Abstract

The theory of the discrete-dipole approximation (DDA) for light scattering is extended to allow for the calculation of radiation forces on each dipole in the DDA model. Starting with the theory of Draine and Weingartner [Astrophys. J. 470, 551 (1996)] we derive an expression for the radiation force on each dipole. These expressions are reformulated into discrete convolutions, allowing for an efficient, O(N log N) evaluation of the forces. The total radiation pressure on the particle is obtained by summation of the individual forces. The theory is tested on spherical particles. The resulting accumulated radiation forces are compared with Mie theory. The accuracy is within the order of a few percent, i.e., comparable with that obtained for extinction cross sections calculated with the DDA.

© 2001 Optical Society of America

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  1. P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. (Leipzig) 30, 57–136 (1909).
    [CrossRef]
  2. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  3. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
    [CrossRef]
  4. A. Ashkin, J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).
    [CrossRef]
  5. A. Ashkin, J. M. Dziedzic, “Observation of light scattering from nonspherical particles using optical levitation,” Appl. Opt. 19, 660–668 (1980).
    [CrossRef] [PubMed]
  6. A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
    [CrossRef] [PubMed]
  7. S. Chu, “The manipulation of neutral particles,” Rev. Mod. Phys. 60, 685–706 (1998).
    [CrossRef]
  8. K. Visscher, G. J. Brakenhoff, J. J. Krol, “Micromanipulation by “multiple” optical traps created by a single fast scanning trap integrated with the bilateral confocal scanning laser microscope,” Cytometry 14, 105–114 (1993).
    [CrossRef]
  9. K. O. Greulich, Micromanipulation by Light in Biology and Medicine: The Laser Microbeam and Optical Tweezers (Birkhauser, Boston, Mass., 1999).
  10. P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69, 1666–1673 (1995).
  11. S. B. Smith, Y. Cui, C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271, 795–799 (1996).
    [CrossRef] [PubMed]
  12. T. R. Lettieri, W. D. Jenkins, D. A. Swyt, “Sizing of individual optically levitated evaporating droplets by measurement of resonances in the polarization ratio,” Appl. Opt. 20, 2799–2805 (1981).
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  13. F. Guilloteau, G. Grehan, G. Gousbet, “Optical levitation experiments to assess the validity of the generalized Lorenz–Mie theory,” Appl. Opt. 31, 2942–2951 (1992).
    [CrossRef] [PubMed]
  14. R. M. P. Doornbos, M. Schaeffer, A. G. Hoekstra, P. M. A. Sloot, B. G. de Grooth, J. Greve, “Elastic light scattering measurements of single biological cells in an optical trap,” Appl. Opt. 34, 729–734 (1996).
    [CrossRef]
  15. B. T. Draine, J. C. Weingartner, “Radiative torques on interstellar grains I. Superthermal spin-up,” Astrophys. J. 470, 551–565 (1996).
    [CrossRef]
  16. B. T. Draine, J. C. Weingartner, “Radiative torques on interstellar grains II. Grain alignment,” Astrophys. J. 480, 633–646 (1997).
    [CrossRef]
  17. A. Kriviv, H. Kimura, I. Mann, “Dynamics of dust near the sun,” Icarus 134, 311–327 (1998).
    [CrossRef]
  18. H. Kimura, I. Mann, “Radiation pressure cross section for fluffy aggregates,” J. Quant. Spectrosc. Radiat. Transf. 60, 425–438 (1998).
    [CrossRef]
  19. T. Mukai, H. Ishimoto, T. Kozasca, J. Blum, J. M. Greenberg, “Radiation pressure forces of fluffy porous grains,” Astron. Astrophys. 262, 315–320 (1992).
  20. C. Dominik, A. G. G. M. Tielens, “The physics of dust coagulation and the structure of dust aggregates in space,” Astrophys. J. 480, 647–673 (1997).
    [CrossRef]
  21. C. Dominik, R. Waters, University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands (personal communication, 1999).
  22. M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds., Light Scattering by Nonspherical Particles (Academic, San Diego, Calif., 1999).
  23. K. Lumme, J. Rahola, “Light scattering by porous dust particles in the discrete-dipole approximation,” Astrophys. J. 425, 653–667 (1994).
    [CrossRef]
  24. Z. Xing, M. S. Hanner, “Light scattering by aggregate particles,” Astron. Astrophys. 324, 805–820 (1997).
  25. T. Kozasa, J. Blum, T. Mukai, “Optical properties of dust aggregates I. Wavelength dependence,” Astron. Astrophys. 263, 423–432 (1992).
  26. T. Kozasa, J. Blum, H. Okamoto, T. Mukai, “Optical properties of dust aggregates II. Angular dependence of scattered light,” Astron. Astrophys. 276, 278–288 (1993).
  27. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [CrossRef]
  28. B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
    [CrossRef]
  29. B. T. Draine, “The discrete dipole approximation for light scattering by irregular targets,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 1999), Chap. 5.
  30. J. P. Gordon, “Radiation force and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
    [CrossRef]
  31. J. J. Goodman, B. T. Draine, P. J. Flatau, “Application of fast-Fourier-transform techniques to the discrete-dipole approximation,” Opt. Lett. 16, 1198–2000 (1991).
    [CrossRef] [PubMed]
  32. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, UK, 1988).
  33. A. G. Hoekstra, P. M. A. Sloot, “Coupled dipole simulations of elastic light scattering on parallel systems,” Int. J. Mod. Phys. C 6, 663–679 (1995).
    [CrossRef]
  34. A. G. Hoekstra, M. D. Grimminck, P. M. A. Sloot, “Large scale simulations of elastic light scattering by a fast discrete dipole approximation,” Int. J. Mod. Phys. C 9, 87–102 (1998).
    [CrossRef]
  35. M. Frijlink, “Application of the discrete dipole approximation to radiation pressure calculations on dust-aggregates: an exploration,” M.Sc. thesis (University of Amsterdam, Amsterdam, 2000).
  36. A. G. Hoekstra, J. Rahola, P. M. A. Sloot, “Accuracy of internal fields in volume integral equation simulations of light scattering,” Appl. Opt. 37, 8482–8497 (1998).
    [CrossRef]
  37. A. G. Hoekstra, “Computer simulations of elastic light scattering, implementations and applications,” Ph.D. dissertation (University of Amsterdam, Amsterdam, 1994).

