Abstract

Magneto-optical spectra (Faraday effect) for nanometer-scale particles and collections of particles are calculated using a modification of the discrete dipole approximation (DDA). The approximation is used as a finite-element method for non-spherical particles whose dimensions are on the order of or smaller than the incident light wavelength, λ. Also, we use the approximation to calculate scattering from arrangements of spherical nanoparticles with diameters ≪λ. We propose that for scattering from subwavelength magnetic particles, the specific Faraday rotation should be defined as the difference in optical extinction for left- and right-circularly polarized light. We apply the model to calculations of Faraday rotation from magnetite nanowires as well as a binary (two-component) nanoparticle arrangement. Enhancements in Faraday rotation are predicted for composites containing both noble metal and ferrite nanoparticles.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. Felidj, J. Aubard, G. Levi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface enhanced Raman scattering," Phys. Rev. B. 65, 075419 (2002).
    [CrossRef]
  2. W.-H. Yang, G. C. Schatz, and R. P. Van Duyne, "Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitrary shapes," J. Chem. Phys. 103, 869 (1995).
    [CrossRef]
  3. F. J. Garcia-Vidal and L. Martin-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured materials," Phys. Rev. B. 66, 155412 (2002).
    [CrossRef]
  4. M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B. 62, R16356 (2000).
    [CrossRef]
  5. S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, "Plasmonics - A route to nanoscale optical devices," Adv. Mater. 13, 1501 (2001).
    [CrossRef]
  6. S. A. Maier, P. G. Kik, M. L. Brongersma, H. A. Atwater, S. Meltzer, A. A. G. Requicha, and B. K. Koel, "Observation of coupled plasmon-polariton modes of plasmon waveguides for electromagnetic energy transport below the diffraction limit," in Mat. Res. Soc. Symp. Proc., vol. 722, R. B. Wehrspohn, S. Noda, C.Soukoulis, and R. Marz, Eds. (Warrendale, PA, MRS, 2002), p. L6.2.
  7. V. M. Shalaev, V. A. Podolskiy, and A. K. Sarychev, "Plasmonic nanophotonics: Manipulating light and sensing molecules," in Proceedings of SPIE vol. 4806, Complex Mediums III: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, G. Dewar, and M. W. McCall, Eds. (Bellingham, WA, SPIE, 2002), p. 32.
  8. L. L. Zhao, K. L. Kelly, and G. C. Schatz, "The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width," J. Phys. Chem. B 107, 7343 (2003).
    [CrossRef]
  9. A. A. Lazarides and G. C. Schatz, "DNA-linked metal nanosphere materials: Structural basis for the optical properties," J. Phys. Chem. B 104, 460 (2000).
    [CrossRef]
  10. V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735 (2003).
    [CrossRef] [PubMed]
  11. V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, S32 (2005).
    [CrossRef]
  12. D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, "Magneto-optical spectra of closely-spaced magnetite nanoparticles," J. Appl. Phys. 97, 10M504 (2005).
    [CrossRef]
  13. J. D. Jackson, Classical Electrodynamics, 3rd ed. (New York, John Wiley and Sons, Inc., 1999).
  14. B. T. Draine, "The discrete dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848 (1988).
    [CrossRef]
  15. A. H. Sihvola, "Dielectric polarizability of a sphere with arbitrary anisotropy," Opt. Lett. 19, 430 (1994).
    [CrossRef] [PubMed]
  16. K. Hinsen, A. Bratz, and B. U. Felderhof, "Anisotropic dielectric tensor and the Hall effect in a suspension of spheres," Phys. Rev. B. 23, 14995 (1992).
    [CrossRef]
  17. B. T. Draine and J. Goodman, "Beyond Clausius-Mossotti: Wave propagation on a polarizable point lattice and the discrete dipole approximation," Astrophys. J. 405, 685 (1993).
    [CrossRef]
  18. 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 (2004).
    [CrossRef]
  19. P. S. Pershan, "Magneto-optical effects," J. Appl. Phys. 38, 1482 (1967).
    [CrossRef]
  20. A. K. Zvezdin and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials (London, Institute of Physics Publishing, 1997).
    [CrossRef]
  21. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (New York, John Wiley and Sons, 1983).
  22. Wolfram Research, Inc., Mathematica, Version 5.1, Champaign, IL (2004).
  23. The MathWorks Inc, MATLAB version 6.5.1, Natick, Massachusetts (2003).
  24. A. Schlegel, S. F. Alvarado, and P. Wachter, "Optical properties of magnetite (Fe3O4)," J. Phys. C: Solid State Phys. 12, 1157 (1979).
    [CrossRef]
  25. X. Zhang, J. Schoenes, and P. Wachter, "Kerr-effect and dielectric tensor elements of magnetite (Fe3O4) between 0.5 and 4.3 eV," Solid State Commun. 39, 189 (1981).
    [CrossRef]
  26. M. R. Pufall, A. Berger, and S. Schultz, "Measurement of the scattered light magneto-optical Kerr effect from plasmon-resonant Ag particles near a magnetic film," J. Appl. Phys. 81, 5689 (1997).
    [CrossRef]
  27. Y. Li, Q. Zhang, A. V. Nurmikko, and S. Sun, "Enhanced magneto-optical response in dumbbell-like Ag-CoFe2O4 nanoparticle pairs," Nano Lett. 5, 1689 (2005).
    [CrossRef] [PubMed]
  28. G. Shemer and G. Markovich, "Enhancement of magneto-optical effects in magnetite near gold surfaces," J. Phys. Chem. B 106, 9195 (2002).
    [CrossRef]
  29. V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, and J. Peretti, "Magneto-optical effects enhanced by surface plasmons in metallic multilayer films," Phys. Rev. Lett. 73, 3584 (1994).
    [CrossRef] [PubMed]
  30. T. Katayama, Y. Suzuki, H. Awano, Y. Nishihara, and N. Koshizuka, "Enhancement of the magneto-optical Kerr rotation in Fe/Cu bilayered films," Phys. Rev. Lett. 60, 1426 (1988).
    [CrossRef] [PubMed]
  31. C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, "Surface-enhanced magneto-optics in metallic multilayer films," Phys. Rev. B. 64, 235422 (2001).
    [CrossRef]
  32. V. A. Kosobukin, "Magneto-optics via the near field," Surf. Science 406, 32 (1998).
    [CrossRef]
  33. W. F. J. Fontijn, P. J. van der Zaag, and L. F. Feiner, "A consistent interpretation of the magneto-optical spectra of spinel-type ferrites," J. Appl. Phys. 85, 5100 (1999).
    [CrossRef]
  34. W. D. Martens, W. L. Peeters, and H. M. van NoortM. Erman, "Optical, magneto-optical and Mossbauer spectroscopy on Co3+ substituted cobalt ferrite," J. Phys. Chem. Solids 46, 411 (1985).
    [CrossRef]
  35. P. B. Johnson and R. W. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  36. E. V. Shevchenko, D. V. Talapin, C. B. Murray, and S. O'Brien, "Structural characterization of self-assembled multifunctional binary nanoparticle superlattices," J. Am. Chem. Soc. 128, 3620 (2006).
    [CrossRef] [PubMed]

