Abstract

Electromagnetic scattering of a zero-order Bessel beam by an anisotropic spherical particle in the off-axis configuration is investigated. Based on the spherical vector wave functions, the expansion expression of the zero-order Bessel beam is derived, and its convergence is numerically discussed in detail. Utilizing the tangential continuity of the electromagnetic fields, the expressions of scattering coefficients are given. The effects of the conical angle of the wave vector components of the zero-order Bessel beam, the ratio of the radius of the sphere to the central spot radius of the zero-order Bessel beam, the shift of the beam waist center position along both the x and y axes, the permittivity and permeability tensor elements, and the loss of the sphere on the radar cross section (RCS) are numerically analyzed. It is revealed that the maximum RCS appears in the conical direction or neighboring direction when the sphere is illuminated by a zero-order Bessel beam. Furthermore, the RCS will decrease and the symmetry is broken with the shift of the beam waist center.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Doicu and T. Wriedt, “Computation of the beam-shape coefficients in the generalized Lorenz-Mie theory for spherical vector wave functions,” Appl. Opt. 36, 2971–2978 (1997).
    [CrossRef]
  2. K. A. Fuller, Electromagnetic Scattering by Spherical Particles (University of Alabama Huntsville, 2000), pp. 3–6.
  3. J. A. Lock and G. Gouesbet, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. I. On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
    [CrossRef]
  4. E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A 6, S157–S161 (2004).
    [CrossRef]
  5. G. Gréhan, B. Maheu, and G. Gouesbet, “Scattering of laser beam by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
    [CrossRef]
  6. Z. J. Li, Z. S. Wu, and H. Y. Li, “Analysis of electromagnetic scattering by uniaxial anisotropic bispheres,” J. Opt. Soc. Am. A 28, 118–125 (2011).
    [CrossRef]
  7. G. Gouesbet and G. Gréhan, Generalized Lorenz-Mie Theories (Springer, 2011), pp. 37–75.
  8. D. Ding and X. Liu, “Approximate description for Bessel, Bessel-Gauss, and Gaussian beams with finite aperture,” J. Opt. Soc. Am. A 16, 1286–1293 (1999).
    [CrossRef]
  9. V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
    [CrossRef]
  10. J. Durnin, “Exact solution for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  11. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), pp. 399–413.
  12. F. G. Mitri, “Gegenbauer expansion to model the incident wave-field of a high-order Bessel vortex beam in spherical coordinates,” Ultrasonics 50, 541–543 (2010).
    [CrossRef]
  13. X. Ma and E. Li, “Scattering of an unpolarized Bessel beam by spheres,” Chin. Opt. Lett. 8, 1195–1198 (2010).
    [CrossRef]
  14. R. Li, K. Ren, X. E. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transfer 126, 69–77 (2013).
    [CrossRef]
  15. F. G. Mitri and G. T. Silva, “Off-axial acoustic scattering of a high-order Bessel vortex beam by a rigid sphere,” Wave Motion 48, 392–400 (2011).
    [CrossRef]
  16. J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
    [CrossRef]
  17. M. Xiubo and L. Enbang, “Scattering of unpolarized Bessel-Gauss beam by a sphere,” Acta Optica Sinica 32, 0829002 (2012).
    [CrossRef]
  18. F. G. Mitri, “Arbitrary scattering of an electromagnetic zero-order Bessel beam by a dielectric sphere,” Opt. Lett. 36, 766–768 (2011).
    [CrossRef]
  19. F. G. Mitri, “Electromagnetic wave scattering of a higher-order Bessel vortex beam by a dielectric sphere,” IEEE Trans. Antennas Propag. 59, 4375–4379 (2011).
    [CrossRef]
  20. P. L. Marston, “Scattering of a Bessel beam by a sphere,” J. Acoust. Soc. Am. 121, 753–758 (2007).
    [CrossRef]
  21. F. G. Mitri, “Linear axial scattering of an acoustical high-order Bessel trigonometric beam by compressible soft fluid spheres,” J. Appl. Phys. 109, 014916 (2011).
    [CrossRef]
  22. F. G. Mitri, “Arbitrary scattering of an acoustical high-order Bessel trigonometric (non-vortex) beam by a compressible soft fluid sphere,” Ultrasonics 53, 956–961 (2013).
    [CrossRef]
  23. F. G. Mitri, “Interaction of a nondiffracting high-order Bessel (vortex) beam of fractional type α and integer order m with a rigid sphere:linear acoustic scattering and net instantaneous axial force,” IEEE Trans Ultrason. Ferroelectr. Freq. Control 57, 395–404 (2010).
    [CrossRef]
  24. F. G. Mitri, “Acoustic beam interaction with a rigid sphere: the case of a first-order non-diffracting Bessel trigonometric beam,” J. Sound Vib. 330, 6053–6060 (2011).
    [CrossRef]
  25. 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]
  26. F. G. Mitri, “Equivalence of expressions for the acoustic scattering of a progressive higher-order Bessel beam by an elastic sphere,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56, 1100–1103 (2009).
    [CrossRef]
  27. L. Haiying, W. Zhensen, S. Mao, L. Bai, and C. Huang, “Scattering of Hermite-Gaussian beam by plasma sphere,” in Proceedings of International Conference on Microwave and Millimeter Wave Technology (ICMMT) (IEEE, 2010), pp. 1405–1408.
  28. Z. S. Wu, Z. J. Li, H. Li, Q. K. Yuan, and H. Y. Li, “Off-axis Gaussian beam scattering by an anisotropic coated sphere,” IEEE Trans. Antennas Propag. 59, 4740–4748 (2011).
    [CrossRef]
  29. Y. L. Geng, “Scattering of a plane wave by an anisotropic ferrite-coated conducting sphere,” IET Microw. Antennas Propag. 2, 158–162 (2008).
    [CrossRef]
  30. B. Stout, M. Nevière, and E. Popov, “Mie scattering by an anisotropic object. Part 1. Homogeneous sphere,” J. Opt. Soc. Am. A 23, 1111–1123 (2006).
    [CrossRef]
  31. K. L. Wong and H. T. Chen, “Electromagnetic scattering by a uniaxially anisotropic sphere,” IEE Proc. 139, 314–318 (1992).
    [CrossRef]
  32. Y. Geng, X. Wu, and L.-W. Li, “Analysis of electromagnetic scattering by a plasma anisotropic sphere,” Radio Sci. 38(6), 12 (2003).
    [CrossRef]
  33. T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8(43), 1–23 (2006).
    [CrossRef]
  34. F. G. Mitri, “Three-dimensional vectorial analysis of an electromagnetic non-diffracting high-order Bessel trigonometric beam,” Wave Motion 49, 561–568 (2012).
    [CrossRef]
  35. S. R. Mishra, “A vector wave analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991).
    [CrossRef]
  36. L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, 1985), pp. 168–177.
  37. K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
    [CrossRef]
  38. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998), pp. 88–92.
  39. Z. J. Li, “Scattering of anisotropic particle system from plane wave/Gaussian beam,” Ph.D. thesis (Xi’dian University, 2012) ( http://cdmd.cnki.com.cn/Article/CDMD-10701-1013114292.htm ).