1998 (5)

S. Chu, “The manipulation of neutral particles,” Rev. Mod. Phys. 60, 685–706 (1998).
[CrossRef]

A. Kriviv, H. Kimura, I. Mann, “Dynamics of dust near the sun,” Icarus 134, 311–327 (1998).
[CrossRef]

H. Kimura, I. Mann, “Radiation pressure cross section for fluffy aggregates,” J. Quant. Spectrosc. Radiat. Transf. 60, 425–438 (1998).
[CrossRef]

A. G. Hoekstra, M. D. Grimminck, P. M. A. Sloot, “Large scale simulations of elastic light scattering by a fast discrete dipole approximation,” Int. J. Mod. Phys. C 9, 87–102 (1998).
[CrossRef]

A. G. Hoekstra, J. Rahola, P. M. A. Sloot, “Accuracy of internal fields in volume integral equation simulations of light scattering,” Appl. Opt. 37, 8482–8497 (1998).
[CrossRef]

1997 (3)

C. Dominik, A. G. G. M. Tielens, “The physics of dust coagulation and the structure of dust aggregates in space,” Astrophys. J. 480, 647–673 (1997).
[CrossRef]

Z. Xing, M. S. Hanner, “Light scattering by aggregate particles,” Astron. Astrophys. 324, 805–820 (1997).

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

1996 (3)

S. B. Smith, Y. Cui, C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271, 795–799 (1996).
[CrossRef] [PubMed]

R. M. P. Doornbos, M. Schaeffer, A. G. Hoekstra, P. M. A. Sloot, B. G. de Grooth, J. Greve, “Elastic light scattering measurements of single biological cells in an optical trap,” Appl. Opt. 34, 729–734 (1996).
[CrossRef]

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

1995 (2)

P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69, 1666–1673 (1995).

