Abstract

Acoustical and optical non-diffracting beams are potentially useful for manipulating particles and larger objects. An extended optical theorem for a non-diffracting beam was given recently in the context of acoustics. The theorem relates the extinction by an object to the scattering at the forward direction of the beam’s plane wave components. Here we use this theorem to examine the extinction cross section of a sphere centered on the axis of the beam, with a non-diffracting Bessel beam as an example. The results are applied to recover the axial radiation force and torque on the sphere by the Bessel beam.

© 2013 OSA

Full Article  |  PDF Article

Errata

Likun Zhang and Philip L. Marston, "Optical theorem for acoustic non-diffracting beams and application to radiation force and torque: erratum," Biomed. Opt. Express 4, 2988-2988 (2013)
https://www.osapublishing.org/boe/abstract.cfm?uri=boe-4-12-2988

References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2013 (5)

N.  Wang, J.  Chen, S. Y.  Liu, Z. F.  Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87, 063812 (2013).
[CrossRef]

O.  Brzobohatý, V.  Karásek, M.  Šiler, L.  Chvátal, T.  Čižmár, P.  Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ’tractor beam’,” Nat. Photonics 7, 123–127 (2013).
[CrossRef]

D.  Baresch, J.-L.  Thomas, R.  Marchiano, “Three-dimensional acoustic radiation force on an arbitrarily located elastic sphere,” J. Acoust. Soc. Am. 133, 25–36 (2013).
[CrossRef] [PubMed]

C. R. P.  Courtney, B. W.  Drinkwater, C. E. M.  Demore, S.  Cochran, A.  Grinenko, P. D.  Wilcox, “Dexterous manipulation of microparticles using Bessel-function acoustic pressure fields,” Appl. Phys. Lett. 102, 123508 (2013).
[CrossRef]

P. L.  Marston, “Viscous contributions to low-frequency scattering, power absorption, radiation force, and radiation torque for spheres in acoustic beams,” Proceedings of Meetings on Acoustics (POMA) 19, 045005 (2013).
[CrossRef]

2012 (5)

C. E. M.  Demore, Z.  Yang, A.  Volovick, S.  Cochran, M. P.  MacDonald, G. C.  Spalding, “Mechanical evidence of the orbital angular momentum to energy ratio of vortex beams,” Phys. Rev. Lett. 108, 194301 (2012).
[CrossRef] [PubMed]

S.  Xu, C.  Qiu, Z.  Liu, “Transversally stable acoustic pulling force produced by two crossed plane waves,” Europhys. Lett. 99, 44003 (2012).
[CrossRef]

F. G.  Mitri, T. P.  Lobo, G. T.  Silva, “Axial acoustic radiation torque of a Bessel vortex beam on spherical shells,” Phys. Rev. E 85, 026602 (2012).
[CrossRef]

G. T.  Silva, T. P.  Lobo, F. G.  Mitri, “Radiation torque produced by an arbitrary acoustic wave,” Europhys. Lett. 97, 54003 (2012).
[CrossRef]

L. K.  Zhang, P. L.  Marston, “Axial radiation force exerted by general non-diffracting beams,” J. Acoust. Soc. Am. 131, EL329–EL335 (2012).
[CrossRef] [PubMed]

2011 (9)

S.  Sukhov, A.  Dogariu, “Negative nonconservative forces: Optical tractor beams for arbitrary objects,” Phys. Rev. Lett. 107, 203602 (2011).
[CrossRef]

L. K.  Zhang, P. L.  Marston, “Geometrical interpretation of negative radiation forces of acoustical Bessel beams on spheres,” Phys. Rev. E 84, 035601(R) (2011).
[CrossRef]

J.  Chen, J.  Ng, Z. F.  Lin, C. T.  Chan, “Optical pulling force,” Nat. Photonics 5, 531–534 (2011).
[CrossRef]

A.  Novitsky, C.-W.  Qiu, H. F.  Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107, 203601 (2011).
[CrossRef] [PubMed]

Y.  Choe, J. W.  Kim, K. K.  Shung, E. S.  Kim, “Microparticle trapping in an ultrasonic Bessel beam,” Appl. Phys. Lett. 99, 233704 (2011).
[CrossRef]

G. T.  Silva, “Off-axis scattering of an ultrasound Bessel beam by a sphere,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 298–304 (2011).
[CrossRef] [PubMed]

L. K.  Zhang, P. L.  Marston, “Radiation torque on solid spheres and drops centered on an acoustic helicoidal Bessel beam,” J. Acoust. Soc. Am. 129, 2381–2381 (2011).
[CrossRef]

L. K.  Zhang, P. L.  Marston, “Acoustic radiation torque and the conservation of angular momentum,” J. Acoust. Soc. Am. 129, 1679–1680 (2011).
[CrossRef] [PubMed]

L. K.  Zhang, P. L.  Marston, “Angular momentum flux of nonparaxial acoustic vortex beams and torques on axisymmetric objects,” Phys. Rev. E 84, 065601(R) (2011).
[CrossRef]

2009 (5)

F. G.  Mitri, “Equivalence of expressions for the acoustic scattering of a progressive high-order Bessel beam by an elastic sphere,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56, 1100–1103 (2009).
[CrossRef] [PubMed]

L. K.  Zhang, P. L.  Marston, “Radiation torque on a sphere centered on an acoustic helicoidal (vortex) Bessel beam.” J. Acoust. Soc. Am. 125, 2552–2552 (2009).

