Abstract

We have extended the contour-path effective-permittivity (CP-EP) finite-difference time-domain (FDTD) algorithm by A. Mohammadi et al., Opt. Express 13, 10367 (2005), to linear dispersive materials using the Z-transform formalism. We test our method against staircasing and the exact solution for plasmon spectra of metal nanoparticles. We show that the dispersive contour-path (DCP) approach yields better results than staircasing, especially for the cancellation of spurious resonances.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2007 (4)

F. Kaminski, V. Sandoghdar, and M. Agio, "Finite-difference time-domain modeling of decay rates in the near field of metal nanostructures," J. Comput. Theor. Nanosci. 4, 635-643 (2007).

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007).
[CrossRef]

Y. Zhao and Y. Hao, "Finite-difference time-domain study of guided modes in nano-plasmonic waveguides," IEEE Trans. Antennas Propag. 55, 3070-3077 (2007).
[CrossRef]

A. Deinega and I. Valuev, "Subpixel smoothing for conductive and dispersive media in the finite-difference time-domain method," Opt. Lett. 32, 3429-3431 (2007) http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-23-3429.
[CrossRef] [PubMed]

2006 (5)

2005 (6)

S. A. Maier and H. A. Atwater, "Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

A. Mohammadi, H. Nadgaran, and M. Agio, "Contour-path effective permittivities for the twodimensional finite-difference time-domain method," Opt. Express 13, 10367-10381 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10367.
[CrossRef] [PubMed]

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, "Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas," Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

P. M¨uhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

A. Vial, A.-S. Grimault, D. Macıas, D. Biarchesi, and M. Lamy de la Chapelle, "Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416 (2005).
[CrossRef]

C. Oubre and P. Nordlander, "Finite-difference time-domain studies of the optical properties of nanoshell dimers," J. Phys. Chem. B 109, 10042-10051 (2005).
[CrossRef]

2004 (1)

C. Oubre and P. Nordlander, "Optical properties of metallodielectric nanostructures calculated using the finite difference time domain method," J. Phys. Chem. B 108, 17740-17747 (2004).
[CrossRef]

2003 (4)

T. I. Kosmanis and T. D. Tsiboukis, "A systematic and topologically stable conformal finite-difference timedomain algorithm for modeling curved dielectric interfaces in three dimensions," IEEE Trans. Microwave Theory Tech. 51, 839-847 (2003).
[CrossRef]

J. Nadobny, D. Sullivan, W. Wlodarczyk, P. Deuflhard, and P. Wust, "A 3-D tensor FDTD-formulation for treatment of slopes interfaces in electrically inhomogeneous media," IEEE Trans. Antennas Propag. 51, 1760-1770 (2003).
[CrossRef]

O. Ramadan and A. Y. Oztoprak, "Z-transform implementation of the perfectly matched layer for truncating FDTD domains," IEEE Microwave Wirel. Compon. Lett. 13, 402-404 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

2001 (3)

A. Ditkowski, K. Dridi, and J. S. Hesthaven, "Convergent Cartesian grid methods for Maxwell�??s equations in complex geometries," J. Comput. Phys. 170, 39-80 (2001).
[CrossRef]

W. Yu and R. Mittra, "A conformal finite difference time domain technique for modeling curved dielectric surfaces," Microwave Opt. Technol. Lett. 11, 25-27 (2001).

K. H. Dridi, J. S. Hesthaven, and A. Ditkowski, "Staircase-free finite-difference time-domain formulation for general materials in complex geometries," IEEE Trans. Antennas Propag. 49, 749-756 (2001).
[CrossRef]

2000 (1)

H. Xu, J. Aizpurua, M. Kall, and P. Apell, "Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering," Phys. Rev. E 62, 4318-4324 (2000).
[CrossRef]

1999 (1)

J.-Y. Lee and N.-H. Myung, "Locally tensor conformal FDTD method for modeling arbitrary dielectric surfaces," Microwave Opt. Technol. Lett. 23, 245-249 (1999).
[CrossRef]

1996 (1)

D. M. Sullivan, "Z-transform theory and the FDTD method," IEEE Trans. Antennas Propag. 44, 28-34 (1996).
[CrossRef]

1991 (1)

A. C. Cangellaris, and D. B. Wright, "Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena," IEEE Trans. Antennas Propag. 39, 1518-1524 (1991).
[CrossRef]

Agio, M.

