Abstract

The three-dimensional split-field finite-difference time-domain (SF-FDTD) method is combined with the total-field–scattered-field method for injecting a plane wave. A formulation is derived for calculating the incidence transformed fields of SF-FDTD on a one-dimensional auxiliary grid. The resulting fields obtained in the scattered zone are used to calculate the far fields, based on a proposed fully time-domain near-to-far-field transformation. The far-field information is used to calculate the extinction cross section of the periodic structure under oblique incidence. To analyze metallic periodic structures, a formulation with a reduced number of variables is proposed based on the auxiliary differential equation method for dispersive media.

© 2011 Optical Society of America

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    [Crossref]
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2010 (2)

C. P. Burrows and W. L. Barnes, “Large spectral extinction due to overlap of dipolar and quadrupolar plasmonic modes of metallic nanoparticles in arrays,” Opt. Express 18, 3187–3198(2010).
[Crossref] [PubMed]

A. Belkhir, O. Arar, S. S. Benabbes, O. Lamrous, and F. I. Baida, “Implementation of dispersion models in the split-field–finite-difference-time-domain algorithm for the study of metallic periodic structures at oblique incidence,” Phys. Rev. E 81, 046705 (2010).
[Crossref]

2009 (1)

2008 (7)

I. Valuev, A. Deinega, and S. Belousov, “Iterative technique for analysis of periodic structures at oblique incidence in the finite-difference time-domain method,” Opt. Lett. 33, 1491–1493(2008).
[Crossref] [PubMed]

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77, 035440 (2008).
[Crossref]

B. Auguie and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101, 143902(2008).
[Crossref] [PubMed]

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93, 181108 (2008).
[Crossref]

W. R. Hendren, A. Murphy, P. Evans, D. O. Connor, G. A. Wurtz, A. V. Zayats, R. Atkinson, and R. J. Pollard, “Fabrication and optical properties of gold nanotube arrays,” J. Phys. Condens. Matter 20, 362203 (2008).
[Crossref]

S. M. Amjadi and M. Soleimani, “Design of band-pass waveguide filter using frequency selective surfaces loaded with surface mount capacitors based on split-field update FDTD method,” Prog. Electromagn. Res. B 3, 271–281 (2008).
[Crossref]

A. Belkhir and F. I. Baida, “Three-dimensional finite-difference time-domain algorithm for oblique incidence with adaptation of perfectly matched layers and nonuniform meshing: application to the study of a radar dome,” Phys. Rev. E 77, 056701(2008).
[Crossref]

2006 (2)

A. Aminian and Y. Rahmat-Samii, “Spectral FDTD: a novel technique for the analysis of oblique incident plane wave on periodic structures,” IEEE Trans. Antennas Propag. 54, 1818–1825(2006).
[Crossref]

C. Oh and M. J. Escuti, “Time-domain analysis of periodic anisotropic media at oblique incidence: an efficient FDTD implementation,” Opt. Express 14, 11870–11884 (2006).
[Crossref] [PubMed]

2005 (5)

J. A. Roden, J. P. Skinner, and S. L. Johns, “Shielding effectiveness of three dimensional gratings using the periodic FDTD technique and CPML absorbing boundary condition,” in IEEE/ACES International Conference on Wireless Communications and Applied Computational Electromagnetics (IEEE, 2005), pp. 128–131.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, “Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography,” Nano Lett. 5, 1065–1070 (2005).
[Crossref] [PubMed]

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

S. Zou and G. C. Schatz, “Silver nanoparticle array structures that produce giant enhancements in electromagnetic fields,” Chem. Phys. Lett. 403, 62–67 (2005).
[Crossref]

A. Vial, A. Grimault, D. Macías, D. Barchiesi, and M. L. 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]

2004 (3)

E. Hao and G. C. Schatz, “Electromagnetic fields around silver nanoparticles and dimmers,” J. Chem. Phys. 120, 357–366(2004).
[Crossref] [PubMed]

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[Crossref] [PubMed]

S. Zou and G. C. Schatz, “Narrow plasmonic/photonic extinction and scattering line shapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121, 12606–12612(2004).
[Crossref] [PubMed]

