Abstract

We present a time-domain formulation of electrodynamics based on the self-consistent derivation of the electromagnetic field in a linear, dispersive, lossy object via the coupled dipole method.

© 2008 Optical Society of America

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References

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  1. F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 775–824 (2003).
    [Crossref]
  2. 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]
  3. M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express 15, 17,902–17,911 (2007).
    [Crossref]
  4. P. C. Chaumet, A. Sentenac, and A. Rahmani, “Coupled dipole method for scatterers with large permittivity,” Phys. Rev. E 70, 036,606–6 (2004).
    [Crossref]
  5. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. 14, 302–307 (1969).
  6. A. Taflove and M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. 23, 623”630 (1975).
    [Crossref]
  7. A. Taflove and S. C. Hagness, “Computational Electrodynamics: The Finite-Difference Time-Domain Method”, 3rd edition, (Artech House Publishers, 2005).
  8. Z. Q. Peng and A. G. Tijhuis, “Transient scattering by a lossy dielectric cylinder: marching-on-in-frequency approach,” J. Elect. Waves Appl. 7, 739–763 (1993).
    [Crossref]
  9. K. Muinonen and E. Zubko, “Optimizing the discrete-dipole approximation for sequences of scatterers with identical shapes but differing sizes or refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 100, 288–294 (2006).
    [Crossref]
  10. Y. Okada, I. Mann, I. Sano, and S. Mukai, “Acceleration of the iterative solver in the discrete dipole approximation: Application to the orientation variation of irregularly shaped particles,” J. Quant. Spectrosc. Radiat. Transf. 109, 1461–1473 (2008).
    [Crossref]
  11. E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
    [Crossref]
  12. J. D. Jackson, Classical Electrodynamics (Wiley, 1975), 2nd ed.
  13. P. C. Chaumet, “Comment on “Trapping force, force constant, and potential depths for dielectric spheres in the presence of spherical aberrations,”” Appl. Opt. 43, 1825–1826 (2004).
    [Crossref] [PubMed]
  14. A. Rahmani, P. C. Chaumet, F. de Fornel, and C. Girard, “Field propagator of a dressed junction: Fluorescence lifetime calculations in a confined geometry,” Phys. Rev. A 56, 3245–3254 (1997).
    [Crossref]
  15. 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]
  16. F. Bordas, N. Louvion, S. Callard, P. C. Chaumet, and A. Rahmani, “Coupled dipole method for radiation dynamics in finite photonic crystal structures,” Phys. Rev. E 73, 056,601 (2006).
    [Crossref]
  17. RSoft Inc., RSoft Fullwave FDTD code, http://www.rsoftdesign.com.
  18. P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164,705–3 (2006).
    [Crossref]
  19. 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]
  20. A. Rahmani, P. C. Chaumet, and G. W. Bryant, “Local-field correction for an interstitial impurity in a crystal,” Opt. Lett. 27, 430–432 (2002).
    [Crossref]
  21. A. Rahmani, P. C. Chaumet, and F. de Fornel, “Environment-induced modification of spontaneous emission: Single-molecule near-field probe,” Phys. Rev. A. 63023819 (2001).
    [Crossref]
  22. A. Rahmani and G. W. Bryant, “Spontaneous emission in microcavity electrodynamics,” Phys. Rev. A. 65033817 (2002).
    [Crossref]
  23. P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, “Optical trapping and manipulation of nano-objects with an apertureless probe,” Phys. Rev. Lett. 88123601 (2002).
    [Crossref] [PubMed]
  24. A. Rahmani and P. C. Chaumet, “Optical trapping near a photonic crystal,” Opt. Express 14, 6353–6358 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-13-6353
    [Crossref] [PubMed]
  25. 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 (2001).
    [Crossref]
  26. P. C. Chaumet, K. Belkebir, and A. Sentenac, “Three-dimensional sub-wavelength optical imaging using the coupled dipole method,” Phys. Rev. B 69, 245,405–7 (2004).
    [Crossref]
  27. K. Belkebir, P. C. Chaumet, and A. Sentenac, “Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography,” J. Opt. Soc. Am. A 23, 586–569 (2006).
    [Crossref]
  28. A. Dubois, J. M. Geffrin, K. Belkebir, and M. Saillard, “Imaging of dielectric cylinders from experimental stepped-frequency data,” Appl. Phys. Lett. 88, 164,104 (2006).
    [Crossref]

