Abstract

We develop a general computational approach, based on the discrete dipole approximation, for the study of radiation dynamics near or inside an object with arbitrary linear dielectric permittivity, and magnetic permeability tensors. Our method can account for dispersion and losses and provides insight on the role of local-field corrections in discrete magnetodielectric structures. We illustrate our method in the case of a source inside a magneto-dielectric, isotropic sphere for which the spontaneous emission rate of a source can be computed analytically. We show that our approach is in excellent agreement with the exact result, providing an approach capable of handling both the electric and magnetic response of advanced metamaterials.

© 2010 Optical Society of America

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  1. E. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 681 (1946).
  2. K. Drexhage, "Influence of a dielectric interface on fluorescence decay time," J. Lumin. 1, 693 (1970).
    [CrossRef]
  3. S. Haroche, "Cavity quantum electrodynamics," in Fundamental Systems in Quantum Optics, J. Dalibard, J. M. Raimond, and J. Zinn-Justin, eds. (North-Holland, Amsterdam, 1992), pp. 767-940.
  4. N. Litchinitser and V. Shalaev, "Photonic metamaterials," Laser Phys. Lett. 5, 411-420 (2008).
    [CrossRef]
  5. E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
    [CrossRef]
  6. B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
    [CrossRef]
  7. B. T. Draine and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
    [CrossRef]
  8. A. Rahmani, P. Chaumet, and G. Bryant, "Coupled dipole method with an exact long-wavelength limit and improved accuracy at finite frequencies," Opt. Lett. 27, 2118-2120 (2002).
    [CrossRef]
  9. 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]
  10. M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, "The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength," J. Quant. Spect. Rad. Transf. 106, 546-557 (2007).
    [CrossRef]
  11. M. A. Yurkin and A. G. Hoekstra, "The discrete dipole approximation: An overview and recent developments," J. Quant. Spect. Rad. Transf. 106, 558-589 (2007).
    [CrossRef]
  12. P. C. Chaumet, A. Rahmani, and G. W. Bryant, "Generalization of the coupled dipole method to periodic structure," Phys. Rev. B 67, 165404 (2003).
    [CrossRef]
  13. B. T. Draine and P. J. Flatau, "The discrete dipole approximation for periodic targets: Theory and tests," J. Opt. Soc. Am. A 25 (2008).
    [CrossRef]
  14. B. T. Draine and J. C. Weingartner, "Radiative Torques on Interstellar Grains: I. Superthermal Spinup," Astrophys. J. 470, 551-565 (1996).
    [CrossRef]
  15. A. G. Hoekstra, M. Frijlink, L. B. F. M. Waters, and P. M. A. Sloot, "Radiation forces in the discrete-dipole approximation," J. Opt. Soc. Am. A 18, 1944-1953 (2001).
    [CrossRef]
  16. M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, "Near-field photonic forces," Phil. Trans. Roy. Soc. Lond. A 362, 719-737 (2004).
    [CrossRef]
  17. 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 (2002).
    [CrossRef] [PubMed]
  18. A. Rahmani and P. C. Chaumet, "Optical Trapping near a Photonic Crystal," Opt. Express 14, 6353-6358 (2006). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-13-6353
    [CrossRef] [PubMed]
  19. 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 (2001).
    [CrossRef]
  20. A. Rahmani and G. W. Bryant, "Spontaneous emission in microcavity electrodynamics," Phys. Rev. A 65, 033817 (2002).
    [CrossRef]
  21. 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, 056601 (2006).
    [CrossRef]
  22. Q5. A. Lakhtakia, "Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetic fields," Int. J. Mod. Phys. C 3, 583-603 (1992).
    [CrossRef]
  23. 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), http://www.opticsinfobase.org/oe/ abstract.cfm?URI=oe-16-3-2068
    [CrossRef] [PubMed]
  24. P. C. Chaumet and A. Rahmani, "Coupled-dipole method for magnetic and negative refraction materials," J. Quant. Spect. Rad. Transf. 110, 22-29 (2009).
  25. P. C. Chaumet and A. Rahmani, "Electromagnetic force and torque on magnetic and negative-index scatterers," Opt. Express 17, 2224-2234 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI= oe-17-4-2224
    [CrossRef] [PubMed]
  26. G. S. Agarwal, "Quantum electrodynamics in the presence of dielectrics and conductors. i. electromagnetic-field response functions and black-body fluctuations in finite geometries," Phys. Rev. A 11, 230-242 (1975).
    [CrossRef]
  27. P. C. Chaumet and A. Rahmani, "Efficient iterative solution of the discrete dipole approximation for magnetodielectric scatterers," Opt. Lett 34, 1-3 (2009).
    [CrossRef]
  28. H. Chew, "Radiation and lifetimes of atoms inside dielectric particles," Phys. Rev. A 38, 3410-3416 (1988).
    [CrossRef] [PubMed]
  29. 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]
  30. H. T. Dung, S. Y. Buhmann, L. Kn¨oll, D.-G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
    [CrossRef]

2009 (2)

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 A. Rahmani, "Efficient iterative solution of the discrete dipole approximation for magnetodielectric scatterers," Opt. Lett 34, 1-3 (2009).
[CrossRef]

