Abstract

The torque exerted by radiation on small particles is recognized to have a considerable relevance, e.g., on the dynamics of cosmic dust grains and for the manipulation of micro and nanoparticles under controlled conditions. In the present paper we derive, in the transition matrix formalism, the radiation torque applied by a plane polarized wave on nonspherical particles. In case of circularly polarized waves impinging on spherical particles our equations reproduce the findings of Marston and Crichton [Phys. Rev. A30, 2508–2516 (1984)]. Our equations were applied to calculate the torque on a few model particles shaped as aggregates of identical spheres, both axially symmetric and lacking any symmetry, and the conditions for the stability of the induced rotational motion are discussed.

© 2006 Optical Society of America

Full Article  |  PDF Article

Corrections

Ferdinando Borghese, Paolo Denti, Rosalba Saija, and Maria Antonia Iatì, "Radiation torque on nonspherical particles in the transition matrix formalism: erratum," Opt. Express 15, 6946-6946 (2007)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-15-11-6946

References

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  1. J. D. Jackson, Classical electrodynamics, 2d edition (Wiley, New York, 1975)
  2. E. M. Purcell, “Suprathermal rotation of interstellar grains,” Astrophys. J. 231, 404–416 (1979)
    [CrossRef]
  3. M. E. J. Friese, T.A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–349 (1998); “Erratum”, ibid.  395, 621 (1998)
    [CrossRef]
  4. B. T. Draine and J. C. Weingartner, “Radiative torques on interstellar grains. I. Superthermal spin-up,” Astrophys. J. 470, 551–565 (1996)
    [CrossRef]
  5. B. T. Draine and J. C. Weingartner, “Radiative torques on interstellar grains. II. Grain alignment,” Astrophys. J. 480, 633–646 (1997)
    [CrossRef]
  6. E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973)
    [CrossRef]
  7. B. T. Draine and P. J. Flatau, “Discrete dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994)
    [CrossRef]
  8. P. C. Waterman, “Symmetry, unitarity and geometry in electromagnetic scattering,” Phys. Rev. D 4, 825–839 (1971)
    [CrossRef]
  9. F. Borghese, P. Denti, and R. Saija, Scattering from model nonspherical particles (Springer, Heidelberg, 2002)
  10. P. L. Marston and J. H. Crichton, “Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave,” Phys. Rev. A 30, 2508–2516 (1984)
    [CrossRef]
  11. F. J. García de, “Momentum transfer to small particles by passing electron beams,” Phys. Rev. B 70, 115422 (2004)
    [CrossRef]
  12. F. J. García de Abajo, “Electromagnetic forces and torques in nanoparticles irradiated by plane waves,” J. Quant. Spectrosc. Radiat. Transfer 89, 3–9 (2004)
    [CrossRef]
  13. M. I. Mishchenko, “Radiation force caused by scattering, absorption and emission of light by nonspherical particles,” J. Quant. Spectrosc. Radiat. Transfer 70, 811–816 (2001)
    [CrossRef]
  14. E. Fucile, F. Borghese, P. Denti, R. Saija, and O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. AP 45, 868–875 (1997)
    [CrossRef]
  15. E. M. Rose, Elementary theory of angular momentum, (Wiley, New York, 1956)
  16. M. Abramowitz and I. Stegun, Handbook of mathematical functions (Dover, New York, 1970)
  17. H. Goldstein, C. Poole, and J. Safko, Classical Mechanics3d edition (Addison-Wesley, Reading, Mass., 2002)
  18. B. T. Draine and H. M. Lee, “Optical properties of interstellar graphite and silicate grains,” Astrophys. J. 285, 89–108 (1984)
    [CrossRef]
  19. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. London A 253, 358–379 (1959)
    [CrossRef]
  20. P. Galajda and P. Ormos, “Rotation of microscopic propellers in laser tweezers,” J. Opt. B: Quantum Semiclass. Opt. 4, S78–S81 (2002)
    [CrossRef]