2008 (1)

Y. Okada, I. Mann, I. Sano, and S. Mukai, “Acceleration of the iterative solver in the discrete dipole approximation: Application to the orientation variation of irregularly shaped particles,” J. Quant. Spectrosc. Radiat. Transf. 109, 1461–1473 (2008).
[Crossref]

2007 (2)

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]

M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express 15, 17,902–17,911 (2007).
[Crossref]

2006 (6)

K. Muinonen and E. Zubko, “Optimizing the discrete-dipole approximation for sequences of scatterers with identical shapes but differing sizes or refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 100, 288–294 (2006).
[Crossref]

F. Bordas, N. Louvion, S. Callard, P. C. Chaumet, and A. Rahmani, “Coupled dipole method for radiation dynamics in finite photonic crystal structures,” Phys. Rev. E 73, 056,601 (2006).
[Crossref]

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164,705–3 (2006).
[Crossref]

A. Dubois, J. M. Geffrin, K. Belkebir, and M. Saillard, “Imaging of dielectric cylinders from experimental stepped-frequency data,” Appl. Phys. Lett. 88, 164,104 (2006).
[Crossref]

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography,” J. Opt. Soc. Am. A 23, 586–569 (2006).
[Crossref]

A. Rahmani and P. C. Chaumet, “Optical trapping near a photonic crystal,” Opt. Express 14, 6353–6358 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-13-6353
[Crossref] [PubMed]

2004 (4)

P. C. Chaumet, “Comment on “Trapping force, force constant, and potential depths for dielectric spheres in the presence of spherical aberrations,”” Appl. Opt. 43, 1825–1826 (2004).
[Crossref] [PubMed]

P. C. Chaumet, K. Belkebir, and A. Sentenac, “Three-dimensional sub-wavelength optical imaging using the coupled dipole method,” Phys. Rev. B 69, 245,405–7 (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, 036,606–6 (2004).
[Crossref]

2003 (1)

F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 775–824 (2003).
[Crossref]

2002 (4)

A. Rahmani and G. W. Bryant, “Spontaneous emission in microcavity electrodynamics,” Phys. Rev. A. 65033817 (2002).
[Crossref]

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, “Optical trapping and manipulation of nano-objects with an apertureless probe,” Phys. Rev. Lett. 88123601 (2002).
[Crossref] [PubMed]

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]

A. Rahmani, P. C. Chaumet, and G. W. Bryant, “Local-field correction for an interstitial impurity in a crystal,” Opt. Lett. 27, 430–432 (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 (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. 63023819 (2001).
[Crossref]

1997 (1)

A. Rahmani, P. C. Chaumet, F. de Fornel, and C. Girard, “Field propagator of a dressed junction: Fluorescence lifetime calculations in a confined geometry,” Phys. Rev. A 56, 3245–3254 (1997).
[Crossref]

1993 (1)

Z. Q. Peng and A. G. Tijhuis, “Transient scattering by a lossy dielectric cylinder: marching-on-in-frequency approach,” J. Elect. Waves Appl. 7, 739–763 (1993).
[Crossref]

1975 (1)

A. Taflove and M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. 23, 623”630 (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]

1969 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. 14, 302–307 (1969).

Belkebir, K.

A. Dubois, J. M. Geffrin, K. Belkebir, and M. Saillard, “Imaging of dielectric cylinders from experimental stepped-frequency data,” Appl. Phys. Lett. 88, 164,104 (2006).
[Crossref]

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography,” J. Opt. Soc. Am. A 23, 586–569 (2006).
[Crossref]

P. C. Chaumet, K. Belkebir, and A. Sentenac, “Three-dimensional sub-wavelength optical imaging using the coupled dipole method,” Phys. Rev. B 69, 245,405–7 (2004).
[Crossref]

Bordas, F.

