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

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 Abajo, "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. Quantum 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. Quantum 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 Mechanics 3d 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]

Astrophys. J.

• 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

• 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.

• 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

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

J. Quantum Spectrosc. Radiat. Transfer

• F. J. García de Abajo, "Electromagnetic forces and torques in nanoparticles irradiated by plane waves," J. Quantum 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. Quantum Spectrosc. Radiat. Transfer 70, 811-816 (2001) [CrossRef]

Nature

• 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

• 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

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

Phys. Rev. D

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

Proc. Roy. Soc. London A

• 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

• 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 Mechanics 3d 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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