2004 (2)

F. J. García de, “Momentum transfer to small particles by passing electron beams,” Phys. Rev. B 70, 115422 (2004)
[CrossRef]

F. J. García de Abajo, “Electromagnetic forces and torques in nanoparticles irradiated by plane waves,” J. Quant. Spectrosc. Radiat. Transfer 89, 3–9 (2004)
[CrossRef]

2002 (1)

P. Galajda and P. Ormos, “Rotation of microscopic propellers in laser tweezers,” J. Opt. B: Quantum Semiclass. Opt. 4, S78–S81 (2002)
[CrossRef]

2001 (1)

M. I. Mishchenko, “Radiation force caused by scattering, absorption and emission of light by nonspherical particles,” J. Quant. Spectrosc. Radiat. Transfer 70, 811–816 (2001)
[CrossRef]

1998 (1)

M. E. J. Friese, T.A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–349 (1998); “Erratum”, ibid.  395, 621 (1998)
[CrossRef]

1997 (2)

B. T. Draine and J. C. Weingartner, “Radiative torques on interstellar grains. II. Grain alignment,” Astrophys. J. 480, 633–646 (1997)
[CrossRef]

E. Fucile, F. Borghese, P. Denti, R. Saija, and O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. AP 45, 868–875 (1997)
[CrossRef]

1996 (1)

B. T. Draine and J. C. Weingartner, “Radiative torques on interstellar grains. I. Superthermal spin-up,” Astrophys. J. 470, 551–565 (1996)
[CrossRef]

1994 (1)

1984 (2)

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

B. T. Draine and H. M. Lee, “Optical properties of interstellar graphite and silicate grains,” Astrophys. J. 285, 89–108 (1984)
[CrossRef]

1979 (1)

E. M. Purcell, “Suprathermal rotation of interstellar grains,” Astrophys. J. 231, 404–416 (1979)
[CrossRef]

1973 (1)

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973)
[CrossRef]

1971 (1)

P. C. Waterman, “Symmetry, unitarity and geometry in electromagnetic scattering,” Phys. Rev. D 4, 825–839 (1971)
[CrossRef]

1959 (1)

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

Abramowitz, M.

M. Abramowitz and I. Stegun, Handbook of mathematical functions (Dover, New York, 1970)

Borghese, F.

E. Fucile, F. Borghese, P. Denti, R. Saija, and O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. AP 45, 868–875 (1997)
[CrossRef]

F. Borghese, P. Denti, and R. Saija, Scattering from model nonspherical particles (Springer, Heidelberg, 2002)

Crichton, J. H.

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

Denti, P.

E. Fucile, F. Borghese, P. Denti, R. Saija, and O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. AP 45, 868–875 (1997)
[CrossRef]

F. Borghese, P. Denti, and R. Saija, Scattering from model nonspherical particles (Springer, Heidelberg, 2002)

Draine, B. T.

B. T. Draine and J. C. Weingartner, “Radiative torques on interstellar grains. II. Grain alignment,” Astrophys. J. 480, 633–646 (1997)
[CrossRef]

B. T. Draine and J. C. Weingartner, “Radiative torques on interstellar grains. I. Superthermal spin-up,” Astrophys. J. 470, 551–565 (1996)
[CrossRef]

B. T. Draine and P. J. Flatau, “Discrete dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994)
[CrossRef]

B. T. Draine and H. M. Lee, “Optical properties of interstellar graphite and silicate grains,” Astrophys. J. 285, 89–108 (1984)
[CrossRef]

Flatau, P. J.

Friese, M. E. J.

M. E. J. Friese, T.A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–349 (1998); “Erratum”, ibid.  395, 621 (1998)
[CrossRef]

Fucile, E.

E. Fucile, F. Borghese, P. Denti, R. Saija, and O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. AP 45, 868–875 (1997)
[CrossRef]

Galajda, P.