A. G. Hoekstra, P. M. A. Sloot, “Coupled dipole simulations of elastic light scattering on parallel systems,” Int. J. Mod. Phys. C 6, 663–679 (1995).
[CrossRef]

1994 (2)

K. Lumme, J. Rahola, “Light scattering by porous dust particles in the discrete-dipole approximation,” Astrophys. J. 425, 653–667 (1994).
[CrossRef]

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

1993 (2)

T. Kozasa, J. Blum, H. Okamoto, T. Mukai, “Optical properties of dust aggregates II. Angular dependence of scattered light,” Astron. Astrophys. 276, 278–288 (1993).

K. Visscher, G. J. Brakenhoff, J. J. Krol, “Micromanipulation by “multiple” optical traps created by a single fast scanning trap integrated with the bilateral confocal scanning laser microscope,” Cytometry 14, 105–114 (1993).
[CrossRef]

1992 (3)

F. Guilloteau, G. Grehan, G. Gousbet, “Optical levitation experiments to assess the validity of the generalized Lorenz–Mie theory,” Appl. Opt. 31, 2942–2951 (1992).
[CrossRef] [PubMed]

T. Mukai, H. Ishimoto, T. Kozasca, J. Blum, J. M. Greenberg, “Radiation pressure forces of fluffy porous grains,” Astron. Astrophys. 262, 315–320 (1992).

T. Kozasa, J. Blum, T. Mukai, “Optical properties of dust aggregates I. Wavelength dependence,” Astron. Astrophys. 263, 423–432 (1992).

1991 (1)

1988 (1)

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

1987 (1)

A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[CrossRef] [PubMed]

1981 (1)

1980 (1)

1973 (1)

J. P. Gordon, “Radiation force and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
[CrossRef]

1971 (1)

A. Ashkin, J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).
[CrossRef]

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

1909 (1)

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. (Leipzig) 30, 57–136 (1909).
[CrossRef]

Ashkin, A.

A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observation of light scattering from nonspherical particles using optical levitation,” Appl. Opt. 19, 660–668 (1980).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).
[CrossRef]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

Blum, J.

T. Kozasa, J. Blum, H. Okamoto, T. Mukai, “Optical properties of dust aggregates II. Angular dependence of scattered light,” Astron. Astrophys. 276, 278–288 (1993).

T. Kozasa, J. Blum, T. Mukai, “Optical properties of dust aggregates I. Wavelength dependence,” Astron. Astrophys. 263, 423–432 (1992).

T. Mukai, H. Ishimoto, T. Kozasca, J. Blum, J. M. Greenberg, “Radiation pressure forces of fluffy porous grains,” Astron. Astrophys. 262, 315–320 (1992).

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Brakenhoff, G. J.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69, 1666–1673 (1995).

K. Visscher, G. J. Brakenhoff, J. J. Krol, “Micromanipulation by “multiple” optical traps created by a single fast scanning trap integrated with the bilateral confocal scanning laser microscope,” Cytometry 14, 105–114 (1993).
[CrossRef]

Bronkhorst, P. J. H.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69, 1666–1673 (1995).

Bustamante, C.

S. B. Smith, Y. Cui, C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271, 795–799 (1996).
[CrossRef] [PubMed]

Chu, S.

S. Chu, “The manipulation of neutral particles,” Rev. Mod. Phys. 60, 685–706 (1998).
[CrossRef]

Cui, Y.

S. B. Smith, Y. Cui, C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271, 795–799 (1996).
[CrossRef] [PubMed]

de Grooth, B. G.

Debye, P.

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. (Leipzig) 30, 57–136 (1909).
[CrossRef]

Dominik, C.

C. Dominik, A. G. G. M. Tielens, “The physics of dust coagulation and the structure of dust aggregates in space,” Astrophys. J. 480, 647–673 (1997).
[CrossRef]

C. Dominik, R. Waters, University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands (personal communication, 1999).

Doornbos, R. M. P.

Draine, B. T.

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

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

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

J. J. Goodman, B. T. Draine, P. J. Flatau, “Application of fast-Fourier-transform techniques to the discrete-dipole approximation,” Opt. Lett. 16, 1198–2000 (1991).
[CrossRef] [PubMed]

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

B. T. Draine, “The discrete dipole approximation for light scattering by irregular targets,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 1999), Chap. 5.