Aizpurua, J.

H. Xu, J. Aizpurua, M. Kall, and P. Apell, "Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering," Phys. Rev. E 62, 4318-4324 (2000).
[CrossRef]

Apell, P.

H. Xu, J. Aizpurua, M. Kall, and P. Apell, "Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering," Phys. Rev. E 62, 4318-4324 (2000).
[CrossRef]

Atwater, H. A.

S. A. Maier and H. A. Atwater, "Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Basov, D. N.

W. J. Padilla, D. N. Basov, and D. R. Smith, "Negative refractive index metamaterials," Mat. Today 9, 28-35 (2006).
[CrossRef]

Bermel, P.

Biarchesi, D.

A. Vial, A.-S. Grimault, D. Macıas, D. Biarchesi, and M. Lamy de la Chapelle, "Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Brongersma, M. L.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Mat. Today 9,20-27 (2006).
[CrossRef]

Burr, G. W.

Cangellaris, A. C.

A. C. Cangellaris, and D. B. Wright, "Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena," IEEE Trans. Antennas Propag. 39, 1518-1524 (1991).
[CrossRef]

Chandran, A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Mat. Today 9,20-27 (2006).
[CrossRef]

Deinega, A.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Deuflhard, P.

J. Nadobny, D. Sullivan, W. Wlodarczyk, P. Deuflhard, and P. Wust, "A 3-D tensor FDTD-formulation for treatment of slopes interfaces in electrically inhomogeneous media," IEEE Trans. Antennas Propag. 51, 1760-1770 (2003).
[CrossRef]

Ditkowski, A.

K. H. Dridi, J. S. Hesthaven, and A. Ditkowski, "Staircase-free finite-difference time-domain formulation for general materials in complex geometries," IEEE Trans. Antennas Propag. 49, 749-756 (2001).
[CrossRef]

A. Ditkowski, K. Dridi, and J. S. Hesthaven, "Convergent Cartesian grid methods for Maxwell�??s equations in complex geometries," J. Comput. Phys. 170, 39-80 (2001).
[CrossRef]

Dridi, K.

A. Ditkowski, K. Dridi, and J. S. Hesthaven, "Convergent Cartesian grid methods for Maxwell�??s equations in complex geometries," J. Comput. Phys. 170, 39-80 (2001).
[CrossRef]

Dridi, K. H.

K. H. Dridi, J. S. Hesthaven, and A. Ditkowski, "Staircase-free finite-difference time-domain formulation for general materials in complex geometries," IEEE Trans. Antennas Propag. 49, 749-756 (2001).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Eisler, H.-J.

P. M¨uhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Farjadpour, A.

Fromm, D. P.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, "Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas," Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Grimault, A.-S.

A. Vial, A.-S. Grimault, D. Macıas, D. Biarchesi, and M. Lamy de la Chapelle, "Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Hao, Y.

Y. Zhao and Y. Hao, "Finite-difference time-domain study of guided modes in nano-plasmonic waveguides," IEEE Trans. Antennas Propag. 55, 3070-3077 (2007).
[CrossRef]

Hecht, B.

P. M¨uhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Hesthaven, J. S.

A. Ditkowski, K. Dridi, and J. S. Hesthaven, "Convergent Cartesian grid methods for Maxwell�??s equations in complex geometries," J. Comput. Phys. 170, 39-80 (2001).
[CrossRef]

K. H. Dridi, J. S. Hesthaven, and A. Ditkowski, "Staircase-free finite-difference time-domain formulation for general materials in complex geometries," IEEE Trans. Antennas Propag. 49, 749-756 (2001).
[CrossRef]

Ibanescu, M.

Joannopoulos, J. D.

Johnson, S. G.

Kall, M.

H. Xu, J. Aizpurua, M. Kall, and P. Apell, "Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering," Phys. Rev. E 62, 4318-4324 (2000).
[CrossRef]

Kaminski, F.

F. Kaminski, V. Sandoghdar, and M. Agio, "Finite-difference time-domain modeling of decay rates in the near field of metal nanostructures," J. Comput. Theor. Nanosci. 4, 635-643 (2007).