2006 (1)

E. V. Shevchenko, D. V. Talapin, C. B. Murray, and S. O'Brien, "Structural characterization of self-assembled multifunctional binary nanoparticle superlattices," J. Am. Chem. Soc. 128, 3620 (2006).
[CrossRef] [PubMed]

2005 (3)

Y. Li, Q. Zhang, A. V. Nurmikko, and S. Sun, "Enhanced magneto-optical response in dumbbell-like Ag-CoFe2O4 nanoparticle pairs," Nano Lett. 5, 1689 (2005).
[CrossRef] [PubMed]

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, S32 (2005).
[CrossRef]

D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, "Magneto-optical spectra of closely-spaced magnetite nanoparticles," J. Appl. Phys. 97, 10M504 (2005).
[CrossRef]

2004 (1)

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 (2004).
[CrossRef]

2003 (2)

L. L. Zhao, K. L. Kelly, and G. C. Schatz, "The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width," J. Phys. Chem. B 107, 7343 (2003).
[CrossRef]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735 (2003).
[CrossRef] [PubMed]

2002 (3)

N. Felidj, J. Aubard, G. Levi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface enhanced Raman scattering," Phys. Rev. B. 65, 075419 (2002).
[CrossRef]

F. J. Garcia-Vidal and L. Martin-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured materials," Phys. Rev. B. 66, 155412 (2002).
[CrossRef]

G. Shemer and G. Markovich, "Enhancement of magneto-optical effects in magnetite near gold surfaces," J. Phys. Chem. B 106, 9195 (2002).
[CrossRef]

2001 (2)

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, "Surface-enhanced magneto-optics in metallic multilayer films," Phys. Rev. B. 64, 235422 (2001).
[CrossRef]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, "Plasmonics - A route to nanoscale optical devices," Adv. Mater. 13, 1501 (2001).
[CrossRef]

2000 (2)

A. A. Lazarides and G. C. Schatz, "DNA-linked metal nanosphere materials: Structural basis for the optical properties," J. Phys. Chem. B 104, 460 (2000).
[CrossRef]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B. 62, R16356 (2000).
[CrossRef]

1999 (1)

W. F. J. Fontijn, P. J. van der Zaag, and L. F. Feiner, "A consistent interpretation of the magneto-optical spectra of spinel-type ferrites," J. Appl. Phys. 85, 5100 (1999).
[CrossRef]

1998 (1)

V. A. Kosobukin, "Magneto-optics via the near field," Surf. Science 406, 32 (1998).
[CrossRef]

1997 (1)