P. L.  Marston, L. K.  Zhang, “Radiation torques and forces in scattering from spheres and acoustical analogues,” in Optical Trapping Applications, OSA Technical Digest (CD) (Optical Society of America, 2009), p. OMB5.

P. L.  Marston, “Radiation force of a helicoidal Bessel beam on a sphere,” J. Acoust. Soc. Am 125, 3539–3547 (2009).
[CrossRef] [PubMed]

F. G.  Mitri, “Negative axial radiation force on a fluid and elastic spheres illuminated by a high-order Bessel beam of progressive waves,” J. Phys. A: Math. Theor. 42, 245202 (2009).
[CrossRef]

2008 (1)

2007 (2)

P. L.  Marston, “Scattering of a Bessel beam by a sphere,” J. Acoust. Soc. Am 121, 753 (2007).
[CrossRef] [PubMed]

P. L.  Marston, “Negative axial radiation forces on solid spheres and shells in a Bessel beam,” J. Acoust. Soc. Am 122, 3162–3165 (2007).
[CrossRef]

2006 (1)

P. L.  Marston, “Axial radiation force of a Bessel beam on a sphere and direction reversal of the force,” J. Acoust. Soc. Am 120, 3518–3524 (2006).
[CrossRef]

2003 (1)

A.  Belafhal, A.  Chafiq, Z.  Hricha, “Scattering of Mathieu beams by a rigid sphere,” Opt. Commun. 284, 3030–3035 (2003).
[CrossRef]

2001 (1)

P. L.  Marston, “Generalized optical theorem for scatterers having inversion symmetry: applications to acoustic backscattering,” J. Acoust. Soc. Am. 109, 1291–1295 (2001).
[CrossRef] [PubMed]

2000 (1)

1999 (1)

B. T.  Hefner, P. L.  Marston, “An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems,” J. Acoust. Soc. Am. 106, 3313 (1999).
[CrossRef]

1996 (1)

X. C.  Chen, R. E.  Apfel, “Radiation force on a spherical object in an axisymmetric wave field and its application to the calibration of high-frequency transducers,” J. Acoust. Soc. Am. 99, 713–724 (1996).
[CrossRef] [PubMed]

1995 (1)

1992 (1)

L.  Allen, M. W.  Beijersbergen, R. J. C.  Spreeuw, J. P.  Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

1987 (1)

1984 (1)

P. L.  Marston, J. H.  Crichton, “Radiation torque on a sphere caused by a circularly polarized electromagnetic wave,” Phys. Rev. A 30, 2508–2516 (1984).
[CrossRef]

1976 (1)

R. G.  Newton, “Optical theorem and beyond,” Am. J. Phys. 44, 639–642 (1976).
[CrossRef]

1975 (1)

T.  Hasegawa, K.  Yosioka, “Acoustic radiation force on fused silica spheres, and intensity determination,” J. Acoust. Soc. Am. 58, 581–585 (1975).
[CrossRef]

Allen, L.

L.  Allen, M. W.  Beijersbergen, R. J. C.  Spreeuw, J. P.  Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Apfel, R. E.

X. C.  Chen, R. E.  Apfel, “Radiation force on a spherical object in an axisymmetric wave field and its application to the calibration of high-frequency transducers,” J. Acoust. Soc. Am. 99, 713–724 (1996).
[CrossRef] [PubMed]

Bandres, M. A.

Baresch, D.

D.  Baresch, J.-L.  Thomas, R.  Marchiano, “Three-dimensional acoustic radiation force on an arbitrarily located elastic sphere,” J. Acoust. Soc. Am. 133, 25–36 (2013).
[CrossRef] [PubMed]

D.  Baresch, J.-L.  Thomas, R.  Marchiano, “Spherical vortex beams of high radial degree for enhanced single-beam tweezers,” J. Appl. Phys. 113, 184901 (2013).

Beijersbergen, M. W.

L.  Allen, M. W.  Beijersbergen, R. J. C.  Spreeuw, J. P.  Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Belafhal, A.

A.  Belafhal, A.  Chafiq, Z.  Hricha, “Scattering of Mathieu beams by a rigid sphere,” Opt. Commun. 284, 3030–3035 (2003).
[CrossRef]

Brzobohatý, O.

O.  Brzobohatý, V.  Karásek, M.  Šiler, L.  Chvátal, T.  Čižmár, P.  Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ’tractor beam’,” Nat. Photonics 7, 123–127 (2013).
[CrossRef]

Chafiq, A.

A.  Belafhal, A.  Chafiq, Z.  Hricha, “Scattering of Mathieu beams by a rigid sphere,” Opt. Commun. 284, 3030–3035 (2003).
[CrossRef]

Chan, C. T.

J.  Chen, J.  Ng, Z. F.  Lin, C. T.  Chan, “Optical pulling force,” Nat. Photonics 5, 531–534 (2011).
[CrossRef]

Chávez-Cerda, S.

Chen, J.

N.  Wang, J.  Chen, S. Y.  Liu, Z. F.  Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87, 063812 (2013).
[CrossRef]

J.  Chen, J.  Ng, Z. F.  Lin, C. T.  Chan, “Optical pulling force,” Nat. Photonics 5, 531–534 (2011).
[CrossRef]

Chen, X. C.

