Abstract

The radiation force of highly focused Lorentz-Gauss beams (LG beam) on a dielectric sphere in the Rayleigh scattering regime is theoretically studied. The numerical results show that the Lorentz-Gauss beam can be used to trap particles with the refractive index larger than that of the ambient. The radiation force distribution has been studied under different beam widths of the Lorentz part. The trapping stability under different conditions is also analyzed.

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  1. O. E. Gawhary and S. Severini, “Lorentz beams and symmetry properties in paraxial optics,” J. Opt. A, Pure Appl. Opt. 8(5), 409–414 (2006).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  5. A. Torre, W A B. Evans, O. E. Gawhary, and S. Severini, “Relativistic Hermite polynomials and Lorentz beams,” J. Opt. A, Pure Appl. Opt. 10(11), 115007 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  14. D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, “The bacteriophage straight phi29 portal motor can package DNA against a large internal force,” Nature 413(6857), 748–752 (2001).
    [CrossRef] [PubMed]
  15. L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97(5), 058301 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
  17. M. Dienerowitz, M. Mazilu, P. J. Reece, T. F. Krauss, and K. Dholakia, “Optical vortex trap for resonant confinement of metal nanoparticles,” Opt. Express 16(7), 4991–4999 (2008).
    [CrossRef] [PubMed]
  18. C. L. Zhao, L. G. Wang, and X. H. Lu, “Radiation forces on a dielectric sphere produced by highly focused hollow Gaussian beams,” Phys. Lett. A 363(5-6), 502–506 (2007).
    [CrossRef]
  19. C. L. Zhao, L. G. Wang, and X. H. Lu, “Radiation forces of highly focused Bessel-Gaussian beams on a dielectric sphere,” Optik (Stuttg.) 119(10), 477–480 (2008).
    [CrossRef]
  20. Q. W. Zhan, “Radiation forces on a dielectric sphere produced by highly focused cylindrical vector beams,” J. Opt. A, Pure Appl. Opt. 5(3), 229–232 (2003).
    [CrossRef]
  21. L. G. Wang, C. L. Zhao, L. Q. Wang, X. H. Lu, and S. Y. Zhu, “Effect of spatial coherence on radiation forces acting on a Rayleigh dielectric sphere,” Opt. Lett. 32(11), 1393–1395 (2007).
    [CrossRef] [PubMed]
  22. C. L. Zhao, Y. J. Cai, X. H. Lu, and H. T. Eyyuboğlu, “Radiation force of coherent and partially coherent flat-topped beams on a Rayleigh particle,” Opt. Express 17(3), 1753–1765 (2009).
    [CrossRef] [PubMed]
  23. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [CrossRef]
  24. Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
    [CrossRef]
  25. M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2(1), 021875 (2008).
    [CrossRef]
  26. K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett. 83(22), 4534–4537 (1999).
    [CrossRef]

2010 (2)

2009 (2)

2008 (5)

C. L. Zhao, L. G. Wang, and X. H. Lu, “Radiation forces of highly focused Bessel-Gaussian beams on a dielectric sphere,” Optik (Stuttg.) 119(10), 477–480 (2008).
[CrossRef]

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2(1), 021875 (2008).
[CrossRef]

M. Dienerowitz, M. Mazilu, P. J. Reece, T. F. Krauss, and K. Dholakia, “Optical vortex trap for resonant confinement of metal nanoparticles,” Opt. Express 16(7), 4991–4999 (2008).
[CrossRef] [PubMed]

A. Torre, W A B. Evans, O. E. Gawhary, and S. Severini, “Relativistic Hermite polynomials and Lorentz beams,” J. Opt. A, Pure Appl. Opt. 10(11), 115007 (2008).
[CrossRef]

G. Q. Zhou, “Focal shift of focused truncated Lorentz-Gauss beam,” J. Opt. Soc. Am. A 25(10), 2594–2599 (2008).
[CrossRef]

2007 (3)

2006 (3)

L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97(5), 058301 (2006).
[CrossRef] [PubMed]

C. Day, “Optical trap resolves the stepwise transfer of genetic information from DNA to RNA,” Phys. Today 59(1), 26–27 (2006).
[CrossRef]

O. E. Gawhary and S. Severini, “Lorentz beams and symmetry properties in paraxial optics,” J. Opt. A, Pure Appl. Opt. 8(5), 409–414 (2006).
[CrossRef]

2005 (1)

2003 (1)

Q. W. Zhan, “Radiation forces on a dielectric sphere produced by highly focused cylindrical vector beams,” J. Opt. A, Pure Appl. Opt. 5(3), 229–232 (2003).
[CrossRef]