M. R. Pufall, A. Berger, and S. Schultz, "Measurement of the scattered light magneto-optical Kerr effect from plasmon-resonant Ag particles near a magnetic film," J. Appl. Phys. 81, 5689 (1997).
[CrossRef]

1995 (1)

W.-H. Yang, G. C. Schatz, and R. P. Van Duyne, "Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitrary shapes," J. Chem. Phys. 103, 869 (1995).
[CrossRef]

1994 (2)

A. H. Sihvola, "Dielectric polarizability of a sphere with arbitrary anisotropy," Opt. Lett. 19, 430 (1994).
[CrossRef] [PubMed]

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, and J. Peretti, "Magneto-optical effects enhanced by surface plasmons in metallic multilayer films," Phys. Rev. Lett. 73, 3584 (1994).
[CrossRef] [PubMed]

1993 (1)

B. T. Draine and J. Goodman, "Beyond Clausius-Mossotti: Wave propagation on a polarizable point lattice and the discrete dipole approximation," Astrophys. J. 405, 685 (1993).
[CrossRef]

1992 (1)

K. Hinsen, A. Bratz, and B. U. Felderhof, "Anisotropic dielectric tensor and the Hall effect in a suspension of spheres," Phys. Rev. B. 23, 14995 (1992).
[CrossRef]

1988 (2)

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

T. Katayama, Y. Suzuki, H. Awano, Y. Nishihara, and N. Koshizuka, "Enhancement of the magneto-optical Kerr rotation in Fe/Cu bilayered films," Phys. Rev. Lett. 60, 1426 (1988).
[CrossRef] [PubMed]

1985 (1)

W. D. Martens, W. L. Peeters, and H. M. van NoortM. Erman, "Optical, magneto-optical and Mossbauer spectroscopy on Co3+ substituted cobalt ferrite," J. Phys. Chem. Solids 46, 411 (1985).
[CrossRef]

1981 (1)

X. Zhang, J. Schoenes, and P. Wachter, "Kerr-effect and dielectric tensor elements of magnetite (Fe3O4) between 0.5 and 4.3 eV," Solid State Commun. 39, 189 (1981).
[CrossRef]

1979 (1)

A. Schlegel, S. F. Alvarado, and P. Wachter, "Optical properties of magnetite (Fe3O4)," J. Phys. C: Solid State Phys. 12, 1157 (1979).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4370 (1972).
[CrossRef]

1967 (1)

P. S. Pershan, "Magneto-optical effects," J. Appl. Phys. 38, 1482 (1967).
[CrossRef]

Alvarado, S. F.

A. Schlegel, S. F. Alvarado, and P. Wachter, "Optical properties of magnetite (Fe3O4)," J. Phys. C: Solid State Phys. 12, 1157 (1979).
[CrossRef]

Atwater, H. A.

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, "Plasmonics - A route to nanoscale optical devices," Adv. Mater. 13, 1501 (2001).
[CrossRef]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B. 62, R16356 (2000).
[CrossRef]

Aubard, J.

N. Felidj, J. Aubard, G. Levi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface enhanced Raman scattering," Phys. Rev. B. 65, 075419 (2002).
[CrossRef]

Aussenegg, F. R.

N. Felidj, J. Aubard, G. Levi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface enhanced Raman scattering," Phys. Rev. B. 65, 075419 (2002).
[CrossRef]

Awano, H.

T. Katayama, Y. Suzuki, H. Awano, Y. Nishihara, and N. Koshizuka, "Enhancement of the magneto-optical Kerr rotation in Fe/Cu bilayered films," Phys. Rev. Lett. 60, 1426 (1988).
[CrossRef] [PubMed]

Barnakov, Y. A.

D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, "Magneto-optical spectra of closely-spaced magnetite nanoparticles," J. Appl. Phys. 97, 10M504 (2005).
[CrossRef]

Berger, A.

M. R. Pufall, A. Berger, and S. Schultz, "Measurement of the scattered light magneto-optical Kerr effect from plasmon-resonant Ag particles near a magnetic film," J. Appl. Phys. 81, 5689 (1997).
[CrossRef]

Bertrand, P.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, "Surface-enhanced magneto-optics in metallic multilayer films," Phys. Rev. B. 64, 235422 (2001).
[CrossRef]

Bratz, A.

K. Hinsen, A. Bratz, and B. U. Felderhof, "Anisotropic dielectric tensor and the Hall effect in a suspension of spheres," Phys. Rev. B. 23, 14995 (1992).
[CrossRef]

Brongersma, M. L.

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, "Plasmonics - A route to nanoscale optical devices," Adv. Mater. 13, 1501 (2001).
[CrossRef]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B. 62, R16356 (2000).
[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 (2004).
[CrossRef]

Chaumet, P. C.

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 (2004).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Draine, B. T.

B. T. Draine and J. Goodman, "Beyond Clausius-Mossotti: Wave propagation on a polarizable point lattice and the discrete dipole approximation," Astrophys. J. 405, 685 (1993).
[CrossRef]

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

Erman, M.

