Abstract

We derive the analytic expressions of the electromagnetic force and torque on a dipolar particle, with arbitrary dielectric permittivity and magnetic permeability. We then develop a general framework, based on the coupled dipole method, for computing the electromagnetic force and torque experienced by an object with arbitrary shape, dielectric permittivity and magnetic permeability.

© 2009 Optical Society of America

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  1. E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
    [CrossRef]
  2. B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
    [CrossRef]
  3. B. T. Draine and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
    [CrossRef]
  4. M. A. Yurkin and A. G. Hoekstra, "The discrete dipole approximation: An overview and recent developments," J. Quant. Spectrosc. Radiat. Transf. 106, 558-589 (2007).
    [CrossRef]
  5. A. Rahmani, P. C. Chaumet, and F. de Fornel, "Environment-induced modification of spontaneous emission: Single-molecule near-field probe," Phys. Rev. A 63, 023819-11 (2001).
    [CrossRef]
  6. A. Rahmani and G. W. Bryant, "Spontaneous emission in microcavity electrodynamics," Phys. Rev. A 65, 033817-12 (2002).
    [CrossRef]
  7. A. Sentenac, P. C. Chaumet, and K. Belkebir, "Beyond the Rayleigh criterion: Grating assisted far-field optical diffraction tomography," Phys. Rev. Lett. 97, 243901-4 (2006).
    [CrossRef]
  8. P. C. Chaumet and M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B 64, 035422-7 (2001).
    [CrossRef]
  9. P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Optical trapping and manipulation of nano-object with an apertureless probe," Phys. Rev. Lett. 88, 123601-4 (2002).
    [CrossRef] [PubMed]
  10. M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, "Near-field photonic forces," Phil. Trans. Roy. Soc. Lond. A 362, 719-737 (2004).
    [CrossRef]
  11. P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Photonic force spectroscopy on metallic and absorbing nanoparticles," Phys. Rev. B 71, 045425-7 (2005).
    [CrossRef]
  12. A. Rahmani and P. C. Chaumet, "Optical Trapping near a Photonic Crystal," Opt. Express 14, 6353-6358 (2006).
    [CrossRef] [PubMed]
  13. B. T. Draine and J. C. Weingartner, "Radiative Torques on Interstellar Grains: I. Superthermal Spinup," Astrophys. J. 470, 551-565 (1996).
    [CrossRef]
  14. P. C. Chaumet and C. Billaudeau, "Coupled dipole method to compute optical torque: Application to a micropropeller," J. Appl. Phys. 101, 023106-6 (2007).
    [CrossRef]
  15. A. Lakhtakia, "General theory of the PurcellPennypacker scattering approach and its extension to bianisotropic scatterers," Astrophys J 394, 494-499 (1192).
    [CrossRef]
  16. G. W. Mulholland, C. F. Bohren, and K. A. Fuller, "Light Scattering by Agglomerates Coupled Electric and Magnetic Dipole Method," Langmuir 10, 2533-2546 (1994).
    [CrossRef]
  17. O. Merchiers, F. Moreno, F. Gonzalez, and J. M. Saiz, "Light scattering by an ensemble of interacting dipolar particleswith both electric and magnetic," Phys. Rev. A 76, 043834-12 (2007).
    [CrossRef]
  18. Y. You, G. W. Kattawar, P.-W. Zhai, and p. Yang, "Zero-backscatter cloak for aspherical particles using a generalized dda formalism," Opt. Express 16, 2068-2079 (2008).
    [CrossRef] [PubMed]
  19. P. C. Chaumet and A. Rahmani, "Coupled-dipole method for magnetic and negative refraction materials," J. Quant. Spect. Rad. Transf. 110, 22-29 (2009).
  20. B. Kemp, T. Grzegorczyk, and J. Kong, "Ab initio study of the radiation pressure on dielectric and magnetic media," Opt. Express 13, 9280-9291 (2005). http://www.opticsinfobase.org/oe/abstract.cfm>? URI=oe-13-23-9280
    [CrossRef] [PubMed]
  21. B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Lorentz force on dielectric and magnetic particles," J. Electromagn. Waves Appl. 20, 827-839 (2006).
    [CrossRef]
  22. A. Lakhtakia, "Radiation Pressure Efficiencies of Spheres Made of Isotropic, Achiral, Passive, Homogeneous, Negative-Phase-Velocity Materials," Electromagnetics 28, 346-353 (2008)
    [CrossRef]
  23. P. C. Chaumet and M. Nieto-Vesperinas, "Time-averaged total force on a dipolar sphere in an electromagnetic field," Opt. Lett. 25, 1065-1067 (2000).
    [CrossRef]
  24. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New-York, 1941).
  25. J. D. Jackson, Classical Electrodynamics (Wiley, 1975), 2nd ed.
  26. G. S. Agarwal, "Quantum electrodynamics in the presence of dielectrics and conductors. I Electromagnetic-field response functions and black-body fluctuations in finite geometry," Phys. Rev. A 11, 230-242 (1975).
    [CrossRef]
  27. G. H. Goedecke and S. G. O’Brien, "Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm," Appl. Opt. 27, 2431-2438 (1988)
    [CrossRef] [PubMed]
  28. M. Dienerowitz, M. Mazilu, and K. Dholakia, "Optical trapping of nanoparticles: a review," J. Nanophoton. 2, 021875-32 (2008).
    [CrossRef]
  29. P. C. Waterman, "Symmetry, Unitary, and Geometry in Electromagnetic Scattering," Phys. Rev. D 3, 825-839 (1971).
    [CrossRef]
  30. 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]
  31. T. A. Nieminen, "Comment on Geometric absorption of electromagnetic angular momentum, C. Konz, G. Benford," Opt. Commun. 235, 227-229 (2004).
    [CrossRef]
  32. A. Rahmani, P. C. Chaumet, and G. W. Bryant, "On the Importance of Local-Field Corrections for Polarizable Particles on a Finite Lattice: Application to the Discrete Dipole Approximation," Astrophys. J. 607, 873-878 (2004).
    [CrossRef]
  33. P. C. Chaumet, A. Rahmani, A. Sentenac, and G. W. Bryant, "Efficient computation of optical forces with the coupled dipole method," Phys. Rev. E 72, 046708-6 (2005).
    [CrossRef]
  34. R. D. Da Cunha and T. Hopkins, "The Parallel Iterative Methods (PIM) package for the solution of systems of linear equations on parallel computers," Appl. Numer. Math. 19, 33-50 (1995).
    [CrossRef]
  35. J. J. Goodman and P. J. Flatau, "Application of fast-fourier-transform techniques to the discrete-dipole approximation," Opt. Lett. 16, 1198-1200 (2002).
    [CrossRef]
  36. A. Lakhtakia, "Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetics fields," Int. J. Mod. Phys. C 3, 583-603 (1992).
    [CrossRef]
  37. C. E. Dungey and C. F. Bohren, "Light scattering by nonspherical particles: a refinement to the coupled-dipole method," J. Opt. Soc. Am. A 8, 81-87 (1991).
    [CrossRef]
  38. P. C. Chaumet, A. Sentenac, and A. Rahmani, "Coupled dipole method for scatterers with large permittivity," Phys. Rev. E 70, 036606-6 (2004).
    [CrossRef]