2013 (2)

F. G. Mitri, “Arbitrary scattering of an acoustical high-order Bessel trigonometric (non-vortex) beam by a compressible soft fluid sphere,” Ultrasonics 53, 956–961 (2013).
[CrossRef]

R. Li, K. Ren, X. E. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transfer 126, 69–77 (2013).
[CrossRef]

2012 (2)

M. Xiubo and L. Enbang, “Scattering of unpolarized Bessel-Gauss beam by a sphere,” Acta Optica Sinica 32, 0829002 (2012).
[CrossRef]

F. G. Mitri, “Three-dimensional vectorial analysis of an electromagnetic non-diffracting high-order Bessel trigonometric beam,” Wave Motion 49, 561–568 (2012).
[CrossRef]

2011 (8)

Z. J. Li, Z. S. Wu, and H. Y. Li, “Analysis of electromagnetic scattering by uniaxial anisotropic bispheres,” J. Opt. Soc. Am. A 28, 118–125 (2011).
[CrossRef]

F. G. Mitri, “Arbitrary scattering of an electromagnetic zero-order Bessel beam by a dielectric sphere,” Opt. Lett. 36, 766–768 (2011).
[CrossRef]

F. G. Mitri and G. T. Silva, “Off-axial acoustic scattering of a high-order Bessel vortex beam by a rigid sphere,” Wave Motion 48, 392–400 (2011).
[CrossRef]