P. Galajda and P. Ormos, “Rotation of microscopic propellers in laser tweezers,” J. Opt. B: Quantum Semiclass. Opt. 4, S78–S81 (2002)
[CrossRef]

García de, F. J.

F. J. García de, “Momentum transfer to small particles by passing electron beams,” Phys. Rev. B 70, 115422 (2004)
[CrossRef]

García de Abajo, F. J.

F. J. García de Abajo, “Electromagnetic forces and torques in nanoparticles irradiated by plane waves,” J. Quant. Spectrosc. Radiat. Transfer 89, 3–9 (2004)
[CrossRef]

Goldstein, H.

H. Goldstein, C. Poole, and J. Safko, Classical Mechanics3d edition (Addison-Wesley, Reading, Mass., 2002)

Heckenberg, N. R.

M. E. J. Friese, T.A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–349 (1998); “Erratum”, ibid.  395, 621 (1998)
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical electrodynamics, 2d edition (Wiley, New York, 1975)

Lee, H. M.

B. T. Draine and H. M. Lee, “Optical properties of interstellar graphite and silicate grains,” Astrophys. J. 285, 89–108 (1984)
[CrossRef]

Marston, P. L.

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

Mishchenko, M. I.

M. I. Mishchenko, “Radiation force caused by scattering, absorption and emission of light by nonspherical particles,” J. Quant. Spectrosc. Radiat. Transfer 70, 811–816 (2001)
[CrossRef]

Nieminen, T.A.

M. E. J. Friese, T.A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–349 (1998); “Erratum”, ibid.  395, 621 (1998)
[CrossRef]

Ormos, P.

P. Galajda and P. Ormos, “Rotation of microscopic propellers in laser tweezers,” J. Opt. B: Quantum Semiclass. Opt. 4, S78–S81 (2002)
[CrossRef]

Pennypacker, C. R.

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973)
[CrossRef]

Poole, C.

H. Goldstein, C. Poole, and J. Safko, Classical Mechanics3d edition (Addison-Wesley, Reading, Mass., 2002)

Purcell, E. M.

E. M. Purcell, “Suprathermal rotation of interstellar grains,” Astrophys. J. 231, 404–416 (1979)
[CrossRef]

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973)
[CrossRef]

Richards, B.

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

Rose, E. M.

E. M. Rose, Elementary theory of angular momentum, (Wiley, New York, 1956)

Rubinsztein-Dunlop, H.

M. E. J. Friese, T.A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–349 (1998); “Erratum”, ibid.  395, 621 (1998)
[CrossRef]

Safko, J.

H. Goldstein, C. Poole, and J. Safko, Classical Mechanics3d edition (Addison-Wesley, Reading, Mass., 2002)

Saija, R.

E. Fucile, F. Borghese, P. Denti, R. Saija, and O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. AP 45, 868–875 (1997)
[CrossRef]

F. Borghese, P. Denti, and R. Saija, Scattering from model nonspherical particles (Springer, Heidelberg, 2002)

Sindoni, O. I.

E. Fucile, F. Borghese, P. Denti, R. Saija, and O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. AP 45, 868–875 (1997)
[CrossRef]

Stegun, I.

M. Abramowitz and I. Stegun, Handbook of mathematical functions (Dover, New York, 1970)

Waterman, P. C.

P. C. Waterman, “Symmetry, unitarity and geometry in electromagnetic scattering,” Phys. Rev. D 4, 825–839 (1971)
[CrossRef]

Weingartner, J. C.

B. T. Draine and J. C. Weingartner, “Radiative torques on interstellar grains. II. Grain alignment,” Astrophys. J. 480, 633–646 (1997)
[CrossRef]

B. T. Draine and J. C. Weingartner, “Radiative torques on interstellar grains. I. Superthermal spin-up,” Astrophys. J. 470, 551–565 (1996)
[CrossRef]

Wolf, E.