2009 (1)

P. C. Chaumet and A. Rahmani, "Coupled-dipole method for magnetic and negative refraction materials," J. Quant. Spect. Rad. Transf. 110, 22-29 (2009).

2008 (3)

A. Lakhtakia, "Radiation Pressure Efficiencies of Spheres Made of Isotropic, Achiral, Passive, Homogeneous, Negative-Phase-Velocity Materials," Electromagnetics 28, 346-353 (2008)
[CrossRef]

Y. You, G. W. Kattawar, P.-W. Zhai, and p. Yang, "Zero-backscatter cloak for aspherical particles using a generalized dda formalism," Opt. Express 16, 2068-2079 (2008).
[CrossRef] [PubMed]

M. Dienerowitz, M. Mazilu, and K. Dholakia, "Optical trapping of nanoparticles: a review," J. Nanophoton. 2, 021875-32 (2008).
[CrossRef]

2007 (3)

M. A. Yurkin and A. G. Hoekstra, "The discrete dipole approximation: An overview and recent developments," J. Quant. Spectrosc. Radiat. Transf. 106, 558-589 (2007).
[CrossRef]

P. C. Chaumet and C. Billaudeau, "Coupled dipole method to compute optical torque: Application to a micropropeller," J. Appl. Phys. 101, 023106-6 (2007).
[CrossRef]

O. Merchiers, F. Moreno, F. Gonzalez, and J. M. Saiz, "Light scattering by an ensemble of interacting dipolar particleswith both electric and magnetic," Phys. Rev. A 76, 043834-12 (2007).
[CrossRef]

2006 (3)

A. Rahmani and P. C. Chaumet, "Optical Trapping near a Photonic Crystal," Opt. Express 14, 6353-6358 (2006).
[CrossRef] [PubMed]

A. Sentenac, P. C. Chaumet, and K. Belkebir, "Beyond the Rayleigh criterion: Grating assisted far-field optical diffraction tomography," Phys. Rev. Lett. 97, 243901-4 (2006).
[CrossRef]

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Lorentz force on dielectric and magnetic particles," J. Electromagn. Waves Appl. 20, 827-839 (2006).
[CrossRef]

2005 (2)