2003 (2)

S. Malynych and G. Chumanov, “Light-induced coherent interactions between silver nanoparticles in two-dimensional arrays,” J. Am. Chem. Soc. 125, 2896–2898 (2003).
[Crossref] [PubMed]

C. L. Haynes, A. D. McFarland, L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: the importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107, 7337–7342 (2003).
[Crossref]

2001 (1)

H. Mosallaei and Y. Rahmat-Samii, “Grand challenges in analyzing EM band-gap structures: an FDTD/Prony technique based on the split-field approach,” in Antennas and Propagation Society International Symposium (IEEE, 2001), pp. 47–50.

2000 (3)

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
[Crossref] [PubMed]

B. Wu, E. Yang, J. A. Kong, J. A. Oswald, K. A. McIntosh, L. Mahoney, and S. Verghese, “Analysis of photonic crystal filters by the finite-difference time-domain technique,” Microwave Opt. Technol. Lett. 27, 81–87 (2000).
[Crossref]

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media,” Microwave Opt. Technol. Lett. 27, 334–339(2000).
[Crossref]

1998 (2)

J. G. Maloney and M. P. Kesler, “Analysis of antenna arrays using the split-field update FDTD method,” in Antennas and Propagation Society International Symposium (IEEE, 1998), pp. 2036–2039.

J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, “Time-domain analysis of periodic structures at oblique incidence: orthogonal and nonorthogonal FDTD implementations,” IEEE Trans. Microwave Theory Tech. 46, 420–427(1998).
[Crossref]

1996 (3)

Y. C. Kao and R. G. Atkins, “A finite-difference time-domain approach for frequency selective surfaces at oblique incidence,” in Proceedings of Antennas and Propagation Society International Symposium (IEEE, 1996), pp. 1432–1435.

S. D. Gedney, “An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[Crossref]

Y. A. Kao and R. G. Atkins, “A finite difference-time domain approach for frequency selective surfaces at oblique incidence,” in Antennas and Propagation Society International Symposium (IEEE, 1996), pp. 1432–1435.

1994 (2)

P. Harms, R. Mittra, and W. Ko, “Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for FSS structures,” IEEE Trans. Antennas Propag. 42, 1317–1324 (1994).
[Crossref]

J. R. Ren, O. P. Gandhi, L. R. Walker, J. Fraschilla, and C. R. Boerman, “Floquet-based FDTD analysis of two-dimensional phased array antennas,” IEEE Microwave Guided Wave Lett. 4, 109–111 (1994).
[Crossref]

1993 (1)

M. E. Veysoglu, R. T. Shin, and J. A. Kong, “A finite-difference time-domain analysis of wave scattering from periodic structures: oblique incidence case,” J. Electromagn. Waves Appl. 7, 1595–1607 (1993).
[Crossref]

1991 (1)

R. J. Luebbers, K. S. Kunz, M. Schneider, and F. Hunsberger, “A finite-difference time-domain near zone to far zone transformation,” IEEE Trans. Antennas Propag. 39, 429–433 (1991).
[Crossref]

1985 (1)

1983 (1)

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

1980 (1)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1980).
[PubMed]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[Crossref]

Aminian, A.

A. Aminian and Y. Rahmat-Samii, “Spectral FDTD: a novel technique for the analysis of oblique incident plane wave on periodic structures,” IEEE Trans. Antennas Propag. 54, 1818–1825(2006).
[Crossref]

Amjadi, S. M.

S. M. Amjadi and M. Soleimani, “Design of band-pass waveguide filter using frequency selective surfaces loaded with surface mount capacitors based on split-field update FDTD method,” Prog. Electromagn. Res. B 3, 271–281 (2008).
[Crossref]

Arar, O.

A. Belkhir, O. Arar, S. S. Benabbes, O. Lamrous, and F. I. Baida, “Implementation of dispersion models in the split-field–finite-difference-time-domain algorithm for the study of metallic periodic structures at oblique incidence,” Phys. Rev. E 81, 046705 (2010).
[Crossref]

Atkins, R. G.