F. G. Mitri, “Acoustic beam interaction with a rigid sphere: the case of a first-order non-diffracting Bessel trigonometric beam,” J. Sound Vib. 330, 6053–6060 (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]

Z. S. Wu, Z. J. Li, H. Li, Q. K. Yuan, and H. Y. Li, “Off-axis Gaussian beam scattering by an anisotropic coated sphere,” IEEE Trans. Antennas Propag. 59, 4740–4748 (2011).
[CrossRef]

F. G. Mitri, “Linear axial scattering of an acoustical high-order Bessel trigonometric beam by compressible soft fluid spheres,” J. Appl. Phys. 109, 014916 (2011).
[CrossRef]

F. G. Mitri, “Electromagnetic wave scattering of a higher-order Bessel vortex beam by a dielectric sphere,” IEEE Trans. Antennas Propag. 59, 4375–4379 (2011).
[CrossRef]

2010 (3)

F. G. Mitri, “Gegenbauer expansion to model the incident wave-field of a high-order Bessel vortex beam in spherical coordinates,” Ultrasonics 50, 541–543 (2010).
[CrossRef]

F. G. Mitri, “Interaction of a nondiffracting high-order Bessel (vortex) beam of fractional type α and integer order m with a rigid sphere:linear acoustic scattering and net instantaneous axial force,” IEEE Trans Ultrason. Ferroelectr. Freq. Control 57, 395–404 (2010).
[CrossRef]

X. Ma and E. Li, “Scattering of an unpolarized Bessel beam by spheres,” Chin. Opt. Lett. 8, 1195–1198 (2010).
[CrossRef]

2009 (1)

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

2008 (1)

Y. L. Geng, “Scattering of a plane wave by an anisotropic ferrite-coated conducting sphere,” IET Microw. Antennas Propag. 2, 158–162 (2008).
[CrossRef]

2007 (1)

P. L. Marston, “Scattering of a Bessel beam by a sphere,” J. Acoust. Soc. Am. 121, 753–758 (2007).
[CrossRef]

2006 (2)

B. Stout, M. Nevière, and E. Popov, “Mie scattering by an anisotropic object. Part 1. Homogeneous sphere,” J. Opt. Soc. Am. A 23, 1111–1123 (2006).
[CrossRef]

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8(43), 1–23 (2006).
[CrossRef]

2004 (1)

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A 6, S157–S161 (2004).
[CrossRef]

2003 (1)

Y. Geng, X. Wu, and L.-W. Li, “Analysis of electromagnetic scattering by a plasma anisotropic sphere,” Radio Sci. 38(6), 12 (2003).
[CrossRef]

1999 (1)

1998 (1)

1997 (1)

1996 (1)

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
[CrossRef]

1994 (1)

1992 (1)

K. L. Wong and H. T. Chen, “Electromagnetic scattering by a uniaxially anisotropic sphere,” IEE Proc. 139, 314–318 (1992).
[CrossRef]

1991 (1)

S. R. Mishra, “A vector wave analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991).
[CrossRef]

1989 (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

1987 (1)

1986 (1)

Abramochkin, E. G.

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A 6, S157–S161 (2004).
[CrossRef]

Alexander, D. R.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

Bagini, V.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
[CrossRef]

Bai, L.

L. Haiying, W. Zhensen, S. Mao, L. Bai, and C. Huang, “Scattering of Hermite-Gaussian beam by plasma sphere,” in Proceedings of International Conference on Microwave and Millimeter Wave Technology (ICMMT) (IEEE, 2010), pp. 1405–1408.

Barton, J. P.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998), pp. 88–92.

Bouchal, Z.

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8(43), 1–23 (2006).
[CrossRef]

Chen, H. T.

K. L. Wong and H. T. Chen, “Electromagnetic scattering by a uniaxially anisotropic sphere,” IEE Proc. 139, 314–318 (1992).
[CrossRef]

Cizmar, T.

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8(43), 1–23 (2006).
[CrossRef]

Ding, D.

Doicu, A.

Durnin, J.

Enbang, L.

M. Xiubo and L. Enbang, “Scattering of unpolarized Bessel-Gauss beam by a sphere,” Acta Optica Sinica 32, 0829002 (2012).
[CrossRef]

Frezza, F.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
[CrossRef]

Fuller, K. A.