2008 (1)

N. Litchinitser and V. Shalaev, "Photonic metamaterials," Laser Phys. Lett. 5, 411-420 (2008).
[CrossRef]

2007 (2)

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, "The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength," J. Quant. Spect. Rad. Transf. 106, 546-557 (2007).
[CrossRef]

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

2006 (2)

A. Rahmani and P. C. Chaumet, "Optical Trapping near a Photonic Crystal," Opt. Express 14, 6353-6358 (2006). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-13-6353
[CrossRef] [PubMed]

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, 056601 (2006).
[CrossRef]

2004 (2)

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

2003 (2)

P. C. Chaumet, A. Rahmani, and G. W. Bryant, "Generalization of the coupled dipole method to periodic structure," Phys. Rev. B 67, 165404 (2003).
[CrossRef]

H. T. Dung, S. Y. Buhmann, L. Kn¨oll, D.-G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
[CrossRef]

2002 (4)

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 65, 033817 (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 (2002).
[CrossRef] [PubMed]

A. Rahmani, P. Chaumet, and G. Bryant, "Coupled dipole method with an exact long-wavelength limit and improved accuracy at finite frequencies," Opt. Lett. 27, 2118-2120 (2002).
[CrossRef]

2001 (2)

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 (2001).
[CrossRef]

A. G. Hoekstra, M. Frijlink, L. B. F. M. Waters, and P. M. A. Sloot, "Radiation forces in the discrete-dipole approximation," J. Opt. Soc. Am. A 18, 1944-1953 (2001).
[CrossRef]

1996 (1)

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

1994 (1)

1992 (1)

Q5. A. Lakhtakia, "Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetic fields," Int. J. Mod. Phys. C 3, 583-603 (1992).
[CrossRef]

1988 (2)

H. Chew, "Radiation and lifetimes of atoms inside dielectric particles," Phys. Rev. A 38, 3410-3416 (1988).
[CrossRef] [PubMed]

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

1970 (1)

K. Drexhage, "Influence of a dielectric interface on fluorescence decay time," J. Lumin. 1, 693 (1970).
[CrossRef]

1946 (1)

E. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 681 (1946).

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 geometries," Phys. Rev. A 11, 230-242 (1975).
[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, 056601 (2006).
[CrossRef]

Bryant, G.

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]

P. C. Chaumet, A. Rahmani, and G. W. Bryant, "Generalization of the coupled dipole method to periodic structure," Phys. Rev. B 67, 165404 (2003).
[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]

Bryant, G.W.

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

Buhmann, S. Y.

H. T. Dung, S. Y. Buhmann, L. Kn¨oll, D.-G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
[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, 056601 (2006).
[CrossRef]

Chaumet, P.

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 A. Rahmani, "Efficient iterative solution of the discrete dipole approximation for magnetodielectric scatterers," Opt. Lett 34, 1-3 (2009).
[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, 056601 (2006).
[CrossRef]

A. Rahmani and P. C. Chaumet, "Optical Trapping near a Photonic Crystal," Opt. Express 14, 6353-6358 (2006). http://www.opticsinfobase.org/oe/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]

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 G. W. Bryant, "Generalization of the coupled dipole method to periodic structure," Phys. Rev. B 67, 165404 (2003).
[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 (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 63, 023819 (2001).
[CrossRef]

Chew, H.

H. Chew, "Radiation and lifetimes of atoms inside dielectric particles," Phys. Rev. A 38, 3410-3416 (1988).
[CrossRef] [PubMed]

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 (2001).
[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]

Drexhage, K.

K. Drexhage, "Influence of a dielectric interface on fluorescence decay time," J. Lumin. 1, 693 (1970).
[CrossRef]

Dung, H. T.

H. T. Dung, S. Y. Buhmann, L. Kn¨oll, D.-G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
[CrossRef]

Flatau, P. J.

Frijlink, M.

Hoekstra, A. G.

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

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, "The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength," J. Quant. Spect. Rad. Transf. 106, 546-557 (2007).
[CrossRef]

Hoekstra, A.G.

Kastel, J.

H. T. Dung, S. Y. Buhmann, L. Kn¨oll, D.-G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
[CrossRef]

Kn¨oll, L.

H. T. Dung, S. Y. Buhmann, L. Kn¨oll, D.-G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
[CrossRef]

Lakhtakia, A.

Q5. A. Lakhtakia, "Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetic fields," Int. J. Mod. Phys. C 3, 583-603 (1992).
[CrossRef]

Litchinitser, N.

N. Litchinitser and V. Shalaev, "Photonic metamaterials," Laser Phys. Lett. 5, 411-420 (2008).
[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, 056601 (2006).
[CrossRef]

Maltsev, V. P.

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, "The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength," J. Quant. Spect. Rad. Transf. 106, 546-557 (2007).
[CrossRef]

Nieto-Vesperinas, M.

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 (2002).
[CrossRef] [PubMed]

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.

E. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 681 (1946).