F. Bordas, N. Louvion, S. Callard, P. C. Chaumet, and A. Rahmani, “Coupled dipole method for radiation dynamics in finite photonic crystal structures,” Phys. Rev. E 73, 056,601 (2006).
[Crossref]

Brock, R. S.

M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express 15, 17,902–17,911 (2007).
[Crossref]

Brodwin, M. E.

A. Taflove and M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. 23, 623”630 (1975).
[Crossref]

Bryant, G. W.

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. 65033817 (2002).
[Crossref]

A. Rahmani, P. C. Chaumet, and G. W. Bryant, “Local-field correction for an interstitial impurity in a crystal,” Opt. Lett. 27, 430–432 (2002).
[Crossref]

Callard, S.

F. Bordas, N. Louvion, S. Callard, P. C. Chaumet, and A. Rahmani, “Coupled dipole method for radiation dynamics in finite photonic crystal structures,” Phys. Rev. E 73, 056,601 (2006).
[Crossref]

Chaumet, P. C.

F. Bordas, N. Louvion, S. Callard, P. C. Chaumet, and A. Rahmani, “Coupled dipole method for radiation dynamics in finite photonic crystal structures,” Phys. Rev. E 73, 056,601 (2006).
[Crossref]

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography,” J. Opt. Soc. Am. A 23, 586–569 (2006).
[Crossref]

A. Rahmani and P. C. Chaumet, “Optical trapping near a photonic crystal,” Opt. Express 14, 6353–6358 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-13-6353
[Crossref] [PubMed]

P. C. Chaumet, “Comment on “Trapping force, force constant, and potential depths for dielectric spheres in the presence of spherical aberrations,”” Appl. Opt. 43, 1825–1826 (2004).
[Crossref] [PubMed]

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, K. Belkebir, and A. Sentenac, “Three-dimensional sub-wavelength optical imaging using the coupled dipole method,” Phys. Rev. B 69, 245,405–7 (2004).
[Crossref]

P. C. Chaumet, A. Sentenac, and A. Rahmani, “Coupled dipole method for scatterers with large permittivity,” Phys. Rev. E 70, 036,606–6 (2004).
[Crossref]

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, “Optical trapping and manipulation of nano-objects with an apertureless probe,” Phys. Rev. Lett. 88123601 (2002).
[Crossref] [PubMed]

A. Rahmani, P. C. Chaumet, and G. W. Bryant, “Local-field correction for an interstitial impurity in a crystal,” Opt. Lett. 27, 430–432 (2002).
[Crossref]

A. Rahmani, P. C. Chaumet, and F. de Fornel, “Environment-induced modification of spontaneous emission: Single-molecule near-field probe,” Phys. Rev. A. 63023819 (2001).
[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 (2001).
[Crossref]

A. Rahmani, P. C. Chaumet, F. de Fornel, and C. Girard, “Field propagator of a dressed junction: Fluorescence lifetime calculations in a confined geometry,” Phys. Rev. A 56, 3245–3254 (1997).
[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. 63023819 (2001).
[Crossref]

A. Rahmani, P. C. Chaumet, F. de Fornel, and C. Girard, “Field propagator of a dressed junction: Fluorescence lifetime calculations in a confined geometry,” Phys. Rev. A 56, 3245–3254 (1997).
[Crossref]

Dubois, A.

A. Dubois, J. M. Geffrin, K. Belkebir, and M. Saillard, “Imaging of dielectric cylinders from experimental stepped-frequency data,” Appl. Phys. Lett. 88, 164,104 (2006).
[Crossref]

Etchegoin, P. G.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164,705–3 (2006).
[Crossref]

Flatau, P. J.

Geffrin, J. M.