W. D. Martens, W. L. Peeters, and H. M. van NoortM. Erman, "Optical, magneto-optical and Mossbauer spectroscopy on Co3+ substituted cobalt ferrite," J. Phys. Chem. Solids 46, 411 (1985).
[CrossRef]

Feiner, L. F.

W. F. J. Fontijn, P. J. van der Zaag, and L. F. Feiner, "A consistent interpretation of the magneto-optical spectra of spinel-type ferrites," J. Appl. Phys. 85, 5100 (1999).
[CrossRef]

Felderhof, B. U.

K. Hinsen, A. Bratz, and B. U. Felderhof, "Anisotropic dielectric tensor and the Hall effect in a suspension of spheres," Phys. Rev. B. 23, 14995 (1992).
[CrossRef]

Felidj, N.

N. Felidj, J. Aubard, G. Levi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface enhanced Raman scattering," Phys. Rev. B. 65, 075419 (2002).
[CrossRef]

Fontijn, W. F. J.

W. F. J. Fontijn, P. J. van der Zaag, and L. F. Feiner, "A consistent interpretation of the magneto-optical spectra of spinel-type ferrites," J. Appl. Phys. 85, 5100 (1999).
[CrossRef]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal and L. Martin-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured materials," Phys. Rev. B. 66, 155412 (2002).
[CrossRef]

Goodman, J.

B. T. Draine and J. Goodman, "Beyond Clausius-Mossotti: Wave propagation on a polarizable point lattice and the discrete dipole approximation," Astrophys. J. 405, 685 (1993).
[CrossRef]

Hartman, J. W.

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B. 62, R16356 (2000).
[CrossRef]

Hermann, C.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, "Surface-enhanced magneto-optics in metallic multilayer films," Phys. Rev. B. 64, 235422 (2001).
[CrossRef]

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, and J. Peretti, "Magneto-optical effects enhanced by surface plasmons in metallic multilayer films," Phys. Rev. Lett. 73, 3584 (1994).
[CrossRef] [PubMed]

Hinsen, K.

K. Hinsen, A. Bratz, and B. U. Felderhof, "Anisotropic dielectric tensor and the Hall effect in a suspension of spheres," Phys. Rev. B. 23, 14995 (1992).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Katayama, T.

T. Katayama, Y. Suzuki, H. Awano, Y. Nishihara, and N. Koshizuka, "Enhancement of the magneto-optical Kerr rotation in Fe/Cu bilayered films," Phys. Rev. Lett. 60, 1426 (1988).
[CrossRef] [PubMed]

Kelly, K. L.

L. L. Zhao, K. L. Kelly, and G. C. Schatz, "The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width," J. Phys. Chem. B 107, 7343 (2003).
[CrossRef]

Kik, P. G.

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, "Plasmonics - A route to nanoscale optical devices," Adv. Mater. 13, 1501 (2001).
[CrossRef]

Koshizuka, N.

T. Katayama, Y. Suzuki, H. Awano, Y. Nishihara, and N. Koshizuka, "Enhancement of the magneto-optical Kerr rotation in Fe/Cu bilayered films," Phys. Rev. Lett. 60, 1426 (1988).
[CrossRef] [PubMed]

Kosobukin, V. A.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, "Surface-enhanced magneto-optics in metallic multilayer films," Phys. Rev. B. 64, 235422 (2001).
[CrossRef]

V. A. Kosobukin, "Magneto-optics via the near field," Surf. Science 406, 32 (1998).
[CrossRef]

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, and J. Peretti, "Magneto-optical effects enhanced by surface plasmons in metallic multilayer films," Phys. Rev. Lett. 73, 3584 (1994).
[CrossRef] [PubMed]

Krenn, J. R.

N. Felidj, J. Aubard, G. Levi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface enhanced Raman scattering," Phys. Rev. B. 65, 075419 (2002).
[CrossRef]

Lampel, G.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, "Surface-enhanced magneto-optics in metallic multilayer films," Phys. Rev. B. 64, 235422 (2001).
[CrossRef]

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, and J. Peretti, "Magneto-optical effects enhanced by surface plasmons in metallic multilayer films," Phys. Rev. Lett. 73, 3584 (1994).
[CrossRef] [PubMed]

Lamprecht, B.

N. Felidj, J. Aubard, G. Levi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface enhanced Raman scattering," Phys. Rev. B. 65, 075419 (2002).
[CrossRef]

Lazarides, A. A.

A. A. Lazarides and G. C. Schatz, "DNA-linked metal nanosphere materials: Structural basis for the optical properties," J. Phys. Chem. B 104, 460 (2000).
[CrossRef]

Leitner, A.

N. Felidj, J. Aubard, G. Levi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface enhanced Raman scattering," Phys. Rev. B. 65, 075419 (2002).
[CrossRef]

Levi, G.