X. C.  Chen, R. E.  Apfel, “Radiation force on a spherical object in an axisymmetric wave field and its application to the calibration of high-frequency transducers,” J. Acoust. Soc. Am. 99, 713–724 (1996).
[CrossRef] [PubMed]

Choe, Y.

Y.  Choe, J. W.  Kim, K. K.  Shung, E. S.  Kim, “Microparticle trapping in an ultrasonic Bessel beam,” Appl. Phys. Lett. 99, 233704 (2011).
[CrossRef]

Chvátal, L.

O.  Brzobohatý, V.  Karásek, M.  Šiler, L.  Chvátal, T.  Čižmár, P.  Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ’tractor beam’,” Nat. Photonics 7, 123–127 (2013).
[CrossRef]

Cižmár, T.

O.  Brzobohatý, V.  Karásek, M.  Šiler, L.  Chvátal, T.  Čižmár, P.  Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ’tractor beam’,” Nat. Photonics 7, 123–127 (2013).
[CrossRef]

Cochran, S.

C. R. P.  Courtney, B. W.  Drinkwater, C. E. M.  Demore, S.  Cochran, A.  Grinenko, P. D.  Wilcox, “Dexterous manipulation of microparticles using Bessel-function acoustic pressure fields,” Appl. Phys. Lett. 102, 123508 (2013).
[CrossRef]

C. E. M.  Demore, Z.  Yang, A.  Volovick, S.  Cochran, M. P.  MacDonald, G. C.  Spalding, “Mechanical evidence of the orbital angular momentum to energy ratio of vortex beams,” Phys. Rev. Lett. 108, 194301 (2012).
[CrossRef] [PubMed]

Courtney, C. R. P.

C. R. P.  Courtney, B. W.  Drinkwater, C. E. M.  Demore, S.  Cochran, A.  Grinenko, P. D.  Wilcox, “Dexterous manipulation of microparticles using Bessel-function acoustic pressure fields,” Appl. Phys. Lett. 102, 123508 (2013).
[CrossRef]

Crichton, J. H.

P. L.  Marston, J. H.  Crichton, “Radiation torque on a sphere caused by a circularly polarized electromagnetic wave,” Phys. Rev. A 30, 2508–2516 (1984).
[CrossRef]

Demore, C. E. M.

C. R. P.  Courtney, B. W.  Drinkwater, C. E. M.  Demore, S.  Cochran, A.  Grinenko, P. D.  Wilcox, “Dexterous manipulation of microparticles using Bessel-function acoustic pressure fields,” Appl. Phys. Lett. 102, 123508 (2013).
[CrossRef]

C. E. M.  Demore, Z.  Yang, A.  Volovick, S.  Cochran, M. P.  MacDonald, G. C.  Spalding, “Mechanical evidence of the orbital angular momentum to energy ratio of vortex beams,” Phys. Rev. Lett. 108, 194301 (2012).
[CrossRef] [PubMed]

Dogariu, A.

S.  Sukhov, A.  Dogariu, “Negative nonconservative forces: Optical tractor beams for arbitrary objects,” Phys. Rev. Lett. 107, 203602 (2011).
[CrossRef]

Drinkwater, B. W.

C. R. P.  Courtney, B. W.  Drinkwater, C. E. M.  Demore, S.  Cochran, A.  Grinenko, P. D.  Wilcox, “Dexterous manipulation of microparticles using Bessel-function acoustic pressure fields,” Appl. Phys. Lett. 102, 123508 (2013).
[CrossRef]

Durnin, J.

Gouesbet, G.

Grinenko, A.

C. R. P.  Courtney, B. W.  Drinkwater, C. E. M.  Demore, S.  Cochran, A.  Grinenko, P. D.  Wilcox, “Dexterous manipulation of microparticles using Bessel-function acoustic pressure fields,” Appl. Phys. Lett. 102, 123508 (2013).
[CrossRef]

Gutiérrez-Vega, J. C.

Hasegawa, T.

T.  Hasegawa, K.  Yosioka, “Acoustic radiation force on fused silica spheres, and intensity determination,” J. Acoust. Soc. Am. 58, 581–585 (1975).
[CrossRef]

Hefner, B. T.

B. T.  Hefner, P. L.  Marston, “An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems,” J. Acoust. Soc. Am. 106, 3313 (1999).
[CrossRef]

Hodges, J. T.

Hricha, Z.

A.  Belafhal, A.  Chafiq, Z.  Hricha, “Scattering of Mathieu beams by a rigid sphere,” Opt. Commun. 284, 3030–3035 (2003).
[CrossRef]

Iturbe-Castillo, M. D.

Karásek, V.

O.  Brzobohatý, V.  Karásek, M.  Šiler, L.  Chvátal, T.  Čižmár, P.  Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ’tractor beam’,” Nat. Photonics 7, 123–127 (2013).
[CrossRef]

Kim, E. S.

Y.  Choe, J. W.  Kim, K. K.  Shung, E. S.  Kim, “Microparticle trapping in an ultrasonic Bessel beam,” Appl. Phys. Lett. 99, 233704 (2011).
[CrossRef]

Kim, J. W.