2001 (1)

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, “The bacteriophage straight phi29 portal motor can package DNA against a large internal force,” Nature 413(6857), 748–752 (2001).
[CrossRef] [PubMed]

1999 (1)

K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett. 83(22), 4534–4537 (1999).
[CrossRef]

1998 (1)

P. Zemánek and C. J. Foot, “Atomic dipole trap formed by blue detuned strong Gaussian standing wave,” Opt. Commun. 146(1-6), 119–123 (1998).
[CrossRef]

1996 (1)

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
[CrossRef]

1990 (2)

S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348(6299), 348–352 (1990).
[CrossRef] [PubMed]

A. Naqwi and F. Durst, “Focusing of diode laser beams: a simple mathematical model,” Appl. Opt. 29(12), 1780–1785 (1990).
[CrossRef] [PubMed]

1988 (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

1986 (1)

1975 (1)

W. P. Dumke, “Angular beam divergence in double-heterojunction lasers with very thin active regions,” IEEE J. Quantum Electron. 11(7), 400–402 (1975).
[CrossRef]

Ambardekar, A. A.

Anderson, D. L.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, “The bacteriophage straight phi29 portal motor can package DNA against a large internal force,” Nature 413(6857), 748–752 (2001).
[CrossRef] [PubMed]

Asakura, T.

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
[CrossRef]

Ashkin, A.

Bandres, M. A.

Bjorkholm, J. E.

Block, S. M.

S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348(6299), 348–352 (1990).
[CrossRef] [PubMed]

Bottka, S.

L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97(5), 058301 (2006).
[CrossRef] [PubMed]

Bustamante, C.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, “The bacteriophage straight phi29 portal motor can package DNA against a large internal force,” Nature 413(6857), 748–752 (2001).
[CrossRef] [PubMed]

Cai, Y. J.

Chu, S.

Chu, X. X.

Day, C.

C. Day, “Optical trap resolves the stepwise transfer of genetic information from DNA to RNA,” Phys. Today 59(1), 26–27 (2006).
[CrossRef]

Dholakia, K.

Dienerowitz, M.

Draine, B. T.

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

Dumke, W. P.

W. P. Dumke, “Angular beam divergence in double-heterojunction lasers with very thin active regions,” IEEE J. Quantum Electron. 11(7), 400–402 (1975).
[CrossRef]

Durst, F.

Dziedzic, J. M.

Evans, W A B.

A. Torre, W A B. Evans, O. E. Gawhary, and S. Severini, “Relativistic Hermite polynomials and Lorentz beams,” J. Opt. A, Pure Appl. Opt. 10(11), 115007 (2008).
[CrossRef]

Eyyuboglu, H. T.

Foot, C. J.

P. Zemánek and C. J. Foot, “Atomic dipole trap formed by blue detuned strong Gaussian standing wave,” Opt. Commun. 146(1-6), 119–123 (1998).
[CrossRef]

Galajda, P.

L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97(5), 058301 (2006).
[CrossRef] [PubMed]

Gawhary, O. E.

A. Torre, W A B. Evans, O. E. Gawhary, and S. Severini, “Relativistic Hermite polynomials and Lorentz beams,” J. Opt. A, Pure Appl. Opt. 10(11), 115007 (2008).
[CrossRef]

O. E. Gawhary and S. Severini, “Lorentz beams and symmetry properties in paraxial optics,” J. Opt. A, Pure Appl. Opt. 8(5), 409–414 (2006).
[CrossRef]

Goldstein, L. S. B.

S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348(6299), 348–352 (1990).
[CrossRef] [PubMed]

Grimes, S.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, “The bacteriophage straight phi29 portal motor can package DNA against a large internal force,” Nature 413(6857), 748–752 (2001).
[CrossRef] [PubMed]

Gutiérrez-Vega, J. C.

Harada, Y.

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
[CrossRef]

Kawata, S.

K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett. 83(22), 4534–4537 (1999).
[CrossRef]

Kirei, H.

L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97(5), 058301 (2006).
[CrossRef] [PubMed]

Krauss, T. F.

Li, Y. Q.

Lu, X. H.