N. Felidj, J. Aubard, G. Levi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface enhanced Raman scattering," Phys. Rev. B. 65, 075419 (2002).
[CrossRef]

Li, Y.

Y. Li, Q. Zhang, A. V. Nurmikko, and S. Sun, "Enhanced magneto-optical response in dumbbell-like Ag-CoFe2O4 nanoparticle pairs," Nano Lett. 5, 1689 (2005).
[CrossRef] [PubMed]

Maier, S. A.

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, "Plasmonics - A route to nanoscale optical devices," Adv. Mater. 13, 1501 (2001).
[CrossRef]

Markovich, G.

G. Shemer and G. Markovich, "Enhancement of magneto-optical effects in magnetite near gold surfaces," J. Phys. Chem. B 106, 9195 (2002).
[CrossRef]

Martens, W. D.

W. D. Martens, W. L. Peeters, and H. M. van NoortM. Erman, "Optical, magneto-optical and Mossbauer spectroscopy on Co3+ substituted cobalt ferrite," J. Phys. Chem. Solids 46, 411 (1985).
[CrossRef]

Martin-Moreno, L.

F. J. Garcia-Vidal and L. Martin-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured materials," Phys. Rev. B. 66, 155412 (2002).
[CrossRef]

Meltzer, S.

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, "Plasmonics - A route to nanoscale optical devices," Adv. Mater. 13, 1501 (2001).
[CrossRef]

Murray, C. B.

E. V. Shevchenko, D. V. Talapin, C. B. Murray, and S. O'Brien, "Structural characterization of self-assembled multifunctional binary nanoparticle superlattices," J. Am. Chem. Soc. 128, 3620 (2006).
[CrossRef] [PubMed]

Narimanov, E. E.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, S32 (2005).
[CrossRef]

Nishihara, Y.

T. Katayama, Y. Suzuki, H. Awano, Y. Nishihara, and N. Koshizuka, "Enhancement of the magneto-optical Kerr rotation in Fe/Cu bilayered films," Phys. Rev. Lett. 60, 1426 (1988).
[CrossRef] [PubMed]

Nurmikko, A. V.

Y. Li, Q. Zhang, A. V. Nurmikko, and S. Sun, "Enhanced magneto-optical response in dumbbell-like Ag-CoFe2O4 nanoparticle pairs," Nano Lett. 5, 1689 (2005).
[CrossRef] [PubMed]

O'Brien, S.

E. V. Shevchenko, D. V. Talapin, C. B. Murray, and S. O'Brien, "Structural characterization of self-assembled multifunctional binary nanoparticle superlattices," J. Am. Chem. Soc. 128, 3620 (2006).
[CrossRef] [PubMed]

Peeters, W. L.

W. D. Martens, W. L. Peeters, and H. M. van NoortM. Erman, "Optical, magneto-optical and Mossbauer spectroscopy on Co3+ substituted cobalt ferrite," J. Phys. Chem. Solids 46, 411 (1985).
[CrossRef]

Peretti, J.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, "Surface-enhanced magneto-optics in metallic multilayer films," Phys. Rev. B. 64, 235422 (2001).
[CrossRef]

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, and J. Peretti, "Magneto-optical effects enhanced by surface plasmons in metallic multilayer films," Phys. Rev. Lett. 73, 3584 (1994).
[CrossRef] [PubMed]

Pershan, P. S.

P. S. Pershan, "Magneto-optical effects," J. Appl. Phys. 38, 1482 (1967).
[CrossRef]

Podolskiy, V. A.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, S32 (2005).
[CrossRef]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735 (2003).
[CrossRef] [PubMed]

Pufall, M. R.

M. R. Pufall, A. Berger, and S. Schultz, "Measurement of the scattered light magneto-optical Kerr effect from plasmon-resonant Ag particles near a magnetic film," J. Appl. Phys. 81, 5689 (1997).
[CrossRef]

Rahmani, A.

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 (2004).
[CrossRef]

Requicha, A. A. G.

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, "Plasmonics - A route to nanoscale optical devices," Adv. Mater. 13, 1501 (2001).
[CrossRef]

Safarov, V. I.

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, "Surface-enhanced magneto-optics in metallic multilayer films," Phys. Rev. B. 64, 235422 (2001).
[CrossRef]

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, and J. Peretti, "Magneto-optical effects enhanced by surface plasmons in metallic multilayer films," Phys. Rev. Lett. 73, 3584 (1994).
[CrossRef] [PubMed]

Salerno, M.

N. Felidj, J. Aubard, G. Levi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface enhanced Raman scattering," Phys. Rev. B. 65, 075419 (2002).
[CrossRef]

Sarychev, A. K.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, S32 (2005).
[CrossRef]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735 (2003).
[CrossRef] [PubMed]

Schatz, G. C.