Y. A. Kao and R. G. Atkins, “A finite difference-time domain approach for frequency selective surfaces at oblique incidence,” in Antennas and Propagation Society International Symposium (IEEE, 1996), pp. 1432–1435.

Y. C. Kao and R. G. Atkins, “A finite-difference time-domain approach for frequency selective surfaces at oblique incidence,” in Proceedings of Antennas and Propagation Society International Symposium (IEEE, 1996), pp. 1432–1435.

Atkinson, R.

W. R. Hendren, A. Murphy, P. Evans, D. O. Connor, G. A. Wurtz, A. V. Zayats, R. Atkinson, and R. J. Pollard, “Fabrication and optical properties of gold nanotube arrays,” J. Phys. Condens. Matter 20, 362203 (2008).
[Crossref]

Auguie, B.

B. Auguie and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101, 143902(2008).
[Crossref] [PubMed]

Aussenegg, F. R.

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
[Crossref] [PubMed]

Baida, F. I.

A. Belkhir, O. Arar, S. S. Benabbes, O. Lamrous, and F. I. Baida, “Implementation of dispersion models in the split-field–finite-difference-time-domain algorithm for the study of metallic periodic structures at oblique incidence,” Phys. Rev. E 81, 046705 (2010).
[Crossref]

F. I. Baida and A. Belkhir, “Split-field FDTD method for oblique incidence study of periodic dispersive metallic structures,” Opt. Lett. 34, 2453–2455 (2009).
[Crossref] [PubMed]

A. Belkhir and F. I. Baida, “Three-dimensional finite-difference time-domain algorithm for oblique incidence with adaptation of perfectly matched layers and nonuniform meshing: application to the study of a radar dome,” Phys. Rev. E 77, 056701(2008).
[Crossref]

Barchiesi, D.

A. Vial, A. Grimault, D. Macías, D. Barchiesi, and M. L. 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]

Barnes, W. L.

Belkhir, A.

A. Belkhir, O. Arar, S. S. Benabbes, O. Lamrous, and F. I. Baida, “Implementation of dispersion models in the split-field–finite-difference-time-domain algorithm for the study of metallic periodic structures at oblique incidence,” Phys. Rev. E 81, 046705 (2010).
[Crossref]

F. I. Baida and A. Belkhir, “Split-field FDTD method for oblique incidence study of periodic dispersive metallic structures,” Opt. Lett. 34, 2453–2455 (2009).
[Crossref] [PubMed]

A. Belkhir and F. I. Baida, “Three-dimensional finite-difference time-domain algorithm for oblique incidence with adaptation of perfectly matched layers and nonuniform meshing: application to the study of a radar dome,” Phys. Rev. E 77, 056701(2008).
[Crossref]

Belousov, S.

Benabbes, S. S.

A. Belkhir, O. Arar, S. S. Benabbes, O. Lamrous, and F. I. Baida, “Implementation of dispersion models in the split-field–finite-difference-time-domain algorithm for the study of metallic periodic structures at oblique incidence,” Phys. Rev. E 81, 046705 (2010).
[Crossref]

Boerman, C. R.

J. R. Ren, O. P. Gandhi, L. R. Walker, J. Fraschilla, and C. R. Boerman, “Floquet-based FDTD analysis of two-dimensional phased array antennas,” IEEE Microwave Guided Wave Lett. 4, 109–111 (1994).
[Crossref]

Bohren, C. F.

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

Borghs, G.

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77, 035440 (2008).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1980).
[PubMed]

Burrows, C. P.

Chu, Y.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93, 181108 (2008).
[Crossref]

Chumanov, G.

S. Malynych and G. Chumanov, “Light-induced coherent interactions between silver nanoparticles in two-dimensional arrays,” J. Am. Chem. Soc. 125, 2896–2898 (2003).
[Crossref] [PubMed]

Connor, D. O.

W. R. Hendren, A. Murphy, P. Evans, D. O. Connor, G. A. Wurtz, A. V. Zayats, R. Atkinson, and R. J. Pollard, “Fabrication and optical properties of gold nanotube arrays,” J. Phys. Condens. Matter 20, 362203 (2008).
[Crossref]

Crozier, K. B.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93, 181108 (2008).
[Crossref]

de la Chapelle, M. L.