Y.  Choe, J. W.  Kim, K. K.  Shung, E. S.  Kim, “Microparticle trapping in an ultrasonic Bessel beam,” Appl. Phys. Lett. 99, 233704 (2011).
[CrossRef]

Lin, Z. F.

N.  Wang, J.  Chen, S. Y.  Liu, Z. F.  Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87, 063812 (2013).
[CrossRef]

J.  Chen, J.  Ng, Z. F.  Lin, C. T.  Chan, “Optical pulling force,” Nat. Photonics 5, 531–534 (2011).
[CrossRef]

Liu, S. Y.

N.  Wang, J.  Chen, S. Y.  Liu, Z. F.  Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87, 063812 (2013).
[CrossRef]

Liu, Z.

S.  Xu, C.  Qiu, Z.  Liu, “Transversally stable acoustic pulling force produced by two crossed plane waves,” Europhys. Lett. 99, 44003 (2012).
[CrossRef]

Lobo, T. P.

F. G.  Mitri, T. P.  Lobo, G. T.  Silva, “Axial acoustic radiation torque of a Bessel vortex beam on spherical shells,” Phys. Rev. E 85, 026602 (2012).
[CrossRef]

G. T.  Silva, T. P.  Lobo, F. G.  Mitri, “Radiation torque produced by an arbitrary acoustic wave,” Europhys. Lett. 97, 54003 (2012).
[CrossRef]

Lock, J. A.

MacDonald, M. P.

C. E. M.  Demore, Z.  Yang, A.  Volovick, S.  Cochran, M. P.  MacDonald, G. C.  Spalding, “Mechanical evidence of the orbital angular momentum to energy ratio of vortex beams,” Phys. Rev. Lett. 108, 194301 (2012).
[CrossRef] [PubMed]

Marchiano, R.

D.  Baresch, J.-L.  Thomas, R.  Marchiano, “Three-dimensional acoustic radiation force on an arbitrarily located elastic sphere,” J. Acoust. Soc. Am. 133, 25–36 (2013).
[CrossRef] [PubMed]

D.  Baresch, J.-L.  Thomas, R.  Marchiano, “Spherical vortex beams of high radial degree for enhanced single-beam tweezers,” J. Appl. Phys. 113, 184901 (2013).

Marston, P. L.

P. L.  Marston, “Viscous contributions to low-frequency scattering, power absorption, radiation force, and radiation torque for spheres in acoustic beams,” Proceedings of Meetings on Acoustics (POMA) 19, 045005 (2013).
[CrossRef]

L. K.  Zhang, P. L.  Marston, “Axial radiation force exerted by general non-diffracting beams,” J. Acoust. Soc. Am. 131, EL329–EL335 (2012).
[CrossRef] [PubMed]

L. K.  Zhang, P. L.  Marston, “Geometrical interpretation of negative radiation forces of acoustical Bessel beams on spheres,” Phys. Rev. E 84, 035601(R) (2011).
[CrossRef]

L. K.  Zhang, P. L.  Marston, “Angular momentum flux of nonparaxial acoustic vortex beams and torques on axisymmetric objects,” Phys. Rev. E 84, 065601(R) (2011).
[CrossRef]

L. K.  Zhang, P. L.  Marston, “Radiation torque on solid spheres and drops centered on an acoustic helicoidal Bessel beam,” J. Acoust. Soc. Am. 129, 2381–2381 (2011).
[CrossRef]

L. K.  Zhang, P. L.  Marston, “Acoustic radiation torque and the conservation of angular momentum,” J. Acoust. Soc. Am. 129, 1679–1680 (2011).
[CrossRef] [PubMed]

L. K.  Zhang, P. L.  Marston, “Radiation torque on a sphere centered on an acoustic helicoidal (vortex) Bessel beam.” J. Acoust. Soc. Am. 125, 2552–2552 (2009).

P. L.  Marston, “Radiation force of a helicoidal Bessel beam on a sphere,” J. Acoust. Soc. Am 125, 3539–3547 (2009).
[CrossRef] [PubMed]

P. L.  Marston, L. K.  Zhang, “Radiation torques and forces in scattering from spheres and acoustical analogues,” in Optical Trapping Applications, OSA Technical Digest (CD) (Optical Society of America, 2009), p. OMB5.

P. L.  Marston, “Negative axial radiation forces on solid spheres and shells in a Bessel beam,” J. Acoust. Soc. Am 122, 3162–3165 (2007).
[CrossRef]

P. L.  Marston, “Scattering of a Bessel beam by a sphere,” J. Acoust. Soc. Am 121, 753 (2007).
[CrossRef] [PubMed]

P. L.  Marston, “Axial radiation force of a Bessel beam on a sphere and direction reversal of the force,” J. Acoust. Soc. Am 120, 3518–3524 (2006).
[CrossRef]

P. L.  Marston, “Generalized optical theorem for scatterers having inversion symmetry: applications to acoustic backscattering,” J. Acoust. Soc. Am. 109, 1291–1295 (2001).
[CrossRef] [PubMed]

B. T.  Hefner, P. L.  Marston, “An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems,” J. Acoust. Soc. Am. 106, 3313 (1999).
[CrossRef]

P. L.  Marston, J. H.  Crichton, “Radiation torque on a sphere caused by a circularly polarized electromagnetic wave,” Phys. Rev. A 30, 2508–2516 (1984).
[CrossRef]

Mitri, F. G.