P. C. Chaumet, A. Rahmani, A. Sentenac, and G. W. Bryant, "Efficient computation of optical forces with the coupled dipole method," Phys. Rev. E 72, 046708-6 (2005).
[CrossRef]

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Photonic force spectroscopy on metallic and absorbing nanoparticles," Phys. Rev. B 71, 045425-7 (2005).
[CrossRef]

2004 (4)

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, "Near-field photonic forces," Phil. Trans. Roy. Soc. Lond. A 362, 719-737 (2004).
[CrossRef]

T. A. Nieminen, "Comment on Geometric absorption of electromagnetic angular momentum, C. Konz, G. Benford," Opt. Commun. 235, 227-229 (2004).
[CrossRef]

A. Rahmani, P. C. Chaumet, and G. W. Bryant, "On the Importance of Local-Field Corrections for Polarizable Particles on a Finite Lattice: Application to the Discrete Dipole Approximation," Astrophys. J. 607, 873-878 (2004).
[CrossRef]

P. C. Chaumet, A. Sentenac, and A. Rahmani, "Coupled dipole method for scatterers with large permittivity," Phys. Rev. E 70, 036606-6 (2004).
[CrossRef]

2002 (3)

J. J. Goodman and P. J. Flatau, "Application of fast-fourier-transform techniques to the discrete-dipole approximation," Opt. Lett. 16, 1198-1200 (2002).
[CrossRef]

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Optical trapping and manipulation of nano-object with an apertureless probe," Phys. Rev. Lett. 88, 123601-4 (2002).
[CrossRef] [PubMed]

A. Rahmani and G. W. Bryant, "Spontaneous emission in microcavity electrodynamics," Phys. Rev. A 65, 033817-12 (2002).
[CrossRef]

2001 (2)

P. C. Chaumet and M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B 64, 035422-7 (2001).
[CrossRef]

A. Rahmani, P. C. Chaumet, and F. de Fornel, "Environment-induced modification of spontaneous emission: Single-molecule near-field probe," Phys. Rev. A 63, 023819-11 (2001).
[CrossRef]

2000 (1)

1996 (1)

B. T. Draine and J. C. Weingartner, "Radiative Torques on Interstellar Grains: I. Superthermal Spinup," Astrophys. J. 470, 551-565 (1996).
[CrossRef]

1995 (1)

R. D. Da Cunha and T. Hopkins, "The Parallel Iterative Methods (PIM) package for the solution of systems of linear equations on parallel computers," Appl. Numer. Math. 19, 33-50 (1995).
[CrossRef]

1994 (2)

G. W. Mulholland, C. F. Bohren, and K. A. Fuller, "Light Scattering by Agglomerates Coupled Electric and Magnetic Dipole Method," Langmuir 10, 2533-2546 (1994).
[CrossRef]

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

1992 (1)

A. Lakhtakia, "Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetics fields," Int. J. Mod. Phys. C 3, 583-603 (1992).
[CrossRef]

1991 (1)

1988 (2)

G. H. Goedecke and S. G. O’Brien, "Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm," Appl. Opt. 27, 2431-2438 (1988)
[CrossRef] [PubMed]

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

1984 (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]

1975 (1)

G. S. Agarwal, "Quantum electrodynamics in the presence of dielectrics and conductors. I Electromagnetic-field response functions and black-body fluctuations in finite geometry," Phys. Rev. A 11, 230-242 (1975).
[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, Unitary, and Geometry in Electromagnetic Scattering," Phys. Rev. D 3, 825-839 (1971).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, "Quantum electrodynamics in the presence of dielectrics and conductors. I Electromagnetic-field response functions and black-body fluctuations in finite geometry," Phys. Rev. A 11, 230-242 (1975).
[CrossRef]

Belkebir, K.

A. Sentenac, P. C. Chaumet, and K. Belkebir, "Beyond the Rayleigh criterion: Grating assisted far-field optical diffraction tomography," Phys. Rev. Lett. 97, 243901-4 (2006).
[CrossRef]

Billaudeau, C.

P. C. Chaumet and C. Billaudeau, "Coupled dipole method to compute optical torque: Application to a micropropeller," J. Appl. Phys. 101, 023106-6 (2007).
[CrossRef]

Bohren, C. F.

G. W. Mulholland, C. F. Bohren, and K. A. Fuller, "Light Scattering by Agglomerates Coupled Electric and Magnetic Dipole Method," Langmuir 10, 2533-2546 (1994).
[CrossRef]

C. E. Dungey and C. F. Bohren, "Light scattering by nonspherical particles: a refinement to the coupled-dipole method," J. Opt. Soc. Am. A 8, 81-87 (1991).
[CrossRef]

Bryant, G. W.