K. A. Fuller, Electromagnetic Scattering by Spherical Particles (University of Alabama Huntsville, 2000), pp. 3–6.

Geng, Y.

Y. Geng, X. Wu, and L.-W. Li, “Analysis of electromagnetic scattering by a plasma anisotropic sphere,” Radio Sci. 38(6), 12 (2003).
[CrossRef]

Geng, Y. L.

Y. L. Geng, “Scattering of a plane wave by an anisotropic ferrite-coated conducting sphere,” IET Microw. Antennas Propag. 2, 158–162 (2008).
[CrossRef]

Gong, S.

R. Li, K. Ren, X. E. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transfer 126, 69–77 (2013).
[CrossRef]

Gouesbet, G.

Gréhan, G.

Guo, L.

R. Li, K. Ren, X. E. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transfer 126, 69–77 (2013).
[CrossRef]

Haiying, L.

L. Haiying, W. Zhensen, S. Mao, L. Bai, and C. Huang, “Scattering of Hermite-Gaussian beam by plasma sphere,” in Proceedings of International Conference on Microwave and Millimeter Wave Technology (ICMMT) (IEEE, 2010), pp. 1405–1408.

Han, X. E.

R. Li, K. Ren, X. E. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transfer 126, 69–77 (2013).
[CrossRef]

Huang, C.

L. Haiying, W. Zhensen, S. Mao, L. Bai, and C. Huang, “Scattering of Hermite-Gaussian beam by plasma sphere,” in Proceedings of International Conference on Microwave and Millimeter Wave Technology (ICMMT) (IEEE, 2010), pp. 1405–1408.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998), pp. 88–92.

Kollarova, V.

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8(43), 1–23 (2006).
[CrossRef]

Kong, J. A.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, 1985), pp. 168–177.

Li, E.

Li, H.

Z. S. Wu, Z. J. Li, H. Li, Q. K. Yuan, and H. Y. Li, “Off-axis Gaussian beam scattering by an anisotropic coated sphere,” IEEE Trans. Antennas Propag. 59, 4740–4748 (2011).
[CrossRef]

Li, H. Y.

Z. S. Wu, Z. J. Li, H. Li, Q. K. Yuan, and H. Y. Li, “Off-axis Gaussian beam scattering by an anisotropic coated sphere,” IEEE Trans. Antennas Propag. 59, 4740–4748 (2011).
[CrossRef]

Z. J. Li, Z. S. Wu, and H. Y. Li, “Analysis of electromagnetic scattering by uniaxial anisotropic bispheres,” J. Opt. Soc. Am. A 28, 118–125 (2011).
[CrossRef]

Li, L.-W.

Y. Geng, X. Wu, and L.-W. Li, “Analysis of electromagnetic scattering by a plasma anisotropic sphere,” Radio Sci. 38(6), 12 (2003).
[CrossRef]

Li, R.

R. Li, K. Ren, X. E. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transfer 126, 69–77 (2013).
[CrossRef]

Li, Z. J.

Z. J. Li, Z. S. Wu, and H. Y. Li, “Analysis of electromagnetic scattering by uniaxial anisotropic bispheres,” J. Opt. Soc. Am. A 28, 118–125 (2011).
[CrossRef]

Z. S. Wu, Z. J. Li, H. Li, Q. K. Yuan, and H. Y. Li, “Off-axis Gaussian beam scattering by an anisotropic coated sphere,” IEEE Trans. Antennas Propag. 59, 4740–4748 (2011).
[CrossRef]

Z. J. Li, “Scattering of anisotropic particle system from plane wave/Gaussian beam,” Ph.D. thesis (Xi’dian University, 2012) ( http://cdmd.cnki.com.cn/Article/CDMD-10701-1013114292.htm ).

Liu, X.

Lock, J. A.

Ma, X.

Maheu, B.

Mao, S.

L. Haiying, W. Zhensen, S. Mao, L. Bai, and C. Huang, “Scattering of Hermite-Gaussian beam by plasma sphere,” in Proceedings of International Conference on Microwave and Millimeter Wave Technology (ICMMT) (IEEE, 2010), pp. 1405–1408.

Marston, P. L.