Kino, G. S.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, "Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas," Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Kosmanis, T. I.

T. I. Kosmanis and T. D. Tsiboukis, "A systematic and topologically stable conformal finite-difference timedomain algorithm for modeling curved dielectric interfaces in three dimensions," IEEE Trans. Microwave Theory Tech. 51, 839-847 (2003).
[CrossRef]

Lamy de la Chapelle, M.

A. Vial, A.-S. Grimault, D. Macıas, D. Biarchesi, and M. Lamy de la Chapelle, "Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Lee, J.-Y.

J.-Y. Lee and N.-H. Myung, "Locally tensor conformal FDTD method for modeling arbitrary dielectric surfaces," Microwave Opt. Technol. Lett. 23, 245-249 (1999).
[CrossRef]

M¨uhlschlegel, P.

P. M¨uhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Macias, D.

A. Vial, A.-S. Grimault, D. Macıas, D. Biarchesi, and M. Lamy de la Chapelle, "Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Maier, S. A.

S. A. Maier and H. A. Atwater, "Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Martin, O. J. F.

P. M¨uhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Mittra, R.

W. Yu and R. Mittra, "A conformal finite difference time domain technique for modeling curved dielectric surfaces," Microwave Opt. Technol. Lett. 11, 25-27 (2001).

Moerner, W. E.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, "Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas," Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Mohammadi, A.

Myung, N.-H.

J.-Y. Lee and N.-H. Myung, "Locally tensor conformal FDTD method for modeling arbitrary dielectric surfaces," Microwave Opt. Technol. Lett. 23, 245-249 (1999).
[CrossRef]

Nadgaran, H.

Nadobny, J.

J. Nadobny, D. Sullivan, W. Wlodarczyk, P. Deuflhard, and P. Wust, "A 3-D tensor FDTD-formulation for treatment of slopes interfaces in electrically inhomogeneous media," IEEE Trans. Antennas Propag. 51, 1760-1770 (2003).
[CrossRef]

Nordlander, P.

C. Oubre and P. Nordlander, "Finite-difference time-domain studies of the optical properties of nanoshell dimers," J. Phys. Chem. B 109, 10042-10051 (2005).
[CrossRef]

C. Oubre and P. Nordlander, "Optical properties of metallodielectric nanostructures calculated using the finite difference time domain method," J. Phys. Chem. B 108, 17740-17747 (2004).
[CrossRef]

Oubre, C.

C. Oubre and P. Nordlander, "Finite-difference time-domain studies of the optical properties of nanoshell dimers," J. Phys. Chem. B 109, 10042-10051 (2005).
[CrossRef]

C. Oubre and P. Nordlander, "Optical properties of metallodielectric nanostructures calculated using the finite difference time domain method," J. Phys. Chem. B 108, 17740-17747 (2004).
[CrossRef]

Ozbay, E.

E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

Oztoprak, A. Y.

O. Ramadan and A. Y. Oztoprak, "Z-transform implementation of the perfectly matched layer for truncating FDTD domains," IEEE Microwave Wirel. Compon. Lett. 13, 402-404 (2003).
[CrossRef]

Padilla, W. J.

W. J. Padilla, D. N. Basov, and D. R. Smith, "Negative refractive index metamaterials," Mat. Today 9, 28-35 (2006).
[CrossRef]

Pohl, D. W.

P. M¨uhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Ramadan, O.

O. Ramadan and A. Y. Oztoprak, "Z-transform implementation of the perfectly matched layer for truncating FDTD domains," IEEE Microwave Wirel. Compon. Lett. 13, 402-404 (2003).
[CrossRef]

Rodriguez, A.

Roundy, D.

Sandoghdar, V.

F. Kaminski, V. Sandoghdar, and M. Agio, "Finite-difference time-domain modeling of decay rates in the near field of metal nanostructures," J. Comput. Theor. Nanosci. 4, 635-643 (2007).

Schuck, P. J.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, "Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas," Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Schuller, J. A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Mat. Today 9,20-27 (2006).
[CrossRef]

Shalaev, V. M.

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007).
[CrossRef]

Smith, D. R.