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observation of light scattering from nonspherical particles using optical levitation,” Appl. Opt. 19, 660–668 (1980).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, UK, 1988).

Flatau, P. J.

Frijlink, M.

M. Frijlink, “Application of the discrete dipole approximation to radiation pressure calculations on dust-aggregates: an exploration,” M.Sc. thesis (University of Amsterdam, Amsterdam, 2000).

Goodman, J. J.

Gordon, J. P.

J. P. Gordon, “Radiation force and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
[CrossRef]

Gousbet, G.

Greenberg, J. M.

T. Mukai, H. Ishimoto, T. Kozasca, J. Blum, J. M. Greenberg, “Radiation pressure forces of fluffy porous grains,” Astron. Astrophys. 262, 315–320 (1992).

Grehan, G.

Greulich, K. O.

K. O. Greulich, Micromanipulation by Light in Biology and Medicine: The Laser Microbeam and Optical Tweezers (Birkhauser, Boston, Mass., 1999).

Greve, J.

Grimbergen, J.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69, 1666–1673 (1995).

Grimminck, M. D.

A. G. Hoekstra, M. D. Grimminck, P. M. A. Sloot, “Large scale simulations of elastic light scattering by a fast discrete dipole approximation,” Int. J. Mod. Phys. C 9, 87–102 (1998).
[CrossRef]

Guilloteau, F.

Hanner, M. S.

Z. Xing, M. S. Hanner, “Light scattering by aggregate particles,” Astron. Astrophys. 324, 805–820 (1997).

Hoekstra, A. G.

A. G. Hoekstra, J. Rahola, P. M. A. Sloot, “Accuracy of internal fields in volume integral equation simulations of light scattering,” Appl. Opt. 37, 8482–8497 (1998).
[CrossRef]

A. G. Hoekstra, M. D. Grimminck, P. M. A. Sloot, “Large scale simulations of elastic light scattering by a fast discrete dipole approximation,” Int. J. Mod. Phys. C 9, 87–102 (1998).
[CrossRef]

R. M. P. Doornbos, M. Schaeffer, A. G. Hoekstra, P. M. A. Sloot, B. G. de Grooth, J. Greve, “Elastic light scattering measurements of single biological cells in an optical trap,” Appl. Opt. 34, 729–734 (1996).
[CrossRef]

A. G. Hoekstra, P. M. A. Sloot, “Coupled dipole simulations of elastic light scattering on parallel systems,” Int. J. Mod. Phys. C 6, 663–679 (1995).
[CrossRef]

A. G. Hoekstra, “Computer simulations of elastic light scattering, implementations and applications,” Ph.D. dissertation (University of Amsterdam, Amsterdam, 1994).

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Ishimoto, H.

T. Mukai, H. Ishimoto, T. Kozasca, J. Blum, J. M. Greenberg, “Radiation pressure forces of fluffy porous grains,” Astron. Astrophys. 262, 315–320 (1992).

Jenkins, W. D.

Kimura, H.

A. Kriviv, H. Kimura, I. Mann, “Dynamics of dust near the sun,” Icarus 134, 311–327 (1998).
[CrossRef]

H. Kimura, I. Mann, “Radiation pressure cross section for fluffy aggregates,” J. Quant. Spectrosc. Radiat. Transf. 60, 425–438 (1998).
[CrossRef]

Kozasa, T.

T. Kozasa, J. Blum, H. Okamoto, T. Mukai, “Optical properties of dust aggregates II. Angular dependence of scattered light,” Astron. Astrophys. 276, 278–288 (1993).

T. Kozasa, J. Blum, T. Mukai, “Optical properties of dust aggregates I. Wavelength dependence,” Astron. Astrophys. 263, 423–432 (1992).

Kozasca, T.

T. Mukai, H. Ishimoto, T. Kozasca, J. Blum, J. M. Greenberg, “Radiation pressure forces of fluffy porous grains,” Astron. Astrophys. 262, 315–320 (1992).

Kriviv, A.

A. Kriviv, H. Kimura, I. Mann, “Dynamics of dust near the sun,” Icarus 134, 311–327 (1998).
[CrossRef]

Krol, J. J.