F. G.  Mitri, T. P.  Lobo, G. T.  Silva, “Axial acoustic radiation torque of a Bessel vortex beam on spherical shells,” Phys. Rev. E 85, 026602 (2012).
[CrossRef]

G. T.  Silva, T. P.  Lobo, F. G.  Mitri, “Radiation torque produced by an arbitrary acoustic wave,” Europhys. Lett. 97, 54003 (2012).
[CrossRef]

F. G.  Mitri, “Equivalence of expressions for the acoustic scattering of a progressive high-order Bessel beam by an elastic sphere,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56, 1100–1103 (2009).
[CrossRef] [PubMed]

F. G.  Mitri, “Negative axial radiation force on a fluid and elastic spheres illuminated by a high-order Bessel beam of progressive waves,” J. Phys. A: Math. Theor. 42, 245202 (2009).
[CrossRef]

Newton, R. G.

R. G.  Newton, “Optical theorem and beyond,” Am. J. Phys. 44, 639–642 (1976).
[CrossRef]

Ng, J.

J.  Chen, J.  Ng, Z. F.  Lin, C. T.  Chan, “Optical pulling force,” Nat. Photonics 5, 531–534 (2011).
[CrossRef]

Novitsky, A.

A.  Novitsky, C.-W.  Qiu, H. F.  Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107, 203601 (2011).
[CrossRef] [PubMed]

Nyborg, W. L.

W. L.  Nyborg, “Acoustic streaming,” in Nonlinear Acoustics, edited by M. F.  Hamilton, D. T.  Blackstock, (Academic Press, CA, 1998), pp. Chap. 7, pp. 207–231.

Qiu, C.

S.  Xu, C.  Qiu, Z.  Liu, “Transversally stable acoustic pulling force produced by two crossed plane waves,” Europhys. Lett. 99, 44003 (2012).
[CrossRef]

Qiu, C.-W.

A.  Novitsky, C.-W.  Qiu, H. F.  Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107, 203601 (2011).
[CrossRef] [PubMed]

Shung, K. K.

Y.  Choe, J. W.  Kim, K. K.  Shung, E. S.  Kim, “Microparticle trapping in an ultrasonic Bessel beam,” Appl. Phys. Lett. 99, 233704 (2011).
[CrossRef]

Šiler, M.

O.  Brzobohatý, V.  Karásek, M.  Šiler, L.  Chvátal, T.  Čižmár, P.  Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ’tractor beam’,” Nat. Photonics 7, 123–127 (2013).
[CrossRef]

Silva, G. T.

F. G.  Mitri, T. P.  Lobo, G. T.  Silva, “Axial acoustic radiation torque of a Bessel vortex beam on spherical shells,” Phys. Rev. E 85, 026602 (2012).
[CrossRef]

G. T.  Silva, T. P.  Lobo, F. G.  Mitri, “Radiation torque produced by an arbitrary acoustic wave,” Europhys. Lett. 97, 54003 (2012).
[CrossRef]

G. T.  Silva, “Off-axis scattering of an ultrasound Bessel beam by a sphere,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 298–304 (2011).
[CrossRef] [PubMed]

Spalding, G. C.

C. E. M.  Demore, Z.  Yang, A.  Volovick, S.  Cochran, M. P.  MacDonald, G. C.  Spalding, “Mechanical evidence of the orbital angular momentum to energy ratio of vortex beams,” Phys. Rev. Lett. 108, 194301 (2012).
[CrossRef] [PubMed]

Spreeuw, R. J. C.

L.  Allen, M. W.  Beijersbergen, R. J. C.  Spreeuw, J. P.  Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Sukhov, S.

S.  Sukhov, A.  Dogariu, “Negative nonconservative forces: Optical tractor beams for arbitrary objects,” Phys. Rev. Lett. 107, 203602 (2011).
[CrossRef]

Thomas, J.-L.

D.  Baresch, J.-L.  Thomas, R.  Marchiano, “Three-dimensional acoustic radiation force on an arbitrarily located elastic sphere,” J. Acoust. Soc. Am. 133, 25–36 (2013).
[CrossRef] [PubMed]

D.  Baresch, J.-L.  Thomas, R.  Marchiano, “Spherical vortex beams of high radial degree for enhanced single-beam tweezers,” J. Appl. Phys. 113, 184901 (2013).

Volovick, A.

C. E. M.  Demore, Z.  Yang, A.  Volovick, S.  Cochran, M. P.  MacDonald, G. C.  Spalding, “Mechanical evidence of the orbital angular momentum to energy ratio of vortex beams,” Phys. Rev. Lett. 108, 194301 (2012).
[CrossRef] [PubMed]

Wang, H. F.

A.  Novitsky, C.-W.  Qiu, H. F.  Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107, 203601 (2011).
[CrossRef] [PubMed]

Wang, N.

N.  Wang, J.  Chen, S. Y.  Liu, Z. F.  Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87, 063812 (2013).
[CrossRef]

Wilcox, P. D.

C. R. P.  Courtney, B. W.  Drinkwater, C. E. M.  Demore, S.  Cochran, A.  Grinenko, P. D.  Wilcox, “Dexterous manipulation of microparticles using Bessel-function acoustic pressure fields,” Appl. Phys. Lett. 102, 123508 (2013).
[CrossRef]

Woerdman, J. P.