A. Dubois, J. M. Geffrin, K. Belkebir, and M. Saillard, “Imaging of dielectric cylinders from experimental stepped-frequency data,” Appl. Phys. Lett. 88, 164,104 (2006).
[Crossref]

Girard, C.

A. Rahmani, P. C. Chaumet, F. de Fornel, and C. Girard, “Field propagator of a dressed junction: Fluorescence lifetime calculations in a confined geometry,” Phys. Rev. A 56, 3245–3254 (1997).
[Crossref]

Goodman, J. J.

Hagness, S. C.

A. Taflove and S. C. Hagness, “Computational Electrodynamics: The Finite-Difference Time-Domain Method”, 3rd edition, (Artech House Publishers, 2005).

Hoekstra, A. G.

M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express 15, 17,902–17,911 (2007).
[Crossref]

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]

Jackson, J. D.

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

Kahnert, F. M.

F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 775–824 (2003).
[Crossref]

Le Ru, E. C.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164,705–3 (2006).
[Crossref]

Louvion, N.

F. Bordas, N. Louvion, S. Callard, P. C. Chaumet, and A. Rahmani, “Coupled dipole method for radiation dynamics in finite photonic crystal structures,” Phys. Rev. E 73, 056,601 (2006).
[Crossref]

Lu, J. Q.

M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express 15, 17,902–17,911 (2007).
[Crossref]

Mann, I.

Y. Okada, I. Mann, I. Sano, and S. Mukai, “Acceleration of the iterative solver in the discrete dipole approximation: Application to the orientation variation of irregularly shaped particles,” J. Quant. Spectrosc. Radiat. Transf. 109, 1461–1473 (2008).
[Crossref]

Meyer, M.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164,705–3 (2006).
[Crossref]

Muinonen, K.

K. Muinonen and E. Zubko, “Optimizing the discrete-dipole approximation for sequences of scatterers with identical shapes but differing sizes or refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 100, 288–294 (2006).
[Crossref]

Mukai, S.

Y. Okada, I. Mann, I. Sano, and S. Mukai, “Acceleration of the iterative solver in the discrete dipole approximation: Application to the orientation variation of irregularly shaped particles,” J. Quant. Spectrosc. Radiat. Transf. 109, 1461–1473 (2008).
[Crossref]

Nieto-Vesperinas, M.

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, “Optical trapping and manipulation of nano-objects with an apertureless probe,” Phys. Rev. Lett. 88123601 (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 (2001).
[Crossref]

Okada, Y.

Y. Okada, I. Mann, I. Sano, and S. Mukai, “Acceleration of the iterative solver in the discrete dipole approximation: Application to the orientation variation of irregularly shaped particles,” J. Quant. Spectrosc. Radiat. Transf. 109, 1461–1473 (2008).
[Crossref]

Peng, Z. Q.

Z. Q. Peng and A. G. Tijhuis, “Transient scattering by a lossy dielectric cylinder: marching-on-in-frequency approach,” J. Elect. Waves Appl. 7, 739–763 (1993).
[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]

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.

F. Bordas, N. Louvion, S. Callard, P. C. Chaumet, and A. Rahmani, “Coupled dipole method for radiation dynamics in finite photonic crystal structures,” Phys. Rev. E 73, 056,601 (2006).
[Crossref]

A. Rahmani and P. C. Chaumet, “Optical trapping near a photonic crystal,” Opt. Express 14, 6353–6358 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-13-6353
[Crossref] [PubMed]

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, 036,606–6 (2004).
[Crossref]

A. Rahmani, P. C. Chaumet, and G. W. Bryant, “Local-field correction for an interstitial impurity in a crystal,” Opt. Lett. 27, 430–432 (2002).
[Crossref]

A. Rahmani and G. W. Bryant, “Spontaneous emission in microcavity electrodynamics,” Phys. Rev. A. 65033817 (2002).
[Crossref]

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, “Optical trapping and manipulation of nano-objects with an apertureless probe,” Phys. Rev. Lett. 88123601 (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. 63023819 (2001).
[Crossref]

A. Rahmani, P. C. Chaumet, F. de Fornel, and C. Girard, “Field propagator of a dressed junction: Fluorescence lifetime calculations in a confined geometry,” Phys. Rev. A 56, 3245–3254 (1997).
[Crossref]

Saillard, M.