K. Visscher, G. J. Brakenhoff, J. J. Krol, “Micromanipulation by “multiple” optical traps created by a single fast scanning trap integrated with the bilateral confocal scanning laser microscope,” Cytometry 14, 105–114 (1993).
[CrossRef]

Lettieri, T. R.

Lumme, K.

K. Lumme, J. Rahola, “Light scattering by porous dust particles in the discrete-dipole approximation,” Astrophys. J. 425, 653–667 (1994).
[CrossRef]

Mann, I.

H. Kimura, I. Mann, “Radiation pressure cross section for fluffy aggregates,” J. Quant. Spectrosc. Radiat. Transf. 60, 425–438 (1998).
[CrossRef]

A. Kriviv, H. Kimura, I. Mann, “Dynamics of dust near the sun,” Icarus 134, 311–327 (1998).
[CrossRef]

Mukai, T.

T. Kozasa, J. Blum, H. Okamoto, T. Mukai, “Optical properties of dust aggregates II. Angular dependence of scattered light,” Astron. Astrophys. 276, 278–288 (1993).

T. Kozasa, J. Blum, T. Mukai, “Optical properties of dust aggregates I. Wavelength dependence,” Astron. Astrophys. 263, 423–432 (1992).

T. Mukai, H. Ishimoto, T. Kozasca, J. Blum, J. M. Greenberg, “Radiation pressure forces of fluffy porous grains,” Astron. Astrophys. 262, 315–320 (1992).

Nijhof, E. J.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69, 1666–1673 (1995).

Okamoto, H.

T. Kozasa, J. Blum, H. Okamoto, T. Mukai, “Optical properties of dust aggregates II. Angular dependence of scattered light,” Astron. Astrophys. 276, 278–288 (1993).

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, UK, 1988).

Rahola, J.

A. G. Hoekstra, J. Rahola, P. M. A. Sloot, “Accuracy of internal fields in volume integral equation simulations of light scattering,” Appl. Opt. 37, 8482–8497 (1998).
[CrossRef]

K. Lumme, J. Rahola, “Light scattering by porous dust particles in the discrete-dipole approximation,” Astrophys. J. 425, 653–667 (1994).
[CrossRef]

Schaeffer, M.

Sixma, J. J.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69, 1666–1673 (1995).

Sloot, P. M. A.

A. G. Hoekstra, J. Rahola, P. M. A. Sloot, “Accuracy of internal fields in volume integral equation simulations of light scattering,” Appl. Opt. 37, 8482–8497 (1998).
[CrossRef]

A. G. Hoekstra, M. D. Grimminck, P. M. A. Sloot, “Large scale simulations of elastic light scattering by a fast discrete dipole approximation,” Int. J. Mod. Phys. C 9, 87–102 (1998).
[CrossRef]

R. M. P. Doornbos, M. Schaeffer, A. G. Hoekstra, P. M. A. Sloot, B. G. de Grooth, J. Greve, “Elastic light scattering measurements of single biological cells in an optical trap,” Appl. Opt. 34, 729–734 (1996).
[CrossRef]

A. G. Hoekstra, P. M. A. Sloot, “Coupled dipole simulations of elastic light scattering on parallel systems,” Int. J. Mod. Phys. C 6, 663–679 (1995).
[CrossRef]

Smith, S. B.

S. B. Smith, Y. Cui, C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271, 795–799 (1996).
[CrossRef] [PubMed]

Streekstra, G. J.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69, 1666–1673 (1995).

Swyt, D. A.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, UK, 1988).

Tielens, A. G. G. M.

C. Dominik, A. G. G. M. Tielens, “The physics of dust coagulation and the structure of dust aggregates in space,” Astrophys. J. 480, 647–673 (1997).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, UK, 1988).

Visscher, K.

K. Visscher, G. J. Brakenhoff, J. J. Krol, “Micromanipulation by “multiple” optical traps created by a single fast scanning trap integrated with the bilateral confocal scanning laser microscope,” Cytometry 14, 105–114 (1993).
[CrossRef]

Waters, R.

C. Dominik, R. Waters, University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands (personal communication, 1999).

Weingartner, J. C.