P. L. Marston, “Scattering of a Bessel beam by a sphere,” J. Acoust. Soc. Am. 121, 753–758 (2007).
[CrossRef]

Mishra, S. R.

S. R. Mishra, “A vector wave analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991).
[CrossRef]

Mitri, F. G.

F. G. Mitri, “Arbitrary scattering of an acoustical high-order Bessel trigonometric (non-vortex) beam by a compressible soft fluid sphere,” Ultrasonics 53, 956–961 (2013).
[CrossRef]

F. G. Mitri, “Three-dimensional vectorial analysis of an electromagnetic non-diffracting high-order Bessel trigonometric beam,” Wave Motion 49, 561–568 (2012).
[CrossRef]

F. G. Mitri, “Acoustic beam interaction with a rigid sphere: the case of a first-order non-diffracting Bessel trigonometric beam,” J. Sound Vib. 330, 6053–6060 (2011).
[CrossRef]

F. G. Mitri, “Electromagnetic wave scattering of a higher-order Bessel vortex beam by a dielectric sphere,” IEEE Trans. Antennas Propag. 59, 4375–4379 (2011).
[CrossRef]

F. G. Mitri, “Linear axial scattering of an acoustical high-order Bessel trigonometric beam by compressible soft fluid spheres,” J. Appl. Phys. 109, 014916 (2011).
[CrossRef]

F. G. Mitri and G. T. Silva, “Off-axial acoustic scattering of a high-order Bessel vortex beam by a rigid sphere,” Wave Motion 48, 392–400 (2011).
[CrossRef]

F. G. Mitri, “Arbitrary scattering of an electromagnetic zero-order Bessel beam by a dielectric sphere,” Opt. Lett. 36, 766–768 (2011).
[CrossRef]

F. G. Mitri, “Gegenbauer expansion to model the incident wave-field of a high-order Bessel vortex beam in spherical coordinates,” Ultrasonics 50, 541–543 (2010).
[CrossRef]

F. G. Mitri, “Interaction of a nondiffracting high-order Bessel (vortex) beam of fractional type α and integer order m with a rigid sphere:linear acoustic scattering and net instantaneous axial force,” IEEE Trans Ultrason. Ferroelectr. Freq. Control 57, 395–404 (2010).
[CrossRef]

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

Nevière, M.

Popov, E.

Ren, K.

R. Li, K. Ren, X. E. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transfer 126, 69–77 (2013).
[CrossRef]

Ren, K. F.

Santarsiero, M.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
[CrossRef]

Schaub, S. A.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

Schettini, G.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
[CrossRef]

Shin, R. T.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, 1985), pp. 168–177.

Silva, G. T.

F. G. Mitri and G. T. Silva, “Off-axial acoustic scattering of a high-order Bessel vortex beam by a rigid sphere,” Wave Motion 48, 392–400 (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]

Spagnolo, G. S.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
[CrossRef]

Stout, B.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), pp. 399–413.

Tsang, L.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, 1985), pp. 168–177.

Volostnikov, V. G.

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A 6, S157–S161 (2004).
[CrossRef]

Wong, K. L.

K. L. Wong and H. T. Chen, “Electromagnetic scattering by a uniaxially anisotropic sphere,” IEE Proc. 139, 314–318 (1992).
[CrossRef]

Wriedt, T.

Wu, X.

Y. Geng, X. Wu, and L.-W. Li, “Analysis of electromagnetic scattering by a plasma anisotropic sphere,” Radio Sci. 38(6), 12 (2003).
[CrossRef]

Wu, Z.

R. Li, K. Ren, X. E. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transfer 126, 69–77 (2013).
[CrossRef]

Wu, Z. S.

Z. J. Li, Z. S. Wu, and H. Y. Li, “Analysis of electromagnetic scattering by uniaxial anisotropic bispheres,” J. Opt. Soc. Am. A 28, 118–125 (2011).
[CrossRef]

Z. S. Wu, Z. J. Li, H. Li, Q. K. Yuan, and H. Y. Li, “Off-axis Gaussian beam scattering by an anisotropic coated sphere,” IEEE Trans. Antennas Propag. 59, 4740–4748 (2011).
[CrossRef]

Xiubo, M.

M. Xiubo and L. Enbang, “Scattering of unpolarized Bessel-Gauss beam by a sphere,” Acta Optica Sinica 32, 0829002 (2012).
[CrossRef]

Yuan, Q. K.