L.  Allen, M. W.  Beijersbergen, R. J. C.  Spreeuw, J. P.  Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Xu, S.

S.  Xu, C.  Qiu, Z.  Liu, “Transversally stable acoustic pulling force produced by two crossed plane waves,” Europhys. Lett. 99, 44003 (2012).
[CrossRef]

Yang, Z.

C. E. M.  Demore, Z.  Yang, A.  Volovick, S.  Cochran, M. P.  MacDonald, G. C.  Spalding, “Mechanical evidence of the orbital angular momentum to energy ratio of vortex beams,” Phys. Rev. Lett. 108, 194301 (2012).
[CrossRef] [PubMed]

Yosioka, K.

T.  Hasegawa, K.  Yosioka, “Acoustic radiation force on fused silica spheres, and intensity determination,” J. Acoust. Soc. Am. 58, 581–585 (1975).
[CrossRef]

Zemánek, P.

O.  Brzobohatý, V.  Karásek, M.  Šiler, L.  Chvátal, T.  Čižmár, P.  Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ’tractor beam’,” Nat. Photonics 7, 123–127 (2013).
[CrossRef]

Zhang, L. K.

L. K.  Zhang, P. L.  Marston, “Axial radiation force exerted by general non-diffracting beams,” J. Acoust. Soc. Am. 131, EL329–EL335 (2012).
[CrossRef] [PubMed]

L. K.  Zhang, P. L.  Marston, “Geometrical interpretation of negative radiation forces of acoustical Bessel beams on spheres,” Phys. Rev. E 84, 035601(R) (2011).
[CrossRef]

L. K.  Zhang, P. L.  Marston, “Radiation torque on solid spheres and drops centered on an acoustic helicoidal Bessel beam,” J. Acoust. Soc. Am. 129, 2381–2381 (2011).
[CrossRef]

L. K.  Zhang, P. L.  Marston, “Acoustic radiation torque and the conservation of angular momentum,” J. Acoust. Soc. Am. 129, 1679–1680 (2011).
[CrossRef] [PubMed]

L. K.  Zhang, P. L.  Marston, “Angular momentum flux of nonparaxial acoustic vortex beams and torques on axisymmetric objects,” Phys. Rev. E 84, 065601(R) (2011).
[CrossRef]

L. K.  Zhang, P. L.  Marston, “Radiation torque on a sphere centered on an acoustic helicoidal (vortex) Bessel beam.” J. Acoust. Soc. Am. 125, 2552–2552 (2009).

P. L.  Marston, L. K.  Zhang, “Radiation torques and forces in scattering from spheres and acoustical analogues,” in Optical Trapping Applications, OSA Technical Digest (CD) (Optical Society of America, 2009), p. OMB5.

Am. J. Phys. (1)

R. G.  Newton, “Optical theorem and beyond,” Am. J. Phys. 44, 639–642 (1976).
[CrossRef]

Appl. Phys. Lett. (1)

C. R. P.  Courtney, B. W.  Drinkwater, C. E. M.  Demore, S.  Cochran, A.  Grinenko, P. D.  Wilcox, “Dexterous manipulation of microparticles using Bessel-function acoustic pressure fields,” Appl. Phys. Lett. 102, 123508 (2013).
[CrossRef]

Appl. Phys. Lett. (1)

Y.  Choe, J. W.  Kim, K. K.  Shung, E. S.  Kim, “Microparticle trapping in an ultrasonic Bessel beam,” Appl. Phys. Lett. 99, 233704 (2011).
[CrossRef]

Europhys. Lett. (2)

S.  Xu, C.  Qiu, Z.  Liu, “Transversally stable acoustic pulling force produced by two crossed plane waves,” Europhys. Lett. 99, 44003 (2012).
[CrossRef]

G. T.  Silva, T. P.  Lobo, F. G.  Mitri, “Radiation torque produced by an arbitrary acoustic wave,” Europhys. Lett. 97, 54003 (2012).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

F. G.  Mitri, “Equivalence of expressions for the acoustic scattering of a progressive high-order Bessel beam by an elastic sphere,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56, 1100–1103 (2009).
[CrossRef] [PubMed]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

G. T.  Silva, “Off-axis scattering of an ultrasound Bessel beam by a sphere,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 298–304 (2011).
[CrossRef] [PubMed]

J. Acoust. Soc. Am. (1)

B. T.  Hefner, P. L.  Marston, “An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems,” J. Acoust. Soc. Am. 106, 3313 (1999).
[CrossRef]

J. Acoust. Soc. Am. (1)

P. L.  Marston, “Generalized optical theorem for scatterers having inversion symmetry: applications to acoustic backscattering,” J. Acoust. Soc. Am. 109, 1291–1295 (2001).
[CrossRef] [PubMed]

J. Acoust. Soc. Am (4)

P. L.  Marston, “Scattering of a Bessel beam by a sphere,” J. Acoust. Soc. Am 121, 753 (2007).
[CrossRef] [PubMed]

P. L.  Marston, “Axial radiation force of a Bessel beam on a sphere and direction reversal of the force,” J. Acoust. Soc. Am 120, 3518–3524 (2006).
[CrossRef]