C. L. Zhao, Y. J. Cai, X. H. Lu, and H. T. Eyyuboğlu, “Radiation force of coherent and partially coherent flat-topped beams on a Rayleigh particle,” Opt. Express 17(3), 1753–1765 (2009).
[CrossRef] [PubMed]

C. L. Zhao, L. G. Wang, and X. H. Lu, “Radiation forces of highly focused Bessel-Gaussian beams on a dielectric sphere,” Optik (Stuttg.) 119(10), 477–480 (2008).
[CrossRef]

C. L. Zhao, L. G. Wang, and X. H. Lu, “Radiation forces on a dielectric sphere produced by highly focused hollow Gaussian beams,” Phys. Lett. A 363(5-6), 502–506 (2007).
[CrossRef]

L. G. Wang, C. L. Zhao, L. Q. Wang, X. H. Lu, and S. Y. Zhu, “Effect of spatial coherence on radiation forces acting on a Rayleigh dielectric sphere,” Opt. Lett. 32(11), 1393–1395 (2007).
[CrossRef] [PubMed]

Mazilu, M.

Naqwi, A.

Okamoto, K.

K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett. 83(22), 4534–4537 (1999).
[CrossRef]

Ormos, P.

L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97(5), 058301 (2006).
[CrossRef] [PubMed]

Oroszi, L.

L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97(5), 058301 (2006).
[CrossRef] [PubMed]

Reece, P. J.

Schnapp, B. J.

S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348(6299), 348–352 (1990).
[CrossRef] [PubMed]

Severini, S.

A. Torre, W A B. Evans, O. E. Gawhary, and S. Severini, “Relativistic Hermite polynomials and Lorentz beams,” J. Opt. A, Pure Appl. Opt. 10(11), 115007 (2008).
[CrossRef]

O. E. Gawhary and S. Severini, “Lorentz beams and symmetry properties in paraxial optics,” J. Opt. A, Pure Appl. Opt. 8(5), 409–414 (2006).
[CrossRef]

Smith, D. E.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, “The bacteriophage straight phi29 portal motor can package DNA against a large internal force,” Nature 413(6857), 748–752 (2001).
[CrossRef] [PubMed]

Smith, S. B.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, “The bacteriophage straight phi29 portal motor can package DNA against a large internal force,” Nature 413(6857), 748–752 (2001).
[CrossRef] [PubMed]

Tans, S. J.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, “The bacteriophage straight phi29 portal motor can package DNA against a large internal force,” Nature 413(6857), 748–752 (2001).
[CrossRef] [PubMed]

Torre, A.

A. Torre, W A B. Evans, O. E. Gawhary, and S. Severini, “Relativistic Hermite polynomials and Lorentz beams,” J. Opt. A, Pure Appl. Opt. 10(11), 115007 (2008).
[CrossRef]

Wang, L. G.

C. L. Zhao, L. G. Wang, and X. H. Lu, “Radiation forces of highly focused Bessel-Gaussian beams on a dielectric sphere,” Optik (Stuttg.) 119(10), 477–480 (2008).
[CrossRef]

C. L. Zhao, L. G. Wang, and X. H. Lu, “Radiation forces on a dielectric sphere produced by highly focused hollow Gaussian beams,” Phys. Lett. A 363(5-6), 502–506 (2007).
[CrossRef]

L. G. Wang, C. L. Zhao, L. Q. Wang, X. H. Lu, and S. Y. Zhu, “Effect of spatial coherence on radiation forces acting on a Rayleigh dielectric sphere,” Opt. Lett. 32(11), 1393–1395 (2007).
[CrossRef] [PubMed]

Wang, L. Q.

Zemánek, P.

P. Zemánek and C. J. Foot, “Atomic dipole trap formed by blue detuned strong Gaussian standing wave,” Opt. Commun. 146(1-6), 119–123 (1998).
[CrossRef]

Zhan, Q. W.

Q. W. Zhan, “Radiation forces on a dielectric sphere produced by highly focused cylindrical vector beams,” J. Opt. A, Pure Appl. Opt. 5(3), 229–232 (2003).
[CrossRef]

Zhao, C. L.

C. L. Zhao, Y. J. Cai, X. H. Lu, and H. T. Eyyuboğlu, “Radiation force of coherent and partially coherent flat-topped beams on a Rayleigh particle,” Opt. Express 17(3), 1753–1765 (2009).
[CrossRef] [PubMed]

C. L. Zhao, L. G. Wang, and X. H. Lu, “Radiation forces of highly focused Bessel-Gaussian beams on a dielectric sphere,” Optik (Stuttg.) 119(10), 477–480 (2008).
[CrossRef]

C. L. Zhao, L. G. Wang, and X. H. Lu, “Radiation forces on a dielectric sphere produced by highly focused hollow Gaussian beams,” Phys. Lett. A 363(5-6), 502–506 (2007).
[CrossRef]

L. G. Wang, C. L. Zhao, L. Q. Wang, X. H. Lu, and S. Y. Zhu, “Effect of spatial coherence on radiation forces acting on a Rayleigh dielectric sphere,” Opt. Lett. 32(11), 1393–1395 (2007).
[CrossRef] [PubMed]

Zhou, G. Q.

