

[18]  Takahi Hasegawa,et al.  Acoustic radiation force on fused silica spheres, and intensity determination , 1975 .

[19]  H. Überall,et al.  Multipole resonances in sound scattering from gas bubbles in a liquid , 1978 .

[20]  R E Apfel,et al.  Radiation force on a spherical object in an axisymmetric wave field and its application to the calibration of high-frequency transducers. , 1996, The Journal of the Acoustical Society of America.

[21]  Dan Cojoc,et al.  Changes in microbubble dynamics near a boundary revealed by combined optical micromanipulation and high-speed imaging , 2007 .

[22]  Philip L Marston,et al.  Axial radiation force of a bessel beam on a sphere and direction reversal of the force. , 2006, The Journal of the Acoustical Society of America.

[23]  Philip L. Marston,et al.  Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave , 1984 .

[24]  P. Marston,et al.  Acoustic radiation force on a compressible cylinder in a standing wave , 2004 .

[25]  C. P. Lee,et al.  Acoustic radiation force on a bubble , 1993 .

[26]  Takahi Hasegawa,et al.  Acoustic radiation force on a solid elastic sphere in a spherical wave field , 1981 .

[27]  W Sibbett,et al.  Manipulation and filtration of low index particles with holographic Laguerre-Gaussian optical trap arrays. , 2004, Optics express.

[28]  Miles J. Padgett,et al.  An acoustic spanner and its associated rotational Doppler shift , 2008 .

[29]  Grover A. Swartzlander,et al.  Trapping of low-index microparticles in an optical vortex , 1998 .

[30]  Louis Vessot King,et al.  On the Acoustic Radiation Pressure on Spheres , 1934 .

[31]  P. Marston,et al.  Backscattering enhancements associated with subsonic Rayleigh waves on polymer spheres in water: observation and modeling for acrylic spheres , 2000, The Journal of the Acoustical Society of America.

[32]  J. Durnin.  Exact solutions for nondiffracting beams. I. The scalar theory , 1987 .

[33]  P. Marston.  Acoustic beam scattering and excitation of sphere resonance: Bessel beam example. , 2007, The Journal of the Acoustical Society of America.

[34]  Norman R. Heckenberg,et al.  Optical tweezers computational toolbox , 2007 .

[35]  P. Dayton,et al.  A method for radiation-force localized drug delivery using gas-filled lipospheres , 2004, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[36]  Mironov,et al.  Mean force on a small sphere in a sound field in a viscous fluid , 2000, The Journal of the Acoustical Society of America.

[37]  Takahi Hasegawa,et al.  Acoustic radiation pressure on an absorbing sphere , 1978 .

[38]  Philip L. Marston,et al.  An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems , 1999 .

[39]  Robert Hickling,et al.  Scattering of Sound by a Rigid Movable Sphere , 1966 .

[40]  P. Marston.  Scattering of a Bessel beam by a sphere. , 2007, The Journal of the Acoustical Society of America.

[41]  K Kirk Shung,et al.  Radiation forces exerted on arbitrarily located sphere by acoustic tweezer. , 2006, The Journal of the Acoustical Society of America.

[42]  Régis Marchiano,et al.  Synthesis and analysis of linear and nonlinear acoustical vortices. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  Z. Fellah,et al.  Theory of the acoustic radiation force exerted on a sphere by standing and quasistanding zero-order Bessel beam tweezers of variable half-cone angles , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[44]  Bruce T. Unger,et al.  Optical levitation of bubbles in water by the radiation pressure of a laser beam: An acoustically quiet levitator , 1988 .

[45]  Alessandra Tesei,et al.  Tank measurements of scattering from a resin-filled fiberglass spherical shell with internal flaws. , 2008, The Journal of the Acoustical Society of America.

[46]  A. Szeri,et al.  Optimized translation of microbubbles driven by acoustic fields. , 2007, The Journal of the Acoustical Society of America.