Z. S. Wu, Z. J. Li, H. Li, Q. K. Yuan, and H. Y. Li, “Off-axis Gaussian beam scattering by an anisotropic coated sphere,” IEEE Trans. Antennas Propag. 59, 4740–4748 (2011).
[CrossRef]

Zemanek, P.

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8(43), 1–23 (2006).
[CrossRef]

Zhensen, W.

L. Haiying, W. Zhensen, S. Mao, L. Bai, and C. Huang, “Scattering of Hermite-Gaussian beam by plasma sphere,” in Proceedings of International Conference on Microwave and Millimeter Wave Technology (ICMMT) (IEEE, 2010), pp. 1405–1408.

Acta Optica Sinica (1)

M. Xiubo and L. Enbang, “Scattering of unpolarized Bessel-Gauss beam by a sphere,” Acta Optica Sinica 32, 0829002 (2012).
[CrossRef]

Appl. Opt. (3)

Chin. Opt. Lett. (1)

IEE Proc. (1)

K. L. Wong and H. T. Chen, “Electromagnetic scattering by a uniaxially anisotropic sphere,” IEE Proc. 139, 314–318 (1992).
[CrossRef]

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

F. G. Mitri, “Interaction of a nondiffracting high-order Bessel (vortex) beam of fractional type α and integer order m with a rigid sphere:linear acoustic scattering and net instantaneous axial force,” IEEE Trans Ultrason. Ferroelectr. Freq. Control 57, 395–404 (2010).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

Z. S. Wu, Z. J. Li, H. Li, Q. K. Yuan, and H. Y. Li, “Off-axis Gaussian beam scattering by an anisotropic coated sphere,” IEEE Trans. Antennas Propag. 59, 4740–4748 (2011).
[CrossRef]

F. G. Mitri, “Electromagnetic wave scattering of a higher-order Bessel vortex beam by a dielectric sphere,” IEEE Trans. Antennas Propag. 59, 4375–4379 (2011).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (2)

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]

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

IET Microw. Antennas Propag. (1)

Y. L. Geng, “Scattering of a plane wave by an anisotropic ferrite-coated conducting sphere,” IET Microw. Antennas Propag. 2, 158–162 (2008).
[CrossRef]

J. Acoust. Soc. Am. (1)

P. L. Marston, “Scattering of a Bessel beam by a sphere,” J. Acoust. Soc. Am. 121, 753–758 (2007).
[CrossRef]

J. Appl. Phys. (2)

F. G. Mitri, “Linear axial scattering of an acoustical high-order Bessel trigonometric beam by compressible soft fluid spheres,” J. Appl. Phys. 109, 014916 (2011).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

J. Mod. Opt. (1)

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
[CrossRef]

J. Opt. A (1)

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A 6, S157–S161 (2004).
[CrossRef]

J. Opt. Soc. Am. A (5)

J. Quant. Spectrosc. Radiat. Transfer (1)

R. Li, K. Ren, X. E. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transfer 126, 69–77 (2013).
[CrossRef]

J. Sound Vib. (1)

F. G. Mitri, “Acoustic beam interaction with a rigid sphere: the case of a first-order non-diffracting Bessel trigonometric beam,” J. Sound Vib. 330, 6053–6060 (2011).
[CrossRef]

New J. Phys. (1)

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8(43), 1–23 (2006).
[CrossRef]

Opt. Commun. (1)

S. R. Mishra, “A vector wave analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991).
[CrossRef]

Opt. Lett. (1)

Radio Sci. (1)

Y. Geng, X. Wu, and L.-W. Li, “Analysis of electromagnetic scattering by a plasma anisotropic sphere,” Radio Sci. 38(6), 12 (2003).
[CrossRef]

Ultrasonics (2)

F. G. Mitri, “Gegenbauer expansion to model the incident wave-field of a high-order Bessel vortex beam in spherical coordinates,” Ultrasonics 50, 541–543 (2010).
[CrossRef]

F. G. Mitri, “Arbitrary scattering of an acoustical high-order Bessel trigonometric (non-vortex) beam by a compressible soft fluid sphere,” Ultrasonics 53, 956–961 (2013).
[CrossRef]

Wave Motion (2)

F. G. Mitri and G. T. Silva, “Off-axial acoustic scattering of a high-order Bessel vortex beam by a rigid sphere,” Wave Motion 48, 392–400 (2011).
[CrossRef]

F. G. Mitri, “Three-dimensional vectorial analysis of an electromagnetic non-diffracting high-order Bessel trigonometric beam,” Wave Motion 49, 561–568 (2012).
[CrossRef]

Other (7)

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, 1985), pp. 168–177.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998), pp. 88–92.

