Abstract

Focusing fields of optical vortex (OV) beams with circular or radial polarizations carry both spin angular momentum (SAM) and orbital angular momentum (OAM), and can realize non-axial spinning and orbiting motion of absorptive particles. Using the T-matrix method, we evaluate the optical forces and torques exerted on micro-sized particles induced by the OV beams. Numerical results demonstrate that the particle is trapped on the circle of intensity maxima, and experiences a transverse spin torque along azimuthal direction, a longitudinal spin torque, and an orbital torque, respectively. The direction of spinning motion is not only related to the sign of topological charge of the OV beam, but also to the polarization state. However, the topological charge controls the direction of orbiting motion individually. Optically induced rotations of particles with varying sizes and absorptivity are investigated in OV beams with different topological charges and polarization states. These results may be exploited in practical optical manipulation, especially for optically induced rotations of micro-particles.

© 2016 Optical Society of America

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References

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2016 (3)

2015 (2)

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

2014 (7)

A. Canaguier-Durand and C. Genet, “Transverse spinning of a sphere in a plasmonic field,” Phys. Rev. A 89(3), 033841 (2014).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
[Crossref] [PubMed]

A. Lehmuskero, Y. Li, P. Johansson, and M. Käll, “Plasmonic particles set into fast orbital motion by an optical vortex beam,” Opt. Express 22(4), 4349–4356 (2014).
[Crossref] [PubMed]

W.-Y. Tsai, J.-S. Huang, and C.-B. Huang, “Selective trapping or rotation of isotropic dielectric microparticles by optical near field in a plasmonic archimedes spiral,” Nano Lett. 14(2), 547–552 (2014).
[Crossref] [PubMed]

M. Li, S. Yan, B. Yao, M. Lei, Y. Yang, J. Min, and D. Dan, “Intrinsic optical torque of cylindrical vector beams on Rayleigh absorptive spherical particles,” J. Opt. Soc. Am. A 31(8), 1710–1715 (2014).
[Crossref] [PubMed]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

K. Y. Bliokh, Y. S. Kivshar, and F. Nori, “Magnetoelectric effects in local light-matter interactions,” Phys. Rev. Lett. 113(3), 033601 (2014).
[Crossref] [PubMed]

2013 (4)

A. Y. Bekshaev, “Subwavelength particles in an inhomogeneous light field: optical forces associated with the spin and orbital energy flows,” J. Opt. 15(4), 044004 (2013).
[Crossref]

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88(3), 033831 (2013).
[Crossref]

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13(7), 3129–3134 (2013).
[Crossref] [PubMed]

Z. Yan and N. F. Scherer, “Optical vortex induced rotation of silver nanowires,” J. Phys. Chem. Lett. 4(17), 2937–2942 (2013).
[Crossref]

2012 (2)

2011 (1)

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

2010 (1)

2009 (3)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

S. Sato and Y. Kozawa, “Hollow vortex beams,” J. Opt. Soc. Am. A 26(1), 142–146 (2009).
[Crossref] [PubMed]

M. Berry, “Optical currents,” J. Opt. A, Pure Appl. Opt. 11(9), 094001 (2009).
[Crossref]

2007 (1)

Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[Crossref] [PubMed]

2004 (1)

M. Padgett, J. Courtial, and L. Allen, “Light’s orbital angular momentum,” Phys. Today 57(5), 35–40 (2004).
[Crossref]

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

2000 (1)

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

1989 (1)

J. Barton, D. Alexander, and S. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66(10), 4594–4602 (1989).
[Crossref]

1986 (1)

S. Stenholm, “The semiclassical theory of laser cooling,” Rev. Mod. Phys. 58(3), 699–739 (1986).
[Crossref]

1983 (1)

1965 (1)

P. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53(8), 805–812 (1965).
[Crossref]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Ser. A 253(1274), 358–379 (1959).

Aiello, A.

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

Alexander, D.

J. Barton, D. Alexander, and S. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66(10), 4594–4602 (1989).
[Crossref]

Allen, L.

M. Padgett, J. Courtial, and L. Allen, “Light’s orbital angular momentum,” Phys. Today 57(5), 35–40 (2004).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Ashkin, A.

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

Banzer, P.

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

Barton, J.

J. Barton, D. Alexander, and S. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66(10), 4594–4602 (1989).
[Crossref]

Bauer, T.

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Bekshaev, A. Y.

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
[Crossref] [PubMed]

A. Y. Bekshaev, “Subwavelength particles in an inhomogeneous light field: optical forces associated with the spin and orbital energy flows,” J. Opt. 15(4), 044004 (2013).
[Crossref]

Berry, M.

M. Berry, “Optical currents,” J. Opt. A, Pure Appl. Opt. 11(9), 094001 (2009).
[Crossref]

Bliokh, K. Y.