W. J. Padilla, D. N. Basov, and D. R. Smith, "Negative refractive index metamaterials," Mat. Today 9, 28-35 (2006).
[CrossRef]

Sullivan, D.

J. Nadobny, D. Sullivan, W. Wlodarczyk, P. Deuflhard, and P. Wust, "A 3-D tensor FDTD-formulation for treatment of slopes interfaces in electrically inhomogeneous media," IEEE Trans. Antennas Propag. 51, 1760-1770 (2003).
[CrossRef]

Sullivan, D. M.

D. M. Sullivan, "Z-transform theory and the FDTD method," IEEE Trans. Antennas Propag. 44, 28-34 (1996).
[CrossRef]

Sundaramurthy, A.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, "Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas," Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Tsiboukis, T. D.

T. I. Kosmanis and T. D. Tsiboukis, "A systematic and topologically stable conformal finite-difference timedomain algorithm for modeling curved dielectric interfaces in three dimensions," IEEE Trans. Microwave Theory Tech. 51, 839-847 (2003).
[CrossRef]

Valuev, I.

Vial, A.

A. Vial, A.-S. Grimault, D. Macıas, D. Biarchesi, and M. Lamy de la Chapelle, "Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Wlodarczyk, W.

J. Nadobny, D. Sullivan, W. Wlodarczyk, P. Deuflhard, and P. Wust, "A 3-D tensor FDTD-formulation for treatment of slopes interfaces in electrically inhomogeneous media," IEEE Trans. Antennas Propag. 51, 1760-1770 (2003).
[CrossRef]

Wright, D. B.

A. C. Cangellaris, and D. B. Wright, "Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena," IEEE Trans. Antennas Propag. 39, 1518-1524 (1991).
[CrossRef]

Wust, P.

J. Nadobny, D. Sullivan, W. Wlodarczyk, P. Deuflhard, and P. Wust, "A 3-D tensor FDTD-formulation for treatment of slopes interfaces in electrically inhomogeneous media," IEEE Trans. Antennas Propag. 51, 1760-1770 (2003).
[CrossRef]

Xu, H.

H. Xu, J. Aizpurua, M. Kall, and P. Apell, "Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering," Phys. Rev. E 62, 4318-4324 (2000).
[CrossRef]

Yu, W.

W. Yu and R. Mittra, "A conformal finite difference time domain technique for modeling curved dielectric surfaces," Microwave Opt. Technol. Lett. 11, 25-27 (2001).

Zhao, Y.

Y. Zhao and Y. Hao, "Finite-difference time-domain study of guided modes in nano-plasmonic waveguides," IEEE Trans. Antennas Propag. 55, 3070-3077 (2007).
[CrossRef]

Zia, R.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Mat. Today 9,20-27 (2006).
[CrossRef]

IEEE Microwave Wirel. Compon. Lett. (1)

O. Ramadan and A. Y. Oztoprak, "Z-transform implementation of the perfectly matched layer for truncating FDTD domains," IEEE Microwave Wirel. Compon. Lett. 13, 402-404 (2003).
[CrossRef]

IEEE Trans. Antennas Propag. (5)

Y. Zhao and Y. Hao, "Finite-difference time-domain study of guided modes in nano-plasmonic waveguides," IEEE Trans. Antennas Propag. 55, 3070-3077 (2007).
[CrossRef]

J. Nadobny, D. Sullivan, W. Wlodarczyk, P. Deuflhard, and P. Wust, "A 3-D tensor FDTD-formulation for treatment of slopes interfaces in electrically inhomogeneous media," IEEE Trans. Antennas Propag. 51, 1760-1770 (2003).
[CrossRef]

D. M. Sullivan, "Z-transform theory and the FDTD method," IEEE Trans. Antennas Propag. 44, 28-34 (1996).
[CrossRef]

K. H. Dridi, J. S. Hesthaven, and A. Ditkowski, "Staircase-free finite-difference time-domain formulation for general materials in complex geometries," IEEE Trans. Antennas Propag. 49, 749-756 (2001).
[CrossRef]

A. C. Cangellaris, and D. B. Wright, "Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena," IEEE Trans. Antennas Propag. 39, 1518-1524 (1991).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