P. C. Chaumet, A. Rahmani, A. Sentenac, and G. W. Bryant, "Efficient computation of optical forces with the coupled dipole method," Phys. Rev. E 72, 046708-6 (2005).
[CrossRef]

A. Rahmani, P. C. Chaumet, and G. W. Bryant, "On the Importance of Local-Field Corrections for Polarizable Particles on a Finite Lattice: Application to the Discrete Dipole Approximation," Astrophys. J. 607, 873-878 (2004).
[CrossRef]

A. Rahmani and G. W. Bryant, "Spontaneous emission in microcavity electrodynamics," Phys. Rev. A 65, 033817-12 (2002).
[CrossRef]

Chaumet, P. C.

P. C. Chaumet and A. Rahmani, "Coupled-dipole method for magnetic and negative refraction materials," J. Quant. Spect. Rad. Transf. 110, 22-29 (2009).

P. C. Chaumet and C. Billaudeau, "Coupled dipole method to compute optical torque: Application to a micropropeller," J. Appl. Phys. 101, 023106-6 (2007).
[CrossRef]

A. Sentenac, P. C. Chaumet, and K. Belkebir, "Beyond the Rayleigh criterion: Grating assisted far-field optical diffraction tomography," Phys. Rev. Lett. 97, 243901-4 (2006).
[CrossRef]

A. Rahmani and P. C. Chaumet, "Optical Trapping near a Photonic Crystal," Opt. Express 14, 6353-6358 (2006).
[CrossRef] [PubMed]

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Photonic force spectroscopy on metallic and absorbing nanoparticles," Phys. Rev. B 71, 045425-7 (2005).
[CrossRef]

P. C. Chaumet, A. Rahmani, A. Sentenac, and G. W. Bryant, "Efficient computation of optical forces with the coupled dipole method," Phys. Rev. E 72, 046708-6 (2005).
[CrossRef]

A. Rahmani, P. C. Chaumet, and G. W. Bryant, "On the Importance of Local-Field Corrections for Polarizable Particles on a Finite Lattice: Application to the Discrete Dipole Approximation," Astrophys. J. 607, 873-878 (2004).
[CrossRef]

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, "Near-field photonic forces," Phil. Trans. Roy. Soc. Lond. A 362, 719-737 (2004).
[CrossRef]

P. C. Chaumet, A. Sentenac, and A. Rahmani, "Coupled dipole method for scatterers with large permittivity," Phys. Rev. E 70, 036606-6 (2004).
[CrossRef]

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Optical trapping and manipulation of nano-object with an apertureless probe," Phys. Rev. Lett. 88, 123601-4 (2002).
[CrossRef] [PubMed]

P. C. Chaumet and M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B 64, 035422-7 (2001).
[CrossRef]

A. Rahmani, P. C. Chaumet, and F. de Fornel, "Environment-induced modification of spontaneous emission: Single-molecule near-field probe," Phys. Rev. A 63, 023819-11 (2001).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, "Time-averaged total force on a dipolar sphere in an electromagnetic field," Opt. Lett. 25, 1065-1067 (2000).
[CrossRef]

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]

Da Cunha, R. D.

R. D. Da Cunha and T. Hopkins, "The Parallel Iterative Methods (PIM) package for the solution of systems of linear equations on parallel computers," Appl. Numer. Math. 19, 33-50 (1995).
[CrossRef]

de Fornel, F.

A. Rahmani, P. C. Chaumet, and F. de Fornel, "Environment-induced modification of spontaneous emission: Single-molecule near-field probe," Phys. Rev. A 63, 023819-11 (2001).
[CrossRef]

Dholakia, K.

M. Dienerowitz, M. Mazilu, and K. Dholakia, "Optical trapping of nanoparticles: a review," J. Nanophoton. 2, 021875-32 (2008).
[CrossRef]

Dienerowitz, M.

M. Dienerowitz, M. Mazilu, and K. Dholakia, "Optical trapping of nanoparticles: a review," J. Nanophoton. 2, 021875-32 (2008).
[CrossRef]

Draine, B. T.

B. T. Draine and J. C. Weingartner, "Radiative Torques on Interstellar Grains: I. Superthermal Spinup," 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, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

Dungey, C. E.

Flatau, P. J.

Fuller, K. A.

G. W. Mulholland, C. F. Bohren, and K. A. Fuller, "Light Scattering by Agglomerates Coupled Electric and Magnetic Dipole Method," Langmuir 10, 2533-2546 (1994).
[CrossRef]

Goedecke, G. H.

Gonzalez, F.

O. Merchiers, F. Moreno, F. Gonzalez, and J. M. Saiz, "Light scattering by an ensemble of interacting dipolar particleswith both electric and magnetic," Phys. Rev. A 76, 043834-12 (2007).
[CrossRef]

Goodman, J. J.

Grzegorczyk, T. M.