A. Vial, A. Grimault, D. Macías, D. Barchiesi, and M. L. 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]

Deinega, A.

Ditlbacher, H.

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
[Crossref] [PubMed]

Escuti, M. J.

Evans, P.

W. R. Hendren, A. Murphy, P. Evans, D. O. Connor, G. A. Wurtz, A. V. Zayats, R. Atkinson, and R. J. Pollard, “Fabrication and optical properties of gold nanotube arrays,” J. Phys. Condens. Matter 20, 362203 (2008).
[Crossref]

Farahat, N.

N. Farahat and Raj Mittra, “Analysis of frequency selective surfaces using the finite difference time domain (FDTD) method,” in Antennas and Propagation Society International Symposium (IEEE, 2002), pp. 568–571.

Fraschilla, J.

J. R. Ren, O. P. Gandhi, L. R. Walker, J. Fraschilla, and C. R. Boerman, “Floquet-based FDTD analysis of two-dimensional phased array antennas,” IEEE Microwave Guided Wave Lett. 4, 109–111 (1994).
[Crossref]

Gandhi, O. P.

J. R. Ren, O. P. Gandhi, L. R. Walker, J. Fraschilla, and C. R. Boerman, “Floquet-based FDTD analysis of two-dimensional phased array antennas,” IEEE Microwave Guided Wave Lett. 4, 109–111 (1994).
[Crossref]

Gedney, S. D.

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media,” Microwave Opt. Technol. Lett. 27, 334–339(2000).
[Crossref]

J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, “Time-domain analysis of periodic structures at oblique incidence: orthogonal and nonorthogonal FDTD implementations,” IEEE Trans. Microwave Theory Tech. 46, 420–427(1998).
[Crossref]

S. D. Gedney, “An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[Crossref]

Grimault, A.

A. Vial, A. Grimault, D. Macías, D. Barchiesi, and M. L. 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]

Gunnarsson, L.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, “Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography,” Nano Lett. 5, 1065–1070 (2005).
[Crossref] [PubMed]

C. L. Haynes, A. D. McFarland, L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: the importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107, 7337–7342 (2003).
[Crossref]

Hagness, S. C.

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

Hao, E.

E. Hao and G. C. Schatz, “Electromagnetic fields around silver nanoparticles and dimmers,” J. Chem. Phys. 120, 357–366(2004).
[Crossref] [PubMed]

Harms, P.

P. Harms, R. Mittra, and W. Ko, “Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for FSS structures,” IEEE Trans. Antennas Propag. 42, 1317–1324 (1994).
[Crossref]

Harms, P. H.

J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, “Time-domain analysis of periodic structures at oblique incidence: orthogonal and nonorthogonal FDTD implementations,” IEEE Trans. Microwave Theory Tech. 46, 420–427(1998).
[Crossref]

Haynes, C. L.

C. L. Haynes, A. D. McFarland, L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: the importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107, 7337–7342 (2003).
[Crossref]

Hendren, W. R.

W. R. Hendren, A. Murphy, P. Evans, D. O. Connor, G. A. Wurtz, A. V. Zayats, R. Atkinson, and R. J. Pollard, “Fabrication and optical properties of gold nanotube arrays,” J. Phys. Condens. Matter 20, 362203 (2008).
[Crossref]

Hicks, E. M.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, “Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography,” Nano Lett. 5, 1065–1070 (2005).
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C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).

Hunsberger, F.

R. J. Luebbers, K. S. Kunz, M. Schneider, and F. Hunsberger, “A finite-difference time-domain near zone to far zone transformation,” IEEE Trans. Antennas Propag. 39, 429–433 (1991).
[Crossref]

Janel, N.

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[Crossref] [PubMed]

Johns, S. L.

J. A. Roden, J. P. Skinner, and S. L. Johns, “Shielding effectiveness of three dimensional gratings using the periodic FDTD technique and CPML absorbing boundary condition,” in IEEE/ACES International Conference on Wireless Communications and Applied Computational Electromagnetics (IEEE, 2005), pp. 128–131.