T. I. Kosmanis and T. D. Tsiboukis, "A systematic and topologically stable conformal finite-difference timedomain algorithm for modeling curved dielectric interfaces in three dimensions," IEEE Trans. Microwave Theory Tech. 51, 839-847 (2003).
[CrossRef]

J. Appl. Phys. (1)

S. A. Maier and H. A. Atwater, "Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

J. Comput. Phys. (1)

A. Ditkowski, K. Dridi, and J. S. Hesthaven, "Convergent Cartesian grid methods for Maxwell�??s equations in complex geometries," J. Comput. Phys. 170, 39-80 (2001).
[CrossRef]

J. Comput. Theor. Nanosci. (1)

F. Kaminski, V. Sandoghdar, and M. Agio, "Finite-difference time-domain modeling of decay rates in the near field of metal nanostructures," J. Comput. Theor. Nanosci. 4, 635-643 (2007).

J. Phys. Chem. B (2)

C. Oubre and P. Nordlander, "Optical properties of metallodielectric nanostructures calculated using the finite difference time domain method," J. Phys. Chem. B 108, 17740-17747 (2004).
[CrossRef]

C. Oubre and P. Nordlander, "Finite-difference time-domain studies of the optical properties of nanoshell dimers," J. Phys. Chem. B 109, 10042-10051 (2005).
[CrossRef]

Mat. Today (2)

W. J. Padilla, D. N. Basov, and D. R. Smith, "Negative refractive index metamaterials," Mat. Today 9, 28-35 (2006).
[CrossRef]

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Mat. Today 9,20-27 (2006).
[CrossRef]

Microwave Opt. Technol. Lett. (2)

W. Yu and R. Mittra, "A conformal finite difference time domain technique for modeling curved dielectric surfaces," Microwave Opt. Technol. Lett. 11, 25-27 (2001).

J.-Y. Lee and N.-H. Myung, "Locally tensor conformal FDTD method for modeling arbitrary dielectric surfaces," Microwave Opt. Technol. Lett. 23, 245-249 (1999).
[CrossRef]

Nat. Photonics (1)

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007).
[CrossRef]

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. B (1)

A. Vial, A.-S. Grimault, D. Macıas, D. Biarchesi, and M. Lamy de la Chapelle, "Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Phys. Rev. E (1)

H. Xu, J. Aizpurua, M. Kall, and P. Apell, "Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering," Phys. Rev. E 62, 4318-4324 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, "Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas," Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Science (2)

P. M¨uhlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, "Resonant optical antennas," Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

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CRC Handbook of Chemistry and Physics, 87th ed., D. R. Lide, ed. (CRC-Press, 2006) http://www.hbcpnetbase.com.

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

M. Born and E. Wold, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

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

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Figures (4)

Fig. 1.
Fig. 1.

[(a) and (b)] Partially filled cells with curved interfaces crossing both integration lines, [(c) and (d)] crossing only the integration line of Faraday law, [(e) and (f)] crossing only the integration line of Ampère law. m and n represent unit vectors normal to the interface, d and f represent the line filling factors, 1 and 2 refer to the media ε 1 and ε 2, respectively, and Δ is the mesh pitch.

Fig. 2.
Fig. 2.

Total SCS for (a) Δ=0.5 nm, (b) Δ=1.5 nm and (c) Δ=0.4 nm with halved γ in the Drude model. Background index n b=1.7 and NP radius r=25 nm. The inset of (c) sketches the layout of the FDTD simulation: PML layers (gray thick line), total-field/scattered-field line for plane wave excitation (solid line), integration line to collect the total SCS (dashed line). The NP is placed in the total-field region.

Fig. 3.
Fig. 3.

Relative error on the total SCS for (a) Δ=1.5 nm and (b) Δ=0.4 nm with halved γ in the Drude model. (c) Average relative error for λ between 450 and 750 nm; the dashed lines refer to the case with halved γ. Each point represents a computation and lines are drawn to guide the eye.

Fig. 4.
Fig. 4.

Total SCS for two NPs with center-to-center distance (a) d=50 nm and (b) d=80 nm for Δ=1.2 nm. Background index n b=1.7 and NP radius r=20 nm. The inset of (b) sketches the layout of the FDTD simulation: PML layers (gray thick line), totalfield/scattered-field line for plane wave excitation (solid line), integration line to collect the total SCS (dashed line). The two NPs are placed in the total-field region and the incident plane wave is directed along the arrow. (c) Average relative error for λ between 450 and 750 nm for d=50 nm (solid lines) and d=80 nm (dashed lines). Each point represents a computation and lines are drawn to guide the eye.