A. Dubois, J. M. Geffrin, K. Belkebir, and M. Saillard, “Imaging of dielectric cylinders from experimental stepped-frequency data,” Appl. Phys. Lett. 88, 164,104 (2006).
[Crossref]

Sano, I.

Y. Okada, I. Mann, I. Sano, and S. Mukai, “Acceleration of the iterative solver in the discrete dipole approximation: Application to the orientation variation of irregularly shaped particles,” J. Quant. Spectrosc. Radiat. Transf. 109, 1461–1473 (2008).
[Crossref]

Sentenac, A.

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography,” J. Opt. Soc. Am. A 23, 586–569 (2006).
[Crossref]

P. C. Chaumet, K. Belkebir, and A. Sentenac, “Three-dimensional sub-wavelength optical imaging using the coupled dipole method,” Phys. Rev. B 69, 245,405–7 (2004).
[Crossref]

P. C. Chaumet, A. Sentenac, and A. Rahmani, “Coupled dipole method for scatterers with large permittivity,” Phys. Rev. E 70, 036,606–6 (2004).
[Crossref]

Taflove, A.

A. Taflove and M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. 23, 623”630 (1975).
[Crossref]

A. Taflove and S. C. Hagness, “Computational Electrodynamics: The Finite-Difference Time-Domain Method”, 3rd edition, (Artech House Publishers, 2005).

Tijhuis, A. G.

Z. Q. Peng and A. G. Tijhuis, “Transient scattering by a lossy dielectric cylinder: marching-on-in-frequency approach,” J. Elect. Waves Appl. 7, 739–763 (1993).
[Crossref]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. 14, 302–307 (1969).

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]

M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express 15, 17,902–17,911 (2007).
[Crossref]

Zubko, E.

K. Muinonen and E. Zubko, “Optimizing the discrete-dipole approximation for sequences of scatterers with identical shapes but differing sizes or refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 100, 288–294 (2006).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. Dubois, J. M. Geffrin, K. Belkebir, and M. Saillard, “Imaging of dielectric cylinders from experimental stepped-frequency data,” Appl. Phys. Lett. 88, 164,104 (2006).
[Crossref]

Astrophys. J. (2)

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

IEEE Trans. Antennas Propagat. (1)

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IEEE Trans. Microwave Theory Tech. (1)

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[Crossref]

J. Chem. Phys. (1)

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164,705–3 (2006).
[Crossref]

J. Elect. Waves Appl. (1)

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[Crossref]

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

J. Quant. Spectrosc. Radiat. Transf. (4)

K. Muinonen and E. Zubko, “Optimizing the discrete-dipole approximation for sequences of scatterers with identical shapes but differing sizes or refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 100, 288–294 (2006).
[Crossref]

Y. Okada, I. Mann, I. Sano, and S. Mukai, “Acceleration of the iterative solver in the discrete dipole approximation: Application to the orientation variation of irregularly shaped particles,” J. Quant. Spectrosc. Radiat. Transf. 109, 1461–1473 (2008).
[Crossref]

F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 775–824 (2003).
[Crossref]

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[Crossref]

Opt. Express (2)

M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express 15, 17,902–17,911 (2007).
[Crossref]

A. Rahmani and P. C. Chaumet, “Optical trapping near a photonic crystal,” Opt. Express 14, 6353–6358 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-13-6353
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (1)

A. Rahmani, P. C. Chaumet, F. de Fornel, and C. Girard, “Field propagator of a dressed junction: Fluorescence lifetime calculations in a confined geometry,” Phys. Rev. A 56, 3245–3254 (1997).
[Crossref]

Phys. Rev. A. (2)