L. L. Zhao, K. L. Kelly, and G. C. Schatz, "The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width," J. Phys. Chem. B 107, 7343 (2003).
[CrossRef]

A. A. Lazarides and G. C. Schatz, "DNA-linked metal nanosphere materials: Structural basis for the optical properties," J. Phys. Chem. B 104, 460 (2000).
[CrossRef]

W.-H. Yang, G. C. Schatz, and R. P. Van Duyne, "Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitrary shapes," J. Chem. Phys. 103, 869 (1995).
[CrossRef]

Schider, G.

N. Felidj, J. Aubard, G. Levi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface enhanced Raman scattering," Phys. Rev. B. 65, 075419 (2002).
[CrossRef]

Schlegel, A.

A. Schlegel, S. F. Alvarado, and P. Wachter, "Optical properties of magnetite (Fe3O4)," J. Phys. C: Solid State Phys. 12, 1157 (1979).
[CrossRef]

Schoenes, J.

X. Zhang, J. Schoenes, and P. Wachter, "Kerr-effect and dielectric tensor elements of magnetite (Fe3O4) between 0.5 and 4.3 eV," Solid State Commun. 39, 189 (1981).
[CrossRef]

Schultz, S.

M. R. Pufall, A. Berger, and S. Schultz, "Measurement of the scattered light magneto-optical Kerr effect from plasmon-resonant Ag particles near a magnetic film," J. Appl. Phys. 81, 5689 (1997).
[CrossRef]

Scott, B. L.

D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, "Magneto-optical spectra of closely-spaced magnetite nanoparticles," J. Appl. Phys. 97, 10M504 (2005).
[CrossRef]

Shalaev, V. M.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, S32 (2005).
[CrossRef]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735 (2003).
[CrossRef] [PubMed]

Shemer, G.

G. Shemer and G. Markovich, "Enhancement of magneto-optical effects in magnetite near gold surfaces," J. Phys. Chem. B 106, 9195 (2002).
[CrossRef]

Shevchenko, E. V.

E. V. Shevchenko, D. V. Talapin, C. B. Murray, and S. O'Brien, "Structural characterization of self-assembled multifunctional binary nanoparticle superlattices," J. Am. Chem. Soc. 128, 3620 (2006).
[CrossRef] [PubMed]

Sihvola, A. H.

Smith, D. A.

D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, "Magneto-optical spectra of closely-spaced magnetite nanoparticles," J. Appl. Phys. 97, 10M504 (2005).
[CrossRef]

Stokes, K. L.

D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, "Magneto-optical spectra of closely-spaced magnetite nanoparticles," J. Appl. Phys. 97, 10M504 (2005).
[CrossRef]

Sun, S.

Y. Li, Q. Zhang, A. V. Nurmikko, and S. Sun, "Enhanced magneto-optical response in dumbbell-like Ag-CoFe2O4 nanoparticle pairs," Nano Lett. 5, 1689 (2005).
[CrossRef] [PubMed]

Suzuki, Y.

T. Katayama, Y. Suzuki, H. Awano, Y. Nishihara, and N. Koshizuka, "Enhancement of the magneto-optical Kerr rotation in Fe/Cu bilayered films," Phys. Rev. Lett. 60, 1426 (1988).
[CrossRef] [PubMed]

Talapin, D. V.

E. V. Shevchenko, D. V. Talapin, C. B. Murray, and S. O'Brien, "Structural characterization of self-assembled multifunctional binary nanoparticle superlattices," J. Am. Chem. Soc. 128, 3620 (2006).
[CrossRef] [PubMed]

van der Zaag, P. J.

W. F. J. Fontijn, P. J. van der Zaag, and L. F. Feiner, "A consistent interpretation of the magneto-optical spectra of spinel-type ferrites," J. Appl. Phys. 85, 5100 (1999).
[CrossRef]

Van Duyne, R. P.

W.-H. Yang, G. C. Schatz, and R. P. Van Duyne, "Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitrary shapes," J. Chem. Phys. 103, 869 (1995).
[CrossRef]

van Noort, H. M.

W. D. Martens, W. L. Peeters, and H. M. van NoortM. Erman, "Optical, magneto-optical and Mossbauer spectroscopy on Co3+ substituted cobalt ferrite," J. Phys. Chem. Solids 46, 411 (1985).
[CrossRef]

Wachter, P.

X. Zhang, J. Schoenes, and P. Wachter, "Kerr-effect and dielectric tensor elements of magnetite (Fe3O4) between 0.5 and 4.3 eV," Solid State Commun. 39, 189 (1981).
[CrossRef]

A. Schlegel, S. F. Alvarado, and P. Wachter, "Optical properties of magnetite (Fe3O4)," J. Phys. C: Solid State Phys. 12, 1157 (1979).
[CrossRef]

White, S. A.

D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, "Magneto-optical spectra of closely-spaced magnetite nanoparticles," J. Appl. Phys. 97, 10M504 (2005).
[CrossRef]

Yang, W.-H.