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

Astrophys. J. (5)

B. T. Draine and J. C. Weingartner, “Radiative torques on interstellar grains. I. Superthermal spin-up,” Astrophys. J. 470, 551–565 (1996)
[CrossRef]

B. T. Draine and J. C. Weingartner, “Radiative torques on interstellar grains. II. Grain alignment,” Astrophys. J. 480, 633–646 (1997)
[CrossRef]

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973)
[CrossRef]

E. M. Purcell, “Suprathermal rotation of interstellar grains,” Astrophys. J. 231, 404–416 (1979)
[CrossRef]

B. T. Draine and H. M. Lee, “Optical properties of interstellar graphite and silicate grains,” Astrophys. J. 285, 89–108 (1984)
[CrossRef]

IEEE Trans. Antennas Propag. AP (1)

E. Fucile, F. Borghese, P. Denti, R. Saija, and O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. AP 45, 868–875 (1997)
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt. (1)

P. Galajda and P. Ormos, “Rotation of microscopic propellers in laser tweezers,” J. Opt. B: Quantum Semiclass. Opt. 4, S78–S81 (2002)
[CrossRef]

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

J. Quant. Spectrosc. Radiat. Transfer (2)

F. J. García de Abajo, “Electromagnetic forces and torques in nanoparticles irradiated by plane waves,” J. Quant. Spectrosc. Radiat. Transfer 89, 3–9 (2004)
[CrossRef]

M. I. Mishchenko, “Radiation force caused by scattering, absorption and emission of light by nonspherical particles,” J. Quant. Spectrosc. Radiat. Transfer 70, 811–816 (2001)
[CrossRef]

Nature (1)

M. E. J. Friese, T.A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–349 (1998); “Erratum”, ibid.  395, 621 (1998)
[CrossRef]

Phys. Rev. A (1)

P. L. Marston and 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. B (1)

F. J. García de, “Momentum transfer to small particles by passing electron beams,” Phys. Rev. B 70, 115422 (2004)
[CrossRef]

Phys. Rev. D (1)

P. C. Waterman, “Symmetry, unitarity and geometry in electromagnetic scattering,” Phys. Rev. D 4, 825–839 (1971)
[CrossRef]

Proc. Roy. Soc. London A (1)

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

Other (5)

E. M. Rose, Elementary theory of angular momentum, (Wiley, New York, 1956)

M. Abramowitz and I. Stegun, Handbook of mathematical functions (Dover, New York, 1970)

H. Goldstein, C. Poole, and J. Safko, Classical Mechanics3d edition (Addison-Wesley, Reading, Mass., 2002)

F. Borghese, P. Denti, and R. Saija, Scattering from model nonspherical particles (Springer, Heidelberg, 2002)

J. D. Jackson, Classical electrodynamics, 2d edition (Wiley, New York, 1975)

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Figures (5)

Fig. 1.
Fig. 1.

Component of T 1 along k I for a binary cluster composed of astronomical silicates both when the imaginary part of their dielectric function has its actual value [18] and when it is arbitrarily set to zero. The axis of the cluster is orthogonal to k I

Fig. 2.
Fig. 2.

Cartesian components of T 1 and T 2 for the five-spheres cluster of Fig. 4 (a). The direction of the incident wavevector is along the z axis

Fig. 3.
Fig. 3.

Contour plot of T2=Tx2 +Ty2 (left panel) and of T z (right panel) as a function of the polar angles of the wavevector k I incident on the binary cluster with its axis along the y axis of Σ ¯ (see Sect. 3). The incident wave has λ=0.3µm and circular polarization with η=1 is assumed. At ϑ I=0° we find T2=0 for any φ I, and T z=0.2196, and at ϑ I=180°, T2=0 and T z=-0.2196, as expected

Fig. 4.
Fig. 4.