A. Rahmani, P. C. Chaumet, and F. de Fornel, “Environment-induced modification of spontaneous emission: Single-molecule near-field probe,” Phys. Rev. A. 63023819 (2001).
[Crossref]

A. Rahmani and G. W. Bryant, “Spontaneous emission in microcavity electrodynamics,” Phys. Rev. A. 65033817 (2002).
[Crossref]

Phys. Rev. B (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 (2001).
[Crossref]

P. C. Chaumet, K. Belkebir, and A. Sentenac, “Three-dimensional sub-wavelength optical imaging using the coupled dipole method,” Phys. Rev. B 69, 245,405–7 (2004).
[Crossref]

Phys. Rev. E (2)

F. Bordas, N. Louvion, S. Callard, P. C. Chaumet, and A. Rahmani, “Coupled dipole method for radiation dynamics in finite photonic crystal structures,” Phys. Rev. E 73, 056,601 (2006).
[Crossref]

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[Crossref]

Phys. Rev. Lett. (1)

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, “Optical trapping and manipulation of nano-objects with an apertureless probe,” Phys. Rev. Lett. 88123601 (2002).
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Other (3)

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

A. Taflove and S. C. Hagness, “Computational Electrodynamics: The Finite-Difference Time-Domain Method”, 3rd edition, (Artech House Publishers, 2005).

RSoft Inc., RSoft Fullwave FDTD code, http://www.rsoftdesign.com.

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Figures (6)

Fig. 1.
Fig. 1.

(a) Spectrum of the incident field. (b) Component x of the incident field versus time.

Fig. 2.
Fig. 2.

Component x of the field versus time when the point of observation is located at the center of the sphere. In bold line the CDM is used and in dashed line the FDTD is used.

Fig. 3.
Fig. 3.

(a) Number of total iterations required to solve the scattering problem for all the frequencies versus K. The computation is done for a sphere with a radius a=120 mm and f 0=2 GHz with ε r =2.25+2sin2ρ 2/a 2). The line with squares pertains to ε i =0.5i whereas the line with circles pertains to ε i =0. (b) and (c) Number of iterations needed to solve our linear system with the conjugate gradient method at each frequency for K=0 (bold line) and K=5 (dashed line). (b) ε i =0. (c) ε i =0.5i.

Fig. 4.
Fig. 4.

Component x of the electric field versus time. (a) The point of observation is located at the top of the sphere. (b) The point of observation is located at the center of the sphere.

Fig. 5.
Fig. 5.

Spectrum of the pulse used on a gold sphere of radius a=60 nm. The spectrum contains the visible range and is centered at f 0=0.57 PHz (λ0=525 nm).

Fig. 6.
Fig. 6.

Solid line: the incident field. Dashed line: field at the top of the sphere. Dashed line with circles: field at the bottom of the sphere.

Equations (9)

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E ( r i , ω ) = E 0 ( r i , ω ) + j = 1 , j i N T ( r i , r j , ω ) α ( r j , ω ) E ( r j , ω ) ,
α ( r j , ω ) = α 0 ( r j , ω ) [ I ( 2 3 ) ik 0 3 α 0 ( r j , ω ) ] 1 ,
α 0 ( r j , ω ) = 3 d 3 4 π ( ε ( r j , ω ) I ) ( ε ( r j , ω ) + 2 I ) 1 .
E ( r , ω ) = i = 1 N T ( r , r i , ω ) α ( r i , ω ) E ( r i , ω ) .
( t ) = exp [ 16 ( t τ τ ) 2 ] cos ( 2 π f 0 t ) .
[ D ( ω m ) A ( ω m ) ] P ( ω m ) = E 0 ( ω m ) ,
p guess ( ω m ) = k = 1 K < m a k p solution ( ω m k ) .
C ( p guess ( ω m ) ) = [ D ( ω m ) A ( ω m ) ] p guess ( ω m ) E 0 ( ω m ) 2 .
ε ( ω ) = ε ω p 2 ω + i Γ ω + G 1 ( ω ) + G 2 ( ω )

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