Kall, M.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, “Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography,” Nano Lett. 5, 1065–1070 (2005).
[Crossref] [PubMed]

C. L. Haynes, A. D. McFarland, L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: the importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107, 7337–7342 (2003).
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Kao, Y. A.

Y. A. Kao and R. G. Atkins, “A finite difference-time domain approach for frequency selective surfaces at oblique incidence,” in Antennas and Propagation Society International Symposium (IEEE, 1996), pp. 1432–1435.

Kao, Y. C.

Y. C. Kao and R. G. Atkins, “A finite-difference time-domain approach for frequency selective surfaces at oblique incidence,” in Proceedings of Antennas and Propagation Society International Symposium (IEEE, 1996), pp. 1432–1435.

Kasemo, B.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, “Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography,” Nano Lett. 5, 1065–1070 (2005).
[Crossref] [PubMed]

C. L. Haynes, A. D. McFarland, L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: the importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107, 7337–7342 (2003).
[Crossref]

Kesler, M. P.

J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, “Time-domain analysis of periodic structures at oblique incidence: orthogonal and nonorthogonal FDTD implementations,” IEEE Trans. Microwave Theory Tech. 46, 420–427(1998).
[Crossref]

J. G. Maloney and M. P. Kesler, “Analysis of antenna arrays using the split-field update FDTD method,” in Antennas and Propagation Society International Symposium (IEEE, 1998), pp. 2036–2039.

Khanadeyev, V. A.

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77, 035440 (2008).
[Crossref]

Khlebtsov, B. N.

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77, 035440 (2008).
[Crossref]

Khlebtsov, N. G.

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77, 035440 (2008).
[Crossref]

Ko, W.

P. Harms, R. Mittra, and W. Ko, “Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for FSS structures,” IEEE Trans. Antennas Propag. 42, 1317–1324 (1994).
[Crossref]

Kong, J. A.

B. Wu, E. Yang, J. A. Kong, J. A. Oswald, K. A. McIntosh, L. Mahoney, and S. Verghese, “Analysis of photonic crystal filters by the finite-difference time-domain technique,” Microwave Opt. Technol. Lett. 27, 81–87 (2000).
[Crossref]

M. E. Veysoglu, R. T. Shin, and J. A. Kong, “A finite-difference time-domain analysis of wave scattering from periodic structures: oblique incidence case,” J. Electromagn. Waves Appl. 7, 1595–1607 (1993).
[Crossref]

Krenn, J. R.

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
[Crossref] [PubMed]

Kunz, K. S.

R. J. Luebbers, K. S. Kunz, M. Schneider, and F. Hunsberger, “A finite-difference time-domain near zone to far zone transformation,” IEEE Trans. Antennas Propag. 39, 429–433 (1991).
[Crossref]

Lamprecht, B.

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
[Crossref] [PubMed]

Lamrous, O.

A. Belkhir, O. Arar, S. S. Benabbes, O. Lamrous, and F. I. Baida, “Implementation of dispersion models in the split-field–finite-difference-time-domain algorithm for the study of metallic periodic structures at oblique incidence,” Phys. Rev. E 81, 046705 (2010).
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B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
[Crossref] [PubMed]

Leitner, A.

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
[Crossref] [PubMed]

Luebbers, R. J.

R. J. Luebbers, K. S. Kunz, M. Schneider, and F. Hunsberger, “A finite-difference time-domain near zone to far zone transformation,” IEEE Trans. Antennas Propag. 39, 429–433 (1991).
[Crossref]

Macías, D.

A. Vial, A. Grimault, D. Macías, D. Barchiesi, and M. L. 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]

Mackowski, D. W.

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77, 035440 (2008).
[Crossref]

Mahoney, L.

B. Wu, E. Yang, J. A. Kong, J. A. Oswald, K. A. McIntosh, L. Mahoney, and S. Verghese, “Analysis of photonic crystal filters by the finite-difference time-domain technique,” Microwave Opt. Technol. Lett. 27, 81–87 (2000).
[Crossref]

Maloney, J. G.