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
[Crossref] [PubMed]

K. Y. Bliokh, Y. S. Kivshar, and F. Nori, “Magnetoelectric effects in local light-matter interactions,” Phys. Rev. Lett. 113(3), 033601 (2014).
[Crossref] [PubMed]

Bowman, R.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

Brown, T.

Brzobohatý, O.

Canaguier-Durand, A.

A. Canaguier-Durand and C. Genet, “Transverse spinning of a sphere in a plasmonic field,” Phys. Rev. A 89(3), 033841 (2014).
[Crossref]

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88(3), 033831 (2013).
[Crossref]

Cao, Y.

Chantada, L.

Chiu, D. T.

Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[Crossref] [PubMed]

Courtial, J.

M. Padgett, J. Courtial, and L. Allen, “Light’s orbital angular momentum,” Phys. Today 57(5), 35–40 (2004).
[Crossref]

Cuche, A.

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88(3), 033831 (2013).
[Crossref]

Dan, D.

Ding, W.

Ebbesen, T. W.

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88(3), 033831 (2013).
[Crossref]

Edgar, J. S.

Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[Crossref] [PubMed]

Genet, C.

A. Canaguier-Durand and C. Genet, “Transverse spinning of a sphere in a plasmonic field,” Phys. Rev. A 89(3), 033841 (2014).
[Crossref]

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88(3), 033831 (2013).
[Crossref]

Gómez-Medina, R.

Gordon, J. P.

Grier, D. G.

D. B. Ruffner and D. G. Grier, “Optical forces and torques in nonuniform beams of light,” Phys. Rev. Lett. 108(17), 173602 (2012).
[Crossref] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

Gschneidtner, T.

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13(7), 3129–3134 (2013).
[Crossref] [PubMed]

Huang, C.-B.

W.-Y. Tsai, J.-S. Huang, and C.-B. Huang, “Selective trapping or rotation of isotropic dielectric microparticles by optical near field in a plasmonic archimedes spiral,” Nano Lett. 14(2), 547–552 (2014).
[Crossref] [PubMed]

Huang, J.-S.

W.-Y. Tsai, J.-S. Huang, and C.-B. Huang, “Selective trapping or rotation of isotropic dielectric microparticles by optical near field in a plasmonic archimedes spiral,” Nano Lett. 14(2), 547–552 (2014).
[Crossref] [PubMed]

Jákl, P.

Jeffries, G. D.

Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[Crossref] [PubMed]

Johansson, P.

A. Lehmuskero, Y. Li, P. Johansson, and M. Käll, “Plasmonic particles set into fast orbital motion by an optical vortex beam,” Opt. Express 22(4), 4349–4356 (2014).
[Crossref] [PubMed]

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13(7), 3129–3134 (2013).
[Crossref] [PubMed]

Käll, M.

A. Lehmuskero, Y. Li, P. Johansson, and M. Käll, “Plasmonic particles set into fast orbital motion by an optical vortex beam,” Opt. Express 22(4), 4349–4356 (2014).
[Crossref] [PubMed]

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13(7), 3129–3134 (2013).
[Crossref] [PubMed]

Kim, K.-Y.

Kim, S.

Kippenberg, T. J.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

Kivshar, Y. S.

K. Y. Bliokh, Y. S. Kivshar, and F. Nori, “Magnetoelectric effects in local light-matter interactions,” Phys. Rev. Lett. 113(3), 033601 (2014).
[Crossref] [PubMed]

Kozawa, Y.

Lehmuskero, A.

A. Lehmuskero, Y. Li, P. Johansson, and M. Käll, “Plasmonic particles set into fast orbital motion by an optical vortex beam,” Opt. Express 22(4), 4349–4356 (2014).
[Crossref] [PubMed]

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13(7), 3129–3134 (2013).
[Crossref] [PubMed]

Lei, M.

M. Li, S. Yan, B. Yao, Y. Liang, M. Lei, and Y. Yang, “Optically induced rotation of Rayleigh particles by vortex beams with different states of polarization,” Phys. Lett. A 380(1), 311–315 (2016).
[Crossref]

M. Li, S. Yan, B. Yao, M. Lei, Y. Yang, J. Min, and D. Dan, “Intrinsic optical torque of cylindrical vector beams on Rayleigh absorptive spherical particles,” J. Opt. Soc. Am. A 31(8), 1710–1715 (2014).
[Crossref] [PubMed]

Li, M.

M. Li, S. Yan, B. Yao, Y. Liang, M. Lei, and Y. Yang, “Optically induced rotation of Rayleigh particles by vortex beams with different states of polarization,” Phys. Lett. A 380(1), 311–315 (2016).
[Crossref]

M. Li, S. Yan, B. Yao, M. Lei, Y. Yang, J. Min, and D. Dan, “Intrinsic optical torque of cylindrical vector beams on Rayleigh absorptive spherical particles,” J. Opt. Soc. Am. A 31(8), 1710–1715 (2014).
[Crossref] [PubMed]

Li, Y.

Liang, Y.