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Lorentz force on dielectric and magnetic particles," J. Electromagn. Waves Appl. 20, 827-839 (2006).
[CrossRef]

Hoekstra, A. G.

M. A. Yurkin and A. G. Hoekstra, "The discrete dipole approximation: An overview and recent developments," J. Quant. Spectrosc. Radiat. Transf. 106, 558-589 (2007).
[CrossRef]

Hopkins, T.

R. D. Da Cunha and T. Hopkins, "The Parallel Iterative Methods (PIM) package for the solution of systems of linear equations on parallel computers," Appl. Numer. Math. 19, 33-50 (1995).
[CrossRef]

Kattawar, G. W.

Kemp, B. A.

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Lorentz force on dielectric and magnetic particles," J. Electromagn. Waves Appl. 20, 827-839 (2006).
[CrossRef]

Kong, J. A.

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Lorentz force on dielectric and magnetic particles," J. Electromagn. Waves Appl. 20, 827-839 (2006).
[CrossRef]

Lakhtakia, A.

A. Lakhtakia, "Radiation Pressure Efficiencies of Spheres Made of Isotropic, Achiral, Passive, Homogeneous, Negative-Phase-Velocity Materials," Electromagnetics 28, 346-353 (2008)
[CrossRef]

A. Lakhtakia, "Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetics fields," Int. J. Mod. Phys. C 3, 583-603 (1992).
[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]

Mazilu, M.

M. Dienerowitz, M. Mazilu, and K. Dholakia, "Optical trapping of nanoparticles: a review," J. Nanophoton. 2, 021875-32 (2008).
[CrossRef]

Merchiers, O.

O. Merchiers, F. Moreno, F. Gonzalez, and J. M. Saiz, "Light scattering by an ensemble of interacting dipolar particleswith both electric and magnetic," Phys. Rev. A 76, 043834-12 (2007).
[CrossRef]

Moreno, F.

O. Merchiers, F. Moreno, F. Gonzalez, and J. M. Saiz, "Light scattering by an ensemble of interacting dipolar particleswith both electric and magnetic," Phys. Rev. A 76, 043834-12 (2007).
[CrossRef]

Mulholland, G. W.

G. W. Mulholland, C. F. Bohren, and K. A. Fuller, "Light Scattering by Agglomerates Coupled Electric and Magnetic Dipole Method," Langmuir 10, 2533-2546 (1994).
[CrossRef]

Nieminen, T. A.

T. A. Nieminen, "Comment on Geometric absorption of electromagnetic angular momentum, C. Konz, G. Benford," Opt. Commun. 235, 227-229 (2004).
[CrossRef]

Nieto-Vesperinas, M.

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Photonic force spectroscopy on metallic and absorbing nanoparticles," Phys. Rev. B 71, 045425-7 (2005).
[CrossRef]

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, "Near-field photonic forces," Phil. Trans. Roy. Soc. Lond. A 362, 719-737 (2004).
[CrossRef]

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Optical trapping and manipulation of nano-object with an apertureless probe," Phys. Rev. Lett. 88, 123601-4 (2002).
[CrossRef] [PubMed]

P. C. Chaumet and M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B 64, 035422-7 (2001).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, "Time-averaged total force on a dipolar sphere in an electromagnetic field," Opt. Lett. 25, 1065-1067 (2000).
[CrossRef]

O’Brien, S. G.

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]

Purcell, E. M.

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

Rahmani, A.

P. C. Chaumet and A. Rahmani, "Coupled-dipole method for magnetic and negative refraction materials," J. Quant. Spect. Rad. Transf. 110, 22-29 (2009).

A. Rahmani and P. C. Chaumet, "Optical Trapping near a Photonic Crystal," Opt. Express 14, 6353-6358 (2006).
[CrossRef] [PubMed]

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Photonic force spectroscopy on metallic and absorbing nanoparticles," Phys. Rev. B 71, 045425-7 (2005).
[CrossRef]

P. C. Chaumet, A. Rahmani, A. Sentenac, and G. W. Bryant, "Efficient computation of optical forces with the coupled dipole method," Phys. Rev. E 72, 046708-6 (2005).
[CrossRef]

A. Rahmani, P. C. Chaumet, and G. W. Bryant, "On the Importance of Local-Field Corrections for Polarizable Particles on a Finite Lattice: Application to the Discrete Dipole Approximation," Astrophys. J. 607, 873-878 (2004).
[CrossRef]

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, "Near-field photonic forces," Phil. Trans. Roy. Soc. Lond. A 362, 719-737 (2004).
[CrossRef]

P. C. Chaumet, A. Sentenac, and A. Rahmani, "Coupled dipole method for scatterers with large permittivity," Phys. Rev. E 70, 036606-6 (2004).
[CrossRef]

A. Rahmani and G. W. Bryant, "Spontaneous emission in microcavity electrodynamics," Phys. Rev. A 65, 033817-12 (2002).
[CrossRef]

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Optical trapping and manipulation of nano-object with an apertureless probe," Phys. Rev. Lett. 88, 123601-4 (2002).
[CrossRef] [PubMed]

A. Rahmani, P. C. Chaumet, and F. de Fornel, "Environment-induced modification of spontaneous emission: Single-molecule near-field probe," Phys. Rev. A 63, 023819-11 (2001).
[CrossRef]

Saiz, J. M.