Z. J. Li, “Scattering of anisotropic particle system from plane wave/Gaussian beam,” Ph.D. thesis (Xi’dian University, 2012) ( http://cdmd.cnki.com.cn/Article/CDMD-10701-1013114292.htm ).

L. Haiying, W. Zhensen, S. Mao, L. Bai, and C. Huang, “Scattering of Hermite-Gaussian beam by plasma sphere,” in Proceedings of International Conference on Microwave and Millimeter Wave Technology (ICMMT) (IEEE, 2010), pp. 1405–1408.

G. Gouesbet and G. Gréhan, Generalized Lorenz-Mie Theories (Springer, 2011), pp. 37–75.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), pp. 399–413.

K. A. Fuller, Electromagnetic Scattering by Spherical Particles (University of Alabama Huntsville, 2000), pp. 3–6.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1.
Fig. 1.

Geometry for light scattering of a Bessel beam by uniaxial anisotropic sphere.

Fig. 2.
Fig. 2.

Values of BSCs p m n and q m n versus term of n for x -polarized Bessel beam.

Fig. 3.
Fig. 3.

Distribution of the RCS of a uniaxial anisotropic sphere illuminated by a Bessel beam degenerated to a plane wave.

Fig. 4.
Fig. 4.

Tangential and radial components of near surface and internal fields along x axis.

Fig. 5.
Fig. 5.

Effects of conical angle α on the RCS ( ε t = 5.3495 ε 0 , ε z = 4.9284 ε 0 , μ ¯ ¯ = μ 0 I ¯ ¯ , a = λ ).

Fig. 6.
Fig. 6.

Effects of sphere radius compared with the central spot radius of the Bessel beam on the distribution of the RCS.

Fig. 7.
Fig. 7.

Effects of anisotropy on the RCS.

Fig. 8.
Fig. 8.

Effects of permittivity tensor element ε z on the RCS.

Fig. 9.
Fig. 9.

Effects of permeability tensor element μ z on the RCS.

Fig. 10.
Fig. 10.

Effects of the imaginary part A of the permittivity tensor element ε t on the RCS.

Fig. 11.
Fig. 11.

Effects of the imaginary part B of the permittivity tensor element ε z on the RCS.

Fig. 12.
Fig. 12.

Effects of the shift of the beam center along the x axis on the RCS.

Fig. 13.
Fig. 13.

Effects of the shift of the beam center along the y axis on the RCS.

Equations (22)