Equations (35)

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t D · n d s = H · d l , t B · n d s = E · d l ,
E 2 ( z ) = D a , 2 D 2 ( z ) z 1 S 2 ( z ) ,
S 2 ( z ) = C a , 2 z 1 S 2 ( z ) C b , 2 z 2 S 2 ( z ) + C c , 2 E 2 ( z ) ,
C a , 2 = 1 + exp ( γ Δ t ) , C b , 2 = exp ( γ Δ t ) ,
C c , 2 = ω p 2 Δ t γ ε [ 1 exp ( γ Δ t ) ] , D a , 2 = 1 ε .
D = ε [ d + ( 1 d ) m 2 ] ( E 2 + z 1 S 2 ) + ε 1 ( 1 d ) ( 1 m 2 ) E 2 ,
D = ε , m E 2 + ε c , m z 1 S 2 ,
E 2 = D ε , m ε ε , m c , m z 1 S 2 ,
E = f E 2 + ( 1 f ) [ n 2 ε 1 D 2 + E 2 ( 1 n 2 ) ] ,
E = ε ε , n E 2 + ε ε 1 c , n z 1 S 2 ,
E = ε ε , n ε , m D ε ( ε c , m ε , n ε , m c , n ε 1 ) z 1 S 2 .
S 2 = ( C a , 2 ε , n ε 1 c , n C c , 2 ) z 1 S 2 C b , 2 z 2 S 2 + ε , n ε C c , 2 E .
S = ε ( c , m ε eff , m , n c , n ε 1 ) S 2 ,
C a = C a , 2 ε , n ε 1 c , n C c , 2 , C b = C b , 2 ,
C c = ε , n ( c , m ε eff , m , n c , n ε 1 ) C c , 2 , D a = 1 ε eff , m , n .
D = ε , n E 1 + ε g , n z 1 S 2 ,
E = ε 1 ε , m E 1 g , m z 1 S 2 ,
E = ε 1 ε , n ε , m D ( ε 1 ε ε , n ε , m g , n + g , m ) z 1 S 2 .
E 2 = [ ε 1 ε m 2 + ( 1 m 2 ) ] E 1 m 2 z 1 S 2 .
S 2 = [ C a , 2 ( 1 f ) m 2 ε , m ε 1 C c , 2 ] z 1 S 2 C b , 2 z 2 S 2 + ε , m ( m 2 ε + 1 m 2 ε 1 ) C c , 2 E .
S = ( ε ε eff , n , m g , n + g , m ) S 2 ,
C a = C a , 2 ( 1 f ) m 2 ε , m ε 1 C c , 2 , C b = C b , 2 ,
C c = ε , m ( m 2 ε + 1 m 2 ε 1 ) ( ε ε eff , n , m g , n + g , m ) C c , 2 , D a = 1 ε eff , n , m .
C a = C a , 2 ε , n ε 1 c , n C c , 2 , C b = C b , 2 ,
C c = ε , n ( 1 ε , n c , n ε 1 ) C c , 2 , D a = 1 ε , n .
C a = C a , 2 ( 1 f ) m 2 ε , m ε 1 C c , 2 , C b = C b , 2 ,
C c = ε , m ( m 2 ε + 1 m 2 ε 1 ) g , m C c , 2 , D a = 1 ε , m .
C a = C a , 2 ( 1 f ) ε ε 1 C c , 2 , C b = C b , 2 ,
C c = ε ε f C c , 2 , D a = 1 ε .
C a = C a , 2 , C b = C b , 2 ,
C c = ε ε , m c , m C c , 2 , D a = 1 ε , m .
C a = C a , 2 n 2 C c , 2 , C b = C b , 2 ,
C c = ε 1 ( n 2 ε + 1 n 2 ε 1 ) ε ε , n g , n C c , 2 , D a = 1 ε , n .
C a = C a , 2 C b = C b , 2 ,
C c = ε ε dC c , 2 , D a = 1 ε .

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