O. Merchiers, F. Moreno, F. Gonzalez, and J. M. Saiz, "Light scattering by an ensemble of interacting dipolar particleswith both electric and magnetic," Phys. Rev. A 76, 043834-12 (2007).
[CrossRef]

Sentenac, A.

A. Sentenac, P. C. Chaumet, and K. Belkebir, "Beyond the Rayleigh criterion: Grating assisted far-field optical diffraction tomography," Phys. Rev. Lett. 97, 243901-4 (2006).
[CrossRef]

P. C. Chaumet, A. Rahmani, A. Sentenac, and G. W. Bryant, "Efficient computation of optical forces with the coupled dipole method," Phys. Rev. E 72, 046708-6 (2005).
[CrossRef]

P. C. Chaumet, A. Sentenac, and A. Rahmani, "Coupled dipole method for scatterers with large permittivity," Phys. Rev. E 70, 036606-6 (2004).
[CrossRef]

Waterman, P. C.

P. C. Waterman, "Symmetry, Unitary, and Geometry in Electromagnetic Scattering," Phys. Rev. D 3, 825-839 (1971).
[CrossRef]

Weingartner, J. C.

B. T. Draine and J. C. Weingartner, "Radiative Torques on Interstellar Grains: I. Superthermal Spinup," Astrophys. J. 470, 551-565 (1996).
[CrossRef]

You, Y.

Yurkin, M. A.

M. A. Yurkin and A. G. Hoekstra, "The discrete dipole approximation: An overview and recent developments," J. Quant. Spectrosc. Radiat. Transf. 106, 558-589 (2007).
[CrossRef]

Zhai, P.-W.

Appl. Numer. Math. (1)

R. D. Da Cunha and T. Hopkins, "The Parallel Iterative Methods (PIM) package for the solution of systems of linear equations on parallel computers," Appl. Numer. Math. 19, 33-50 (1995).
[CrossRef]

Appl. Opt. (1)

Astrophys. J. (4)

A. Rahmani, P. C. Chaumet, and G. W. Bryant, "On the Importance of Local-Field Corrections for Polarizable Particles on a Finite Lattice: Application to the Discrete Dipole Approximation," Astrophys. J. 607, 873-878 (2004).
[CrossRef]

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

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

B. T. Draine and J. C. Weingartner, "Radiative Torques on Interstellar Grains: I. Superthermal Spinup," Astrophys. J. 470, 551-565 (1996).
[CrossRef]

Electromagnetics (1)

A. Lakhtakia, "Radiation Pressure Efficiencies of Spheres Made of Isotropic, Achiral, Passive, Homogeneous, Negative-Phase-Velocity Materials," Electromagnetics 28, 346-353 (2008)
[CrossRef]

Int. J. Mod. Phys. C (1)

A. Lakhtakia, "Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetics fields," Int. J. Mod. Phys. C 3, 583-603 (1992).
[CrossRef]

J. Appl. Phys. (1)

P. C. Chaumet and C. Billaudeau, "Coupled dipole method to compute optical torque: Application to a micropropeller," J. Appl. Phys. 101, 023106-6 (2007).
[CrossRef]

J. Electromagn. Waves Appl. (1)

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Lorentz force on dielectric and magnetic particles," J. Electromagn. Waves Appl. 20, 827-839 (2006).
[CrossRef]

J. Nanophoton. (1)

M. Dienerowitz, M. Mazilu, and K. Dholakia, "Optical trapping of nanoparticles: a review," J. Nanophoton. 2, 021875-32 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Quant. Spect. Rad. Transf. (1)

P. C. Chaumet and A. Rahmani, "Coupled-dipole method for magnetic and negative refraction materials," J. Quant. Spect. Rad. Transf. 110, 22-29 (2009).