W.-H. Yang, G. C. Schatz, and R. P. Van Duyne, "Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitrary shapes," J. Chem. Phys. 103, 869 (1995).
[CrossRef]

Zhang, Q.

Y. Li, Q. Zhang, A. V. Nurmikko, and S. Sun, "Enhanced magneto-optical response in dumbbell-like Ag-CoFe2O4 nanoparticle pairs," Nano Lett. 5, 1689 (2005).
[CrossRef] [PubMed]

Zhang, X.

X. Zhang, J. Schoenes, and P. Wachter, "Kerr-effect and dielectric tensor elements of magnetite (Fe3O4) between 0.5 and 4.3 eV," Solid State Commun. 39, 189 (1981).
[CrossRef]

Zhao, L. L.

L. L. Zhao, K. L. Kelly, and G. C. Schatz, "The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width," J. Phys. Chem. B 107, 7343 (2003).
[CrossRef]

Adv. Mater. (1)

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, "Plasmonics - A route to nanoscale optical devices," Adv. Mater. 13, 1501 (2001).
[CrossRef]

Astrophys. J. (3)

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

B. T. Draine and J. Goodman, "Beyond Clausius-Mossotti: Wave propagation on a polarizable point lattice and the discrete dipole approximation," Astrophys. J. 405, 685 (1993).
[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 (2004).
[CrossRef]

J. Am. Chem. Soc. (1)

E. V. Shevchenko, D. V. Talapin, C. B. Murray, and S. O'Brien, "Structural characterization of self-assembled multifunctional binary nanoparticle superlattices," J. Am. Chem. Soc. 128, 3620 (2006).
[CrossRef] [PubMed]

J. Appl. Phys. (4)

W. F. J. Fontijn, P. J. van der Zaag, and L. F. Feiner, "A consistent interpretation of the magneto-optical spectra of spinel-type ferrites," J. Appl. Phys. 85, 5100 (1999).
[CrossRef]

M. R. Pufall, A. Berger, and S. Schultz, "Measurement of the scattered light magneto-optical Kerr effect from plasmon-resonant Ag particles near a magnetic film," J. Appl. Phys. 81, 5689 (1997).
[CrossRef]

P. S. Pershan, "Magneto-optical effects," J. Appl. Phys. 38, 1482 (1967).
[CrossRef]

D. A. Smith, Y. A. Barnakov, B. L. Scott, S. A. White, and K. L. Stokes, "Magneto-optical spectra of closely-spaced magnetite nanoparticles," J. Appl. Phys. 97, 10M504 (2005).
[CrossRef]

J. Chem. Phys. (1)

W.-H. Yang, G. C. Schatz, and R. P. Van Duyne, "Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitrary shapes," J. Chem. Phys. 103, 869 (1995).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, S32 (2005).
[CrossRef]

J. Phys. C: Solid State Phys. (1)

A. Schlegel, S. F. Alvarado, and P. Wachter, "Optical properties of magnetite (Fe3O4)," J. Phys. C: Solid State Phys. 12, 1157 (1979).
[CrossRef]

J. Phys. Chem. B (3)

G. Shemer and G. Markovich, "Enhancement of magneto-optical effects in magnetite near gold surfaces," J. Phys. Chem. B 106, 9195 (2002).
[CrossRef]

L. L. Zhao, K. L. Kelly, and G. C. Schatz, "The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width," J. Phys. Chem. B 107, 7343 (2003).
[CrossRef]

A. A. Lazarides and G. C. Schatz, "DNA-linked metal nanosphere materials: Structural basis for the optical properties," J. Phys. Chem. B 104, 460 (2000).
[CrossRef]

J. Phys. Chem. Solids (1)

W. D. Martens, W. L. Peeters, and H. M. van NoortM. Erman, "Optical, magneto-optical and Mossbauer spectroscopy on Co3+ substituted cobalt ferrite," J. Phys. Chem. Solids 46, 411 (1985).
[CrossRef]

Nano Lett. (1)

Y. Li, Q. Zhang, A. V. Nurmikko, and S. Sun, "Enhanced magneto-optical response in dumbbell-like Ag-CoFe2O4 nanoparticle pairs," Nano Lett. 5, 1689 (2005).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Phys. Rev. B. (5)

C. Hermann, V. A. Kosobukin, G. Lampel, J. Peretti, V. I. Safarov, and P. Bertrand, "Surface-enhanced magneto-optics in metallic multilayer films," Phys. Rev. B. 64, 235422 (2001).
[CrossRef]

K. Hinsen, A. Bratz, and B. U. Felderhof, "Anisotropic dielectric tensor and the Hall effect in a suspension of spheres," Phys. Rev. B. 23, 14995 (1992).
[CrossRef]

N. Felidj, J. Aubard, G. Levi, J. R. Krenn, M. Salerno, G. Schider, B. Lamprecht, A. Leitner, and F. R. Aussenegg, "Controlling the optical response of regular arrays of gold particles for surface enhanced Raman scattering," Phys. Rev. B. 65, 075419 (2002).
[CrossRef]