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

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Figures (3)

Fig. 1
Fig. 1

Total radiation force on each dipole for a sphere with x=2.5 and m=1.05. The incident light travels from right to left. The maximum force is scaled to 1. Only one half of the sphere is shown.

Fig. 2
Fig. 2

As Fig. 1 but for m=1.33+0.01i.

Fig. 3
Fig. 3

As Fig. 1 but for m=1.14+038i.

Tables (4)

Tables Icon

Table 1 Range of Refractive Indices Used in the Tests, Together with the Number of Dipoles per Wavelength in the DDA Simulations

Tables Icon

Table 2 Results of Calculations of gzCsca and Cpr,z for Spheres As a Function of the Size Parameter x and Relative Refractive Index m a

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Table 3 As in Table 2 , but with the x and y Component of gCsca a

Tables Icon

Table 4 Relative Error in Cext and Cpr,z in DDA Simulations of Spheres a

Equations (60)

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Cpr=Cext-gCsca,
Fi=Re(pii)Re(Ei)+1cRedpidt × Re(Bi),
Fi = 12Re[(pi*i)Ei+ikpi* × Bi],
Fi=Finc,i+Fsca,i.
Frad=Finc+Fsca=i=1NFinc,i+i=1NFsca,i.
Finc,i=12Re{(pi,0*i)[Einc,0exp(ikri)]+ikpi,0*×[kˆ×Einc,0exp(ikri)]},
Fsca,i=ji12Re[(pi,0*i)Eij+ikpi,0*×Bij],
Eij=exp(ikrij)rij3k2rij×(pj,0×rij)+(1-ikrij)rij2 [3rij(rijpj,0)-rij2pj,0],
Bij=k2exp(ikrij)rij2 (rij×pj,0)1-1ikrij,
Finc,i=12Re[ik(pi,0*Einc,0)exp(ikri)].
Finc=18π Cext|Einc,0|2kˆ.
Fout=k48πdΩnˆi=1N[pi,0-nˆ(nˆpi,0)]×exp(-iknˆri)2,
gj=k4Csca|Einc,0|2dΩnˆe^j×i=1N[pi,0-nˆ(nˆpi,0)]exp(-iknˆri)2,
Fout=18π Csca|Einc,0|2g.
Frad=18π |Einc,0|2Cpr
Cpr=Cextkˆ-Cscag.
Eij=exp(ikrij)k2rij+ikrij2-1rij3pj,0+-k2rij-3ikrij2+3rij3n^ij(n^ijpj,0),
ikpi,0*×Bij=ik3exp(ikrij)rijpi,0*×(n^ij×pj,0)1-1ikrij
=ik3rij-k2rij2[(pi,0*pj,0)n^ij-(pi,0*n^ij)pj,0]exp(ikrij).
Fsca,i=ji12Re(Fij),
Fij=exp(ikrij)[(pi,0*pj,0)n^ij+pi,0*(n^ijpj,0)+(pi,0*n^ij)pj,0-5(pi,0*n^ij)n^ij(n^ijpj,0)]×-k2rij2-3ikrij3+3rij4+[(pi,0*pj,0)n^ij-(pi,0*n^ij)n^ij(n^ijpj,0)]ik3rij-k2rij2.
Fij=(pi,0*Mij,γpj,0)e^γ.
Mij,γ=exp(ikrij)(Uij,γ+Vij,γ+Wij,γ-5Tij,γ)×-k2rij2-3ikrij3+3rij4+(Uij,γ-Tij,γ)ik3rij-k2rij2,