J. Quant. Spectrosc. Radiat. Transf. (1)

M. A. Yurkin and A. G. Hoekstra, "The discrete dipole approximation: An overview and recent developments," J. Quant. Spectrosc. Radiat. Transf. 106, 558-589 (2007).
[CrossRef]

Langmuir (1)

G. W. Mulholland, C. F. Bohren, and K. A. Fuller, "Light Scattering by Agglomerates Coupled Electric and Magnetic Dipole Method," Langmuir 10, 2533-2546 (1994).
[CrossRef]

Opt. Commun. (1)

T. A. Nieminen, "Comment on Geometric absorption of electromagnetic angular momentum, C. Konz, G. Benford," Opt. Commun. 235, 227-229 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phil. Trans. Roy. Soc. Lond. A (1)

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, "Near-field photonic forces," Phil. Trans. Roy. Soc. Lond. A 362, 719-737 (2004).
[CrossRef]

Phys. Rev. A (5)

A. Rahmani, P. C. Chaumet, and F. de Fornel, "Environment-induced modification of spontaneous emission: Single-molecule near-field probe," Phys. Rev. A 63, 023819-11 (2001).
[CrossRef]

A. Rahmani and G. W. Bryant, "Spontaneous emission in microcavity electrodynamics," Phys. Rev. A 65, 033817-12 (2002).
[CrossRef]

O. Merchiers, F. Moreno, F. Gonzalez, and J. M. Saiz, "Light scattering by an ensemble of interacting dipolar particleswith both electric and magnetic," Phys. Rev. A 76, 043834-12 (2007).
[CrossRef]

G. S. Agarwal, "Quantum electrodynamics in the presence of dielectrics and conductors. I Electromagnetic-field response functions and black-body fluctuations in finite geometry," Phys. Rev. A 11, 230-242 (1975).
[CrossRef]

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 (2)

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Photonic force spectroscopy on metallic and absorbing nanoparticles," Phys. Rev. B 71, 045425-7 (2005).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B 64, 035422-7 (2001).
[CrossRef]

Phys. Rev. D (1)

P. C. Waterman, "Symmetry, Unitary, and Geometry in Electromagnetic Scattering," Phys. Rev. D 3, 825-839 (1971).
[CrossRef]

Phys. Rev. E (2)

P. C. Chaumet, A. Rahmani, A. Sentenac, and G. W. Bryant, "Efficient computation of optical forces with the coupled dipole method," Phys. Rev. E 72, 046708-6 (2005).
[CrossRef]

P. C. Chaumet, A. Sentenac, and A. Rahmani, "Coupled dipole method for scatterers with large permittivity," Phys. Rev. E 70, 036606-6 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Optical trapping and manipulation of nano-object with an apertureless probe," Phys. Rev. Lett. 88, 123601-4 (2002).
[CrossRef] [PubMed]

A. Sentenac, P. C. Chaumet, and K. Belkebir, "Beyond the Rayleigh criterion: Grating assisted far-field optical diffraction tomography," Phys. Rev. Lett. 97, 243901-4 (2006).
[CrossRef]

Other (4)

A. Lakhtakia, "General theory of the PurcellPennypacker scattering approach and its extension to bianisotropic scatterers," Astrophys J 394, 494-499 (1192).
[CrossRef]

B. Kemp, T. Grzegorczyk, and J. Kong, "Ab initio study of the radiation pressure on dielectric and magnetic media," Opt. Express 13, 9280-9291 (2005). http://www.opticsinfobase.org/oe/abstract.cfm>? URI=oe-13-23-9280
[CrossRef] [PubMed]

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New-York, 1941).

J. D. Jackson, Classical Electrodynamics (Wiley, 1975), 2nd ed.

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Figures (5)

Fig. 1.
Fig. 1.

Sphere of radius a = λ/2 with ε = μ = 2.25. (a) Computation time versus number N of dipoles for the calculation of the spatial derivatives of the local fields, for the three different methods outlined in the text. (b) Relative error, in percent, between the optical forces computed using the CDM and using Mie theory versus the number of dipoles. Different forms of the polarizability are considered: (CR) Clausius-Mossotti with radiation reaction [2]; (DB) first Mie coefficient [37]; (LA) Lakthakia’s prescription [36].

Fig. 2.
Fig. 2.

(a) Optical force on a sphere of radius a = λ/4 versus ε = μ for N = 113104. (b) zoom on the resonance around ε = μ ≈ 4.

Fig. 3.
Fig. 3.

Sphere of radius a = λ/4 with Re(ε) = Re(μ) = 2.25 and Im(μ) = 0. (a) Optical force versus Im(ε). Note that the three CDM plots corresponding to the three forms of the polarizabilities are superimposed on the scale of the figure. (b) Relative error in percent between the optical force obtained from the CDM and the Mie series. (c) Optical torque versus versus Im(ε). (d) Relative error in percent between the optical torque obtained from the CDM and the Mie series.

Fig. 4.
Fig. 4.

Sphere of radius a = λ/4 with Re(ε) = Re(μ) = 2.25. (a) Optical force versus Im(ε) = Im(μ). (b) Relative error in per cent between the optical force obtained from the CDM and the Mie series. (c) Optical torque versus versus Im(ε) = Im(μ). (d) Relative error in percent between the optical torque obtained from the CDM and the Mie series.