Sketch of the geometry of the 5-spheres aggregate. In (a) is reported the geometry of the aggregate the coordinates of whose centers are given in Table 1. In (b), (c) and (d) is reported the sketch of the same aggregate referred to a coordinate frame with origin in the center of mass and the z axis along one of the principal axes of inertia. The yellow sphere in (b), (c), and (d) is the same that in (a) has its center at the origin of the coordinates

Fig. 5.
Fig. 5.

Contour plot of T2 as a function of the polar angles of the wavevector k I incident on the 5-sphere aggregate in the configurations shown in Fig. 4. λ=0.3µm and circular polarization with η=1 is assumed.

Tables (2)

Tables Icon

Table 1. Coordinates of the centers of the spheres in nm (see Fig. 4 (a))

Tables Icon

Table 2. Values of T2 for the configurations sketched in Fig. 4

Equations (23)

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

Γ Red = n ̂ · T M × r d S ,
T M = 1 8 π Re [ n 2 E E * + B B * 1 2 ( n 2 E · E * + B · B * ) I ]
E= E I + E S , B= B I + B S ,
Γ Red = r 3 Ω r ̂ · T M × r ̂ d Ω .
𝓢 lm l m ( p p ) = 𝓢 l l ; m ( p p ) δ m m
H lm ( 1 ) ( i ) l + 1 e ikr kr Z lm ( 1 ) ,
H lm ( 2 ) ( i ) l k 2 r 2 l ( l + 1 ) e ikr Y lm r ̂ ( i ) l + 1 k 2 r 2 e ikr Z lm ( 2 ) ( i ) l kr e ikr Z lm ( 2 ) ,
J lm ( 1 ) 1 kr sin ( kr l π 2 ) Z lm ( 1 ) ,
J lm ( 2 ) i k 2 r 2 l ( l + 1 ) sin ( kr l π 2 ) Y lm r ̂ 1 k 2 r 2 sin ( kr l π 2 ) Z lm ( 2 )
1 kr sin [ kr ( l 1 ) π 2 ] Z lm ( 2 ) .
Γ Radx = Re [ 1 2 ( Γ 1 Γ 1 ) ] , Γ Rady = Re [ i 2 ( Γ 1 + Γ 1 ) ] , Γ Radz = Re ( Γ 0 ) ,
Γ μ = η η I I η η Γ μ ; η η
K μ ; α α l m l m ( p p ) = δ p 2 d α l m v μ ; α l m ( p ) ,
Γ μ ; η η = n 2 r 3 8 π α α [ p p p l m l m I μ α α l m l m ( 2 p ) ( a α η l m ( 2 ) a α η l m ( p ) * + a α η l m ( 1 ) a α η l m ( p ) * ) ] ,
Γ μ ; η η = n 2 r 3 8 π α α [ p p ' p l m l m I μ α α l m l m ( 2 p ) ( a α η l m ( 2 ) a α η l m ( p ) * + a α η l m ( 1 ) a α η l m ( p ' ) * ) ] ,
Γ μ ; η η = Γ μ ; η η ( ext ) Γ μ ; η η ( sca ) .
Γ μ ; η η ( ext ) = c Γ plm s μ ; l m W I η l , m μ ( p ) A η l m ( p ) * ,
s 1 ; l m = ( l m ) ( l + 1 + m ) 2 , s 0 ; l m = m , s 1 ; l m = ( l + m ) ( l + 1 m ) 2 .
Γ η η ( ext ) k ̂ I = n 2 ( ) n 1 8 π k σ ˇ T η η * .
Γ η η ( sca ) k ̂ I n 2 ( ) η 1 8 π k σ ˇ η *
Γ Rad k ̂ I = n 2 8 π k ( I I 11 I I 22 ) σ A ,
Γ μ ' ; η η = μ Γ μ ; η η μ μ ' ( 1 ) ,
Γ μ ; η η ( ext ) = c Γ plm s μ ; l m W I η l , m μ ( p ) A η l m ( p ) * , Γ μ ; η η ( sca ) = c Γ plm s μ ; l m A η l , m μ ( p ) A η l m ( p ) * .

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