Tij,γ=n^ij,γ(n^ijn^ij),Uij,γ=n^ij,γ1,
Vij,γ=n^ijΔγ,Wij,γ=Δγn^ij,
Mγ=0M12,γM1N,γM21,γMN-1,N,γMN1,γMN,N-1,γ0
P=p1,0pN,0,
Fsca=(P*MγP)e^γ.
Fsca,i=Pi,η*(MγP)3i+ηe^γ,
(pi,0*i)f(rij)=(pi,0*irij)f(rij)=(pi,0*n^ij)f(rij),
(pi,0*i)n^ij(n^ijpj,0)
=1rij [(pi,0*pj,0)n^ij+pi,0*(n^ijpj,0)
-2(pi,0*n^ij)n^ij(n^ijpj,0)].
(pi,0*i)Eij=exp(ikrij)(pi,0*pj,0)n^ij×-k2rij2-3ikrij3+3rij4-(pi,0*n^ij)n^ij(n^ijpj,0)×5-k2rij2-3ikrij3+3rij4+ik3rij-k2rij2+(pi,0*n^ij)pj,0×ik3rij-2k2rij2-3ikrij3+3rij4+pi,0*(n^ijpj,0)-k2rij2-3ikrij3+3rij4.
Fout=k48πi,jNdΩnˆIij(nˆ)=i,jNFI,ij,
Iij(nˆ)=exp(iknˆrij)[pi,0*pj,0-(pi,0*nˆ)(nˆpj,0)].
i=1N[pi,0-nˆ(nˆpi,0)]exp(-iknˆri)2=i,jNIij(nˆ)
exp(-iknˆrij)=exp[ik(rij,xsin θ cos ϕ+rij,ysin θ sin ϕ+rij,zcos θ)],
Θ=0πsin(θ)f(cos θ)exp(ikrijcos θ)dθ,
Θ=-11f(t)exp(ikrijt)dt.
Iu(α)=-11tuexp(ikαt)dt
aij=exp(ikrij),b1,ij=-k2rij2-3ikrij3+3rij4,
b2,ij=ik3rij-k2rij2,
c1,ij=pi,0,x*pj,0,z+pi,0,z*pj,0,xpi,0,y*pj,0,z+pi,0,z*pj,0,ypi,0,x*pj,0,x+pi,0,y*pj,0,y-2pi,0,z*pj,0,z,
c2,ij=(pi,0,x*pj,0,x+pi,0,y*pj,0,y)e^z,
-FI,ij=12 [Im(aijb1,ij)Im(c1,ij)+Im(aijb2,ij)Im(c2,ij)].
12Re(Fij)=12Re(aijb1,ijc1,ij+aijb2,ijc2,ij)=12Re[Re(aijb1,ij)Re(c1,ij)-Im(aijb1,ij)Im(c1,ij)+Re(aijb2,ij)×Re(c2,ij)-Im(aijb2,ij)Im(c2,ij)].
-FI,ij12Re(Fij),
-FI,ij-FI, ji=12Re(Fij)+12Re(Fji).
Iu(α)=-11tuexp(iαt)dt=exp(iα)+exp(-iα)(-1)u+1iα-uIu-1(α)iα,
I0(α)=[exp(iα)-exp(-iα)] 1iα,
I1(α)=[exp(iα)+exp(-iα)] 1iα-[exp(iα)-exp(-iα)] 1(iα)2,
I2(α)=[exp(iα)-exp(-iα)]1iα+2(iα)3-[exp(iα)+exp(-iα)] 2(iα)2,
I3(α)=[exp(iα)+exp(-iα)]1iα+6(iα)3-[exp(iα)-exp(-iα)]×3(iα)2+6(iα)4.
I1(α)=2i Imexp(iα)-iα+1α2,
I3(α)-I1(α)=4i Imexp(iα)1α2+3iα3-3α4.
N(t, ϕ)
=nˆnˆ=cos2(ϕ)s2(t)cos(ϕ)sin(ϕ)s2(t)cos(ϕ)ts(t)cos(ϕ)sin(ϕ)s2(t)sin2(ϕ)s2(t)sin(ϕ)ts(t)cos(ϕ)ts(t)sin(ϕ)ts(t)t2,
FI,ij=k48π02πdϕ-11dtexp(ikrijt)×s(t)cos(ϕ)s(t)sin(ϕ)t[(pi,0*pj,0)-pi,0*N(t, ϕ)pj,0].
FI,ij=k4[I3(krij)-I1(krij)]8×pi,0,x*pj,0,z+pi,0,z*pj,0,xpi,0,y*pj,0,z+pi,0,z*pj,0,ypi,0,x*pj,0,x+pi,0,y*pj,0,y-2pi,0,z*pj,0,z+k4I1(krij)400pi,0,x*pj,0,x+pi,0,y*pj,0,y.

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