Fig. 5.
Fig. 5.

Sphere of radius a = λ/4 with ε = μ = - 1. (a) Optical force versus Im(ε) = Im(μ). (b) Relative error in percent between the optical force obtained from the CDM and the Mie series. (c) Optical torque versus versus Im(ε) = Im(μ). (d) Relative error in percent between the optical torque obtained from the CDM and the Mie series.

Equations (29)

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F = 1 8 π Re [ S [ ( E ( r ) . n ) E * ( r ) + ( H ( r ) . n ) H * ( r ) 1 2 ( E ( r ) 2 + H ( r ) 2 n ) ] d S ] ,
E d ( r ) = e ikr { [ 3 r ̂ ( r ̂ . p ) p ] ( 1 r 3 ik r 2 ) + k 2 r ( r ̂ × p ) × r ̂ k 2 ( r ̂ × m ) ( 1 r + i k r 2 ) }
= T ee p + T em m
H d ( r ) = e ikr { [ 3 r ̂ ( r ̂ . m ) m ] ( 1 r 3 ik r 2 ) + k 2 r ( r ̂ × m ) × r ̂ + k 2 ( r ̂ × p ) ( 1 r + i k r 2 ) }
= T me p + T mm m ,
E 0 ( r ) = E 0 + r ( r ̂ . ) E 0 + and H 0 ( r ) = H 0 + r ( r ̂ . ) H 0 +
F = 1 8 π Re [ S ( E d ( r ) . n ) E 0 * ( r ) + ( E 0 * ( r ) . n ) E d ( r ) + ( H d ( r ) . n ) H 0 * ( r )
+ ( H 0 * ( r ) . n ) H d ( r ) ( E d ( r ) . E 0 * ( r ) + H d ( r ) . H 0 * ( r ) ] n
+ ( E d ( r ) . n ) E d * ( r ) + ( H d ( r ) . n ) H d * ( r ) 1 2 [ E d ( r ) 2 + H d ( r ) 2 n d S ] .
F mix i = 1 6 Re [ 2 p j i E 0 * j p j i E 0 * j + p j i E 0 * j + 2 ik ε ijk H 0 * j p k
2 ik ε ijk E 0 * j m k + 2 m j j H 0 * i m i j H 0 * j + m j i E 0 * j ] ,
F mix i = 1 2 Re [ p j i E 0 * j + m j i H 0 * j ] .
F self = 1 8 π Re [ S [ 1 2 [ E d ( r ) 2 + H d ( r ) 2 n d S ] ,
F self = k 4 8 π Re [ S { [ ( r ̂ × p * ) × r ̂ ] . ( r ̂ × m ) [ ( r ̂ × m * ) × r ̂ ] . ( r ̂ × p ) } n r 2 d S ]
= k 4 3 Re ( p × m * ) .
F i = 1 2 Re [ p j i E 0 * j + m j i H 0 * j 2 k 4 3 ε ijk p j m * k ] .
α 0 e = a 3 ε 1 ε + 2 and α 0 m = a 3 μ 1 μ + 2 .
α e = α 0 e / ( 1 2 3 i k 3 α 0 e ) and α m = α 0 m / ( 1 2 3 i k 3 α 0 m ) ,
F i = 1 2 Re [ α e E 0 j i E 0 * j + α m H 0 j i H 0 * j 2 k 4 3 ε ijk α e E 0 j ( α m H 0 k ) * ] .
Γ int = 1 8 π Re [ S r × [ ( E ( r ) . n ) E * ( r ) + ( H ( r ) . n ) H * ( r ) 1 2 ( E ( r ) 2 + H ( r ) 2 n ) ] d S ] ,
Γ int = 1 8 π Re [ S r × [ ( E ( r ) . n ) E * ( r ) + ( H ( r ) . n ) H * ( r ) ] d S ] .
Γ int = 1 2 Re ( p × E 0 * + m × H 0 * ] .
Γ int = 1 2 Re [ p × ( p / α 0 e ) * + m × ( m / α 0 m ) * ] .
Γ int = E 0 2 Im [ α 0 e + α 0 m ] z ̂ .
E l = E 0 l + n = 1 N [ T ln ee α n e E n + T ln em α n m H n ]
H l = H 0 l + n = 1 N [ T ln me α n e E n + T ln mm α n m H n ] ,
E l = E 0 l + n = 1 N [ T ln ee α n e E n + T ln em α n m H n ]
H l = H 0 l + n = 1 N [ T ln me α n e E n + T ln mm α n m H n ] .
Γ = n = 1 N ( Γ n ext + Γ n int ) = n = 1 N ( r n × F n + 1 2 Re [ p n × ( p n / α 0 , n e ) * + m n × ( m n / α 0 , n m ) * ] ) .

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