Zhu, S. Y.

Appl. Opt. (1)

Astrophys. J. (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. P. Dumke, “Angular beam divergence in double-heterojunction lasers with very thin active regions,” IEEE J. Quantum Electron. 11(7), 400–402 (1975).
[CrossRef]

J. Nanophotonics (1)

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2(1), 021875 (2008).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (3)

Q. W. Zhan, “Radiation forces on a dielectric sphere produced by highly focused cylindrical vector beams,” J. Opt. A, Pure Appl. Opt. 5(3), 229–232 (2003).
[CrossRef]

O. E. Gawhary and S. Severini, “Lorentz beams and symmetry properties in paraxial optics,” J. Opt. A, Pure Appl. Opt. 8(5), 409–414 (2006).
[CrossRef]

A. Torre, W A B. Evans, O. E. Gawhary, and S. Severini, “Relativistic Hermite polynomials and Lorentz beams,” J. Opt. A, Pure Appl. Opt. 10(11), 115007 (2008).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Nature (2)

S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348(6299), 348–352 (1990).
[CrossRef] [PubMed]

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, “The bacteriophage straight phi29 portal motor can package DNA against a large internal force,” Nature 413(6857), 748–752 (2001).
[CrossRef] [PubMed]

Opt. Commun. (2)

P. Zemánek and C. J. Foot, “Atomic dipole trap formed by blue detuned strong Gaussian standing wave,” Opt. Commun. 146(1-6), 119–123 (1998).
[CrossRef]

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
[CrossRef]

Opt. Express (4)

Opt. Lett. (4)

Optik (Stuttg.) (1)

C. L. Zhao, L. G. Wang, and X. H. Lu, “Radiation forces of highly focused Bessel-Gaussian beams on a dielectric sphere,” Optik (Stuttg.) 119(10), 477–480 (2008).
[CrossRef]

Phys. Lett. A (1)

C. L. Zhao, L. G. Wang, and X. H. Lu, “Radiation forces on a dielectric sphere produced by highly focused hollow Gaussian beams,” Phys. Lett. A 363(5-6), 502–506 (2007).
[CrossRef]

Phys. Rev. Lett. (2)

K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett. 83(22), 4534–4537 (1999).
[CrossRef]

L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97(5), 058301 (2006).
[CrossRef] [PubMed]

Phys. Today (1)

C. Day, “Optical trap resolves the stepwise transfer of genetic information from DNA to RNA,” Phys. Today 59(1), 26–27 (2006).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

The sketch of the optical system, in which the Lorentz-Gauss beam is highly focused by the lens.

Fig. 2
Fig. 2

The intensity distribution in the x direction of the Lorentz-Gauss beam (LGB) and the fundamental Gaussian beam (GB) at (a) the input plane; (b) the focus plane. w0 is also the beam waist of GB and wx = 10mm for LGB.

Fig. 3
Fig. 3

The transverse gradient force ((a)-(c)) produced by highly focused Lorentz-Gauss beam with different wx at different positions z1 , and the Longitudinal gradient force ((d)-(f)) and the scattering force ((g) and (h)) at different transverse positions x. The calculation parameters are w0 = 10mm, f = 10mm. GB is the fundamental Gaussian beam with beam waist w0 .

Fig. 4
Fig. 4

Comparison of F g r a d , x m , F g r a d , z m , F b and F g (a) with different wx , while the other parameters are f = 10 mm, a = 30 nm, w0 = 10 mm, and (b) with different particle radius a, while the other parameters are wx = 10 mm, f = 10 mm,w0 = 10 mm.

Equations (8)

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

E 0 = A 0 w x w y 1 [ 1 + ( x 0 / w x ) 2 ] [ 1 + ( y 0 / w y ) 2 ] exp [ i k ( x 0 2 + y 0 2 ) 2 q 0 ] ,
E ( x , y , z ) = i A 0 π 2 4 λ B exp ( i k z ) exp [ i k ( x 2 + y 2 ) 2 q ] ( V x + + V x ) ( V y + + V y ) ,
V j ± = exp [ i k G 2 B ( w j ± i j G ) ] { 1 e r f [ i k G 2 B ( w j ± i j G ) ] } ,
[ A B C D ] = [ z 1 f s z 1 f + f + z 1 1 f s f + 1 ] ,
α = 4 π a 3 ε p ε m ε p + 2 ε m ,
F g r a d = 1 4 ε 0 ε m Re ( α ) | E 2 | ,
F s c a = ε 0 ε m 3 k 4 12 π | α 2 | | E 2 | ,
| F b | = 12 π η a k B T ,

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