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, "Efficient iterative solution of the discrete dipole approximation for magnetodielectric scatterers," Opt. Lett 34, 1-3 (2009).
[CrossRef]

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

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, 056601 (2006).
[CrossRef]

A. Rahmani and P. C. Chaumet, "Optical Trapping near a Photonic Crystal," Opt. Express 14, 6353-6358 (2006). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-13-6353
[CrossRef] [PubMed]

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, "Near-field photonic forces," Phil. Trans. Roy. Soc. Lond. A 362, 719-737 (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. Rahmani, and G. W. Bryant, "Generalization of the coupled dipole method to periodic structure," Phys. Rev. B 67, 165404 (2003).
[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 (2002).
[CrossRef] [PubMed]

A. Rahmani, P. Chaumet, and G. Bryant, "Coupled dipole method with an exact long-wavelength limit and improved accuracy at finite frequencies," Opt. Lett. 27, 2118-2120 (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]

A. Rahmani and G. W. Bryant, "Spontaneous emission in microcavity electrodynamics," Phys. Rev. A 65, 033817 (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 63, 023819 (2001).
[CrossRef]

Scheel, S.

H. T. Dung, S. Y. Buhmann, L. Kn¨oll, D.-G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
[CrossRef]

Shalaev, V.

N. Litchinitser and V. Shalaev, "Photonic metamaterials," Laser Phys. Lett. 5, 411-420 (2008).
[CrossRef]

Sloot, P. M. A.

Waters, L.B.F.M.

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]

Welsch, D.-G.

H. T. Dung, S. Y. Buhmann, L. Kn¨oll, D.-G. Welsch, S. Scheel, and J. Kastel, "Electromagnetic-field quantization and spontaneous decay in left-handed media," Phys. Rev. A 68, 043816 (2003).
[CrossRef]

Yurkin, M. A.

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

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, "The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength," J. Quant. Spect. Rad. Transf. 106, 546-557 (2007).
[CrossRef]

Astrophys. J. (4)

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]

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]

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

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

Q5. A. Lakhtakia, "Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetic fields," Int. J. Mod. Phys. C 3, 583-603 (1992).
[CrossRef]

J. Lumin. (1)

K. Drexhage, "Influence of a dielectric interface on fluorescence decay time," J. Lumin. 1, 693 (1970).
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Opt. Express (1)

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[CrossRef]

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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. (1)

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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 (2002).
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P. C. Chaumet and A. Rahmani, "Electromagnetic force and torque on magnetic and negative-index scatterers," Opt. Express 17, 2224-2234 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI= oe-17-4-2224
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[CrossRef] [PubMed]

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Figures (1)

Fig. 1.
Fig. 1.

Normalized emission rate as a function of the size parameter ka for an electric dipole at the center of a spherical cavity with radius a. (a) Solid lines: analytical calculation for a continuous, homogeneous cavity; open symbols: DDA calculation for a continuous, homogeneous cavity. The corresponding material constants (ε, μ) are given in the inset. (b) DDA calculation for a discrete, homogeneous cavity. The corresponding material constants (ε, μ) are given in the inset. The source is located at the reduced position (½,½,½) within a discretization cell.

Equations (7)

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Γ cav Γ = 1 + 3 2 k 3 p · Im [ 𝓖 ̿ cav ( r 0 , r 0 ; ω ) ] · p ,
α ̿ i e = [ I ̿ 2 3 i k 3 A ̿ i ] 1 A ̿ i , α ̿ i m = [ I ̿ 2 3 i k 3 B ̿ i ] 1 B ̿ i ,
A ̿ i = 3 d 3 4 π [ ε ̿ ( r i ) I ̿ ] [ ε ̿ ( r i ) + 2 I ̿ ] 1 , B ̿ i = 3 d 3 4 π [ μ ̿ ( r i ) I ̿ ] [ μ ̿ ( r i ) + 2 I ̿ ] 1 ,
𝓖 ̿ ee ( r i , r 0 ) = 𝓖 ̿ 0 ee ( r i , r 0 ) + j i [ 𝓖 ̿ 0 ee ( r i , r j ) α ̿ j e 𝓖 ̿ ee ( r j , r 0 ) + 𝓖 ̿ 0 em ( r i , r j ) α ̿ j m 𝓖 ̿ me ( r j , r 0 ) ]
𝓖 ̿ me ( r i , r 0 ) = 𝓖 ̿ 0 me ( r i , r 0 ) + j i [ 𝓖 ̿ 0 me ( r i , r j ) α ̿ j e 𝓖 ̿ ee ( r j , r 0 ) + 𝓖 ̿ 0 mm ( r i , r j ) α ̿ j m 𝓖 ̿ me ( r j , r 0 ) ]
𝓖 ̿ ee ( r 0 , r 0 ) = 𝓖 ̿ 0 ee ( r 0 , r 0 ) + j [ 𝓖 ̿ 0 ee ( r 0 , r j ) α ̿ j e 𝓖 ̿ ee ( r j , r 0 ) + 𝓖 ̿ 0 em ( r 0 , r j ) α ̿ j m 𝓖 ̿ me ( r j , r 0 ) ]
= 𝓖 ̿ 0 ee ( r 0 , r 0 ) + 𝓖 ̿ cav ee ( r 0 , r 0 ) .

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