P. L.  Marston, “Negative axial radiation forces on solid spheres and shells in a Bessel beam,” J. Acoust. Soc. Am 122, 3162–3165 (2007).
[CrossRef]

P. L.  Marston, “Radiation force of a helicoidal Bessel beam on a sphere,” J. Acoust. Soc. Am 125, 3539–3547 (2009).
[CrossRef] [PubMed]

J. Acoust. Soc. Am. (7)

L. K.  Zhang, P. L.  Marston, “Axial radiation force exerted by general non-diffracting beams,” J. Acoust. Soc. Am. 131, EL329–EL335 (2012).
[CrossRef] [PubMed]

D.  Baresch, J.-L.  Thomas, R.  Marchiano, “Three-dimensional acoustic radiation force on an arbitrarily located elastic sphere,” J. Acoust. Soc. Am. 133, 25–36 (2013).
[CrossRef] [PubMed]

L. K.  Zhang, P. L.  Marston, “Radiation torque on a sphere centered on an acoustic helicoidal (vortex) Bessel beam.” J. Acoust. Soc. Am. 125, 2552–2552 (2009).

L. K.  Zhang, P. L.  Marston, “Radiation torque on solid spheres and drops centered on an acoustic helicoidal Bessel beam,” J. Acoust. Soc. Am. 129, 2381–2381 (2011).
[CrossRef]

L. K.  Zhang, P. L.  Marston, “Acoustic radiation torque and the conservation of angular momentum,” J. Acoust. Soc. Am. 129, 1679–1680 (2011).
[CrossRef] [PubMed]

T.  Hasegawa, K.  Yosioka, “Acoustic radiation force on fused silica spheres, and intensity determination,” J. Acoust. Soc. Am. 58, 581–585 (1975).
[CrossRef]

X. C.  Chen, R. E.  Apfel, “Radiation force on a spherical object in an axisymmetric wave field and its application to the calibration of high-frequency transducers,” J. Acoust. Soc. Am. 99, 713–724 (1996).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

D.  Baresch, J.-L.  Thomas, R.  Marchiano, “Spherical vortex beams of high radial degree for enhanced single-beam tweezers,” J. Appl. Phys. 113, 184901 (2013).

J. Opt. Soc. Am. A (2)

J. Phys. A: Math. Theor. (1)

F. G.  Mitri, “Negative axial radiation force on a fluid and elastic spheres illuminated by a high-order Bessel beam of progressive waves,” J. Phys. A: Math. Theor. 42, 245202 (2009).
[CrossRef]

Nat. Photonics (1)

O.  Brzobohatý, V.  Karásek, M.  Šiler, L.  Chvátal, T.  Čižmár, P.  Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ’tractor beam’,” Nat. Photonics 7, 123–127 (2013).
[CrossRef]

Nat. Photonics (1)

J.  Chen, J.  Ng, Z. F.  Lin, C. T.  Chan, “Optical pulling force,” Nat. Photonics 5, 531–534 (2011).
[CrossRef]

Opt. Commun. (1)

A.  Belafhal, A.  Chafiq, Z.  Hricha, “Scattering of Mathieu beams by a rigid sphere,” Opt. Commun. 284, 3030–3035 (2003).
[CrossRef]

Opt. Lett. (2)

Optical Trapping Applications (1)

P. L.  Marston, L. K.  Zhang, “Radiation torques and forces in scattering from spheres and acoustical analogues,” in Optical Trapping Applications, OSA Technical Digest (CD) (Optical Society of America, 2009), p. OMB5.

Phys. Rev. A (3)

N.  Wang, J.  Chen, S. Y.  Liu, Z. F.  Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87, 063812 (2013).
[CrossRef]

L.  Allen, M. W.  Beijersbergen, R. J. C.  Spreeuw, J. P.  Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

P. L.  Marston, J. H.  Crichton, “Radiation torque on a sphere caused by a circularly polarized electromagnetic wave,” Phys. Rev. A 30, 2508–2516 (1984).
[CrossRef]

Phys. Rev. E (3)

L. K.  Zhang, P. L.  Marston, “Angular momentum flux of nonparaxial acoustic vortex beams and torques on axisymmetric objects,” Phys. Rev. E 84, 065601(R) (2011).
[CrossRef]

F. G.  Mitri, T. P.  Lobo, G. T.  Silva, “Axial acoustic radiation torque of a Bessel vortex beam on spherical shells,” Phys. Rev. E 85, 026602 (2012).
[CrossRef]

L. K.  Zhang, P. L.  Marston, “Geometrical interpretation of negative radiation forces of acoustical Bessel beams on spheres,” Phys. Rev. E 84, 035601(R) (2011).
[CrossRef]

Phys. Rev. Lett. (3)

A.  Novitsky, C.-W.  Qiu, H. F.  Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107, 203601 (2011).
[CrossRef] [PubMed]

S.  Sukhov, A.  Dogariu, “Negative nonconservative forces: Optical tractor beams for arbitrary objects,” Phys. Rev. Lett. 107, 203602 (2011).
[CrossRef]

C. E. M.  Demore, Z.  Yang, A.  Volovick, S.  Cochran, M. P.  MacDonald, G. C.  Spalding, “Mechanical evidence of the orbital angular momentum to energy ratio of vortex beams,” Phys. Rev. Lett. 108, 194301 (2012).
[CrossRef] [PubMed]

Proceedings of Meetings on Acoustics (POMA) (1)

P. L.  Marston, “Viscous contributions to low-frequency scattering, power absorption, radiation force, and radiation torque for spheres in acoustic beams,” Proceedings of Meetings on Acoustics (POMA) 19, 045005 (2013).
[CrossRef]

Other (1)

W. L.  Nyborg, “Acoustic streaming,” in Nonlinear Acoustics, edited by M. F.  Hamilton, D. T.  Blackstock, (Academic Press, CA, 1998), pp. Chap. 7, pp. 207–231.