F. J. Garcia-Vidal and L. Martin-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured materials," Phys. Rev. B. 66, 155412 (2002).
[CrossRef]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B. 62, R16356 (2000).
[CrossRef]

Phys. Rev. Lett. (2)

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, and J. Peretti, "Magneto-optical effects enhanced by surface plasmons in metallic multilayer films," Phys. Rev. Lett. 73, 3584 (1994).
[CrossRef] [PubMed]

T. Katayama, Y. Suzuki, H. Awano, Y. Nishihara, and N. Koshizuka, "Enhancement of the magneto-optical Kerr rotation in Fe/Cu bilayered films," Phys. Rev. Lett. 60, 1426 (1988).
[CrossRef] [PubMed]

Solid State Commun. (1)

X. Zhang, J. Schoenes, and P. Wachter, "Kerr-effect and dielectric tensor elements of magnetite (Fe3O4) between 0.5 and 4.3 eV," Solid State Commun. 39, 189 (1981).
[CrossRef]

Surf. Science (1)

V. A. Kosobukin, "Magneto-optics via the near field," Surf. Science 406, 32 (1998).
[CrossRef]

Other (7)

S. A. Maier, P. G. Kik, M. L. Brongersma, H. A. Atwater, S. Meltzer, A. A. G. Requicha, and B. K. Koel, "Observation of coupled plasmon-polariton modes of plasmon waveguides for electromagnetic energy transport below the diffraction limit," in Mat. Res. Soc. Symp. Proc., vol. 722, R. B. Wehrspohn, S. Noda, C.Soukoulis, and R. Marz, Eds. (Warrendale, PA, MRS, 2002), p. L6.2.

V. M. Shalaev, V. A. Podolskiy, and A. K. Sarychev, "Plasmonic nanophotonics: Manipulating light and sensing molecules," in Proceedings of SPIE vol. 4806, Complex Mediums III: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, G. Dewar, and M. W. McCall, Eds. (Bellingham, WA, SPIE, 2002), p. 32.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (New York, John Wiley and Sons, Inc., 1999).

A. K. Zvezdin and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials (London, Institute of Physics Publishing, 1997).
[CrossRef]

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

Wolfram Research, Inc., Mathematica, Version 5.1, Champaign, IL (2004).

The MathWorks Inc, MATLAB version 6.5.1, Natick, Massachusetts (2003).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Model for the magnetite nanowires. The spheres represent the individual discrete dipole elements. The cross section is 2×2 elements with a length L varied from 2 to 100 elements. In all cases the element grid spacing d=1.0 nm.

Fig. 2.
Fig. 2.

Calculations of the Faraday rotation of a magnetite nanowire. The long axis of the nanowire is aligned with the (a) x axis and (b) z axis. In both cases, the magnetic field is applied in the z direction.

Fig. 3.
Fig. 3.

Calculated magneto-optical response of a silver-CoFe2O4 particle pair as a function of interparticle spacing. The optical wave is propagating in the z direction and has linear polarization in the x direction. The calculations are performed for particles aligned on the (a) z axis and (b) y axis.

Fig. 4.
Fig. 4.

Calculated (a) optical extinction and (b) magneto-optical response of a silver-CoFe2O4 particle nanoparticle assembly. The 3×3×3 array of nanoparticles are arranged in a rock-salt structure.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

E loc , j = E inc , j + k j E dp , k .
α 1 P j j k A jk P k = E inc , j ,
A jk P k = exp [ i κ r jk ] r jk { κ 2 ( n jk × P k ) × n jk + [ 3 n jk ( n jk P k ) P k ] ( 1 r jk 2 i κ r jk ) }
A ˜ P ˜ = E ˜ inc .
ε = [ ε xx i Q m z i Q m y i Q m z ε xx i Q m x i Q m y i Q m x ε zz ] ,
P = 4 π a 3 ε 1 ε + 2 1 E loc ,
α = 4 π a 3 ( ε 1 ) · ( ε + 2 1 ) 1 ,
θ + i η = C ext , I C ext , r .
f m , m ' κ 3 E 0 j = 1 N P j ( m ) e ̂ m ' * exp [ i κ z ̂ · r j ] ,
θ + i η = i 2 π κ 2 f xy .
θ + i η = i 2 π κ E 0 j = 1 N P j ( x ) e ̂ y * exp [ i κ z ̂ r j ] .
P j ( x ) = 1 2 ( P j ( l ) e ̂ l + P j ( r ) e ̂ r )
e ̂ y = i 2 ( e ̂ l e ̂ r ) .
θ + i η = π κ E 0 j = 1 N P j ( l ) exp [ i κ z ̂ r j ] π κ E 0 j = 1 N P j ( r ) exp [ i κ z ̂ r j ] ,

Metrics