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

E i ( r ) = E 0 0 2 π e v ( α , β ) exp ( i k · r ) exp ( i k · r 0 ) d β ,
e x ( α , β ) = sin α cos β e ^ r ( α , β ) + cos α cos β e ^ θ ( α , β ) sin β e ^ ϕ ( α , β ) ,
e y ( α , β ) = sin α sin β e ^ r ( α , β ) + cos α sin β e ^ θ ( α , β ) + cos β e ^ ϕ ( α , β ) .
e v ( α , β ) exp ( i k · r ) = n = 1 m = n n D m n [ p m n M m n ( 1 ) ( k r ) + q m n N m n ( 1 ) ( k r ) ] ,
D m n = ( 2 n + 1 ) ( n m ) ! 4 n ( n + 1 ) ( n + m ) ! , p m n = 4 i n + 1 exp ( i m β ) e ^ v ( α , β ) [ π m n ( cos α ) e ^ θ ( α , β ) i τ m n ( cos α ) e ^ ϕ ( α , β ) ] , q m n = 4 i n + 1 exp ( i m β ) e ^ v ( α , β ) [ τ m n ( cos α ) e ^ θ ( α , β ) i π m n ( cos α ) e ^ ϕ ( α , β ) ] .
E i ( r ) = n = 1 m = n n [ p m n v M m n ( 1 ) ( k r ) + q m n v N m n ( 1 ) ( k r ) ] ,
{ p m n v q m n v } = 4 D m n i n + 1 exp ( i k z 0 cos α ) [ cos α { π m n τ m n } I + v + { τ m n π m n } I v ] , I ± x = π exp [ i ( 1 m ) ϕ 0 ] J 1 m ( ρ 0 ) ± π exp [ i ( m + 1 ) ϕ 0 ] J 1 m ( ρ 0 ) , I ± y = π i exp [ i ( 1 m ) ϕ 0 ] J 1 m ( ρ 0 ) ± π i exp [ i ( m + 1 ) ϕ 0 ] J 1 m ( ρ 0 ) , ρ 0 = k x 0 2 + y 0 2 sin α , ϕ 0 = arctan ( y 0 / x 0 ) + π / 2 .
J n ( u ) = ( i ) n 2 π 0 2 π exp [ i ( u cos θ n θ ) ] d θ .
H i ( r ) = k i w μ n = 1 m = n n [ q m n v M m n ( 1 ) ( k r ) + p m n v N m n ( 1 ) ( k r ) ] .
ε ¯ ¯ = ε 0 [ ε t , 0 , 0 0 , ε t , 0 0 , 0 , ε z ] , μ ¯ ¯ = μ 0 [ μ t , 0 , 0 0 , μ t , 0 0 , 0 , μ z ] .
× ( μ ¯ ¯ 1 · × E ) w 2 ε ¯ ¯ · E = 0 ,
E s ( r ) = n = 1 m = n n [ a m n v M m n ( 3 ) ( k r ) + b m n 3 N m n ( 3 ) ( k r ) ] ,
H s ( r ) = k i w μ n = 1 m = n n [ b m n v M m n ( 3 ) ( k r ) + a m n v N m n ( 3 ) ( k r ) ] ,
E I ( r ) = q = 1 2 n = 1 m = n n n = 1 2 π G m n q 0 π [ A m n q e M m n ( 1 ) ( k q r ) + B m n q e N m n ( 1 ) ( k q r ) + C m n q e L m n ( 1 ) ( k q r ) ] × P n m ( cos θ ) k q 2 sin θ d θ ,
H I ( r ) = q = 1 2 n = 1 m = n n n = 1 2 π G m n q 0 π [ A m n q h M m n ( 1 ) ( k q r ) + B m n q h N m n ( 1 ) ( k q r ) + C m n q h L m n ( 1 ) ( k q r ) ] × P n m ( cos θ ) k q 2 sin θ d θ ,
E i θ + E s θ = E I θ , E i ϕ + E s ϕ = E I ϕ , H i θ + H s θ = H I θ , H i ϕ + H s ϕ = H I ϕ .
q = 1 2 n = 1 2 π G m n q 0 π Q m n q P n m ( cos θ ) k q 2 sin θ d θ = p m n v i ( k r ) 2 | r = a , q = 1 2 n = 1 2 π G m n q 0 π R m n q P n m ( cos θ ) k q 2 sin θ d θ = q m n v i ( k r ) 2 | r = a ,
Q m n q = { A m n q e j n ( k q r ) 1 k r d d r [ r h n ( 1 ) ( k r ) ] i w μ k [ B m n q h 1 k q r d d r [ r h n ( 1 ) ( k r ) ] + C m n q h j n ( k q r ) r ] h n ( 1 ) ( k r ) } | r = a ,
R m n q = { i w μ k A m n q h j n ( k q r ) 1 k r d d r [ r h n ( 1 ) ( k r ) ] [ B m n q e 1 k q r d d r [ r j n ( k q r ) ] + C m n q e j n ( k q r ) r ] h n ( 1 ) ( k r ) | r = a .
a m n v = 1 h n ( 1 ) ( k a ) [ q = 1 2 n = 1 2 π G m n q 0 π A m n q e j n ( k q a ) P n m ( cos θ ) k q 2 sin θ d θ p m n v j n ( k r ) ] ,
b m n v = i w μ k h n ( 1 ) ( k a ) [ q = 1 2 n = 1 2 π G m n q 0 π A m n q h j n ( k r ) P n m ( cos θ ) k q 2 sin θ d θ q m n v j n ( k r ) ] .
σ = lim r 4 π r 2 ( | E s θ | 2 + | E s ϕ | 2 ) .

Metrics