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Figures (1)

Fig. 1
Fig. 1

The radiation force and/or torque on an object centered on the axis of an idealized non-diffracting beam relates to the extinction by the object via scattering and/or absorption. The beam, propagating along the z axis, is characterized by an angular function g(ϕ) (refer to text) and by a conical angle β determining the direction of wave vectors k(β, ϕ) = kn(β, ϕ) of the beam’s plane wave components. The scattering and/or absorption are characterized by a far-field scattering complex amplitude As(n(θ, ϕ)).

Equations (27)

Equations on this page are rendered with MathJax. Learn more.

ψ i = ψ i 0 ( x , y ; β ) exp ( i κ z i ω t ) ,
ψ s = ψ 0 A s ( n ) exp ( i k r i ω t ) / r ,
σ ext = 4 π k Im [ 1 2 π 0 2 π g * ( ϕ ) A s ( n ( β , ϕ ) ) d ϕ ] ,
ψ i 0 ( x , y ; β ) = ψ 0 2 π 0 2 π g ( ϕ ) exp [ i μ ( x cos ϕ + y sin ϕ ) ] d ϕ , with μ = k sin β .
k ( μ cos ϕ , μ sin ϕ , κ ) = k ( sin β cos ϕ , sin β sin ϕ , cos β ) = k n ( β , ϕ ) ,
σ sca = | A s ( n ) | 2 d Ω .
σ ext = 4 π k Im [ A s ( 0 , 0 ) ] ,
ψ i = ψ 0 i m J m ( μ ρ ) exp ( i κ z + i m ϕ ) ,
g ( ϕ ) = exp ( i m ϕ ) .
A s ( n ( θ , ϕ ) ) = exp ( i m ϕ ) i k n = | m | ( s n 1 ) 2 ( 2 n + 1 ) ( n m ) ! ( n + m ) ! P n m ( cos β ) P n m ( cos θ ) ,
σ ext = π k 2 n = | m | ( 2 n + 1 ) [ P n m ( cos β ) ] 2 Re [ 2 ( 1 s n ) ] ,
Q ext σ ext / ( π a 2 ) = 1 ( k a ) 2 n = | m | ( 2 n + 1 ) ( n m ) ! ( n + m ) ! [ P n m ( cos β ) ] 2 Re [ 2 ( 1 s n ) ] ,
Re [ 2 ( 1 s n ) ] = ( | s n 1 | 2 ) + ( 1 | s n | 2 ) .
Q sca σ sca / ( π a 2 ) = 1 ( k a ) 2 n = | m | ( 2 n + 1 ) [ P n m ( cos β ) ] 2 ( | s n 1 | 2 ) ,
Q abs σ abs / ( π a 2 ) = 1 ( k a ) 2 n = | m | ( 2 n + 1 ) [ P n m ( cos β ) ] 2 ( 1 | s n | 2 ) .
s n = exp ( i 2 δ n ) ,
Q ext , sca = σ ext , sca / ( π a 2 ) = 4 ( k a ) 2 n = | m | ( 2 n + 1 ) [ P n m ( cos β ) ] 2 sin 2 ( δ n ) .
P ext , sca , abs = I 0 σ ext , sca , abs = I 0 ( π a 2 ) Q ext , sca , abs ,
F z = c 0 1 ( P ext cos β P sca cos θ s )
F z = π a 2 c 0 1 I 0 Y p , Y p = Q ext cos β Q sca cos θ s ,
cos θ s = cos θ | A s ( n ) | 2 d Ω | A s ( n ) | 2 d Ω .
σ asym . sca cos θ | A s ( n ) | 2 d Ω , Q asym . sca σ asym . sca / ( π a 2 ) .
Q asym . sca = σ asym . sca π a 2 = ( 2 k a ) 2 n = | m | [ 2 ( α n α n + 1 + β n β n + 1 ) ] ( n m + 1 ) ! ( n + m ) ! P n m ( b ) P n + 1 m ( b ) .
Y p = cos β ( k a 2 ) n = | m | ( 4 α n ) ( 2 n + 1 ) ( n m ) ! ( n + m ) ! [ P n m ( cos β ) ] 2 ( 2 k a ) 2 n = | m | [ 2 ( α n α n + 1 + β n β n + 1 ) ] ( n m + 1 ) ! ( n + m ) ! P n m ( cos β ) P n + 1 m ( cos β ) ,
T z = m ω P abs ,
T z = π a 2 I 0 Q T / ω , Q T = m Q abs .
Q T = m Q abs = m ( k a ) 2 n = | m | ( 2 n + 1 ) ( n m ) ! ( n + m ) ! [ P n m ( cos β ) ] 2 ( 1 | s n | 2 ) ,

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