M. Li, S. Yan, B. Yao, Y. Liang, M. Lei, and Y. Yang, “Optically induced rotation of Rayleigh particles by vortex beams with different states of polarization,” Phys. Lett. A 380(1), 311–315 (2016).
[Crossref]

Lv, H.

Marquardt, F.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

McGloin, D.

Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[Crossref] [PubMed]

Min, J.

Neugebauer, M.

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

Nieto-Vesperinas, M.

Nori, F.

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
[Crossref] [PubMed]

K. Y. Bliokh, Y. S. Kivshar, and F. Nori, “Magnetoelectric effects in local light-matter interactions,” Phys. Rev. Lett. 113(3), 033601 (2014).
[Crossref] [PubMed]

Ogier, R.

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13(7), 3129–3134 (2013).
[Crossref] [PubMed]

Padgett, M.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

M. Padgett, J. Courtial, and L. Allen, “Light’s orbital angular momentum,” Phys. Today 57(5), 35–40 (2004).
[Crossref]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Ser. A 253(1274), 358–379 (1959).

Ruffner, D. B.

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Z. Yan and N. F. Scherer, “Optical vortex induced rotation of silver nanowires,” J. Phys. Chem. Lett. 4(17), 2937–2942 (2013).
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W.-Y. Tsai, J.-S. Huang, and C.-B. Huang, “Selective trapping or rotation of isotropic dielectric microparticles by optical near field in a plasmonic archimedes spiral,” Nano Lett. 14(2), 547–552 (2014).
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Opt. Express (5)

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Phys. Lett. A (1)

M. Li, S. Yan, B. Yao, Y. Liang, M. Lei, and Y. Yang, “Optically induced rotation of Rayleigh particles by vortex beams with different states of polarization,” Phys. Lett. A 380(1), 311–315 (2016).
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Phys. Rev. A (3)

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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D. B. Ruffner and D. G. Grier, “Optical forces and torques in nonuniform beams of light,” Phys. Rev. Lett. 108(17), 173602 (2012).
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K. Y. Bliokh, Y. S. Kivshar, and F. Nori, “Magnetoelectric effects in local light-matter interactions,” Phys. Rev. Lett. 113(3), 033601 (2014).
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Y. Zhao, J. S. Edgar, G. D. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
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A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5(1), 011039 (2015).
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P. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53(8), 805–812 (1965).
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B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Ser. A 253(1274), 358–379 (1959).

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S. Stenholm, “The semiclassical theory of laser cooling,” Rev. Mod. Phys. 58(3), 699–739 (1986).
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Figures (5)

Fig. 1
Fig. 1 Line scans along the x-axis of intensity distribution for circularly polarized vortex beams (CPV) and radially polarized vortex beams (RPV) with topological charges of m =+ 5 or −5.
Fig. 2
Fig. 2 Radial trapping force curves on the particle under (a) CPV and (b) RPV inputs with topological charges of m =+ 5 or −5.
Fig. 3
Fig. 3 Transverse force distributions experienced by the particle in the focal plane illuminated, respectively, by CPV inputs with topological charges of (a) m = 5 and (c) m = −5, and by RPV inputs with (b) m = 5 and (d) m = −5.
Fig. 4
Fig. 4 Sketch of the spin and orbital motion of the particle illuminated, respectively, by CPV inputs with topological charges of (a) m = 5 and (c) m = −5, and by RPV inputs with (b) m = 5 and (d) m = −5.
Fig. 5
Fig. 5 The changes of the azimuthal forces (a1)-(a3), the spin torques (b1)-(b3) and the orbital torques (c1)-(c3) exerted on the particle with varying radius a (a1)-(c1), and absorptivity nʺ (a2)-(c2), as well as with the topological charge value m (a3)-(c3) in CPV and RPV inputs. R in the inset of (c1) represents the radius of the equilibrium position of the particle.

Tables (1)

Tables Icon

Table 1 Spin and orbital torques exerted on the particle at the equilibrium position under CPV and RPV inputs with topological charge of m = 5 or −5.

Equations (9)

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F= S n ^ T ¯ ds ,
Γ s = S n ^ ( T ¯ ×r)ds ,
T ¯ = ε 1 EE+ μ 1 HH 1 2 ( ε 1 E 2 + μ 1 H 2 ) I ¯ ,
E inc (r)= n=1 m=n n [ a mn M mn 1 (kr)+ b mn N mn 1 (kr) ] ,
E sca (r)= n=1 m=n n [ p mn M mn 3 (kr)+ q mn N mn 3 (kr) ] ,
[ p mn q mn ]=[ T mnm'n' 11 0 0 T mnm'n' 22 ][ a m'n' b m'n' ].
Γ o,z = ρ o F ϕ ,
E inc (r)= ikf 2π 0 θ max 0 2π A(θ,ϕ)exp(ikr)sinθdϕdθ .
A(θ,ϕ)= (cosθ) 1/2 [ e θ 0 0 e ϕ ]( A 0ρ A 0ϕ ),

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