J. G. Maloney and M. P. Kesler, “Analysis of antenna arrays using the split-field update FDTD method,” in Antennas and Propagation Society International Symposium (IEEE, 1998), pp. 2036–2039.

J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, “Time-domain analysis of periodic structures at oblique incidence: orthogonal and nonorthogonal FDTD implementations,” IEEE Trans. Microwave Theory Tech. 46, 420–427(1998).
[Crossref]

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S. Malynych and G. Chumanov, “Light-induced coherent interactions between silver nanoparticles in two-dimensional arrays,” J. Am. Chem. Soc. 125, 2896–2898 (2003).
[Crossref] [PubMed]

McFarland, A. D.

C. L. Haynes, A. D. McFarland, L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: the importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107, 7337–7342 (2003).
[Crossref]

McIntosh, K. A.

B. Wu, E. Yang, J. A. Kong, J. A. Oswald, K. A. McIntosh, L. Mahoney, and S. Verghese, “Analysis of photonic crystal filters by the finite-difference time-domain technique,” Microwave Opt. Technol. Lett. 27, 81–87 (2000).
[Crossref]

Meier, M.

Mittra, R.

P. Harms, R. Mittra, and W. Ko, “Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for FSS structures,” IEEE Trans. Antennas Propag. 42, 1317–1324 (1994).
[Crossref]

Mittra, Raj

N. Farahat and Raj Mittra, “Analysis of frequency selective surfaces using the finite difference time domain (FDTD) method,” in Antennas and Propagation Society International Symposium (IEEE, 2002), pp. 568–571.

Mosallaei, H.

H. Mosallaei and Y. Rahmat-Samii, “Grand challenges in analyzing EM band-gap structures: an FDTD/Prony technique based on the split-field approach,” in Antennas and Propagation Society International Symposium (IEEE, 2001), pp. 47–50.

Murphy, A.

W. R. Hendren, A. Murphy, P. Evans, D. O. Connor, G. A. Wurtz, A. V. Zayats, R. Atkinson, and R. J. Pollard, “Fabrication and optical properties of gold nanotube arrays,” J. Phys. Condens. Matter 20, 362203 (2008).
[Crossref]

Oh, C.

Oswald, J. A.

B. Wu, E. Yang, J. A. Kong, J. A. Oswald, K. A. McIntosh, L. Mahoney, and S. Verghese, “Analysis of photonic crystal filters by the finite-difference time-domain technique,” Microwave Opt. Technol. Lett. 27, 81–87 (2000).
[Crossref]

Pollard, R. J.

W. R. Hendren, A. Murphy, P. Evans, D. O. Connor, G. A. Wurtz, A. V. Zayats, R. Atkinson, and R. J. Pollard, “Fabrication and optical properties of gold nanotube arrays,” J. Phys. Condens. Matter 20, 362203 (2008).
[Crossref]

Prikulis, J.

C. L. Haynes, A. D. McFarland, L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: the importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107, 7337–7342 (2003).
[Crossref]

Rahmat-Samii, Y.

A. Aminian and Y. Rahmat-Samii, “Spectral FDTD: a novel technique for the analysis of oblique incident plane wave on periodic structures,” IEEE Trans. Antennas Propag. 54, 1818–1825(2006).
[Crossref]

H. Mosallaei and Y. Rahmat-Samii, “Grand challenges in analyzing EM band-gap structures: an FDTD/Prony technique based on the split-field approach,” in Antennas and Propagation Society International Symposium (IEEE, 2001), pp. 47–50.

Ren, J. R.

J. R. Ren, O. P. Gandhi, L. R. Walker, J. Fraschilla, and C. R. Boerman, “Floquet-based FDTD analysis of two-dimensional phased array antennas,” IEEE Microwave Guided Wave Lett. 4, 109–111 (1994).
[Crossref]

Rindzevicius, T.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, “Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography,” Nano Lett. 5, 1065–1070 (2005).
[Crossref] [PubMed]

Roden, J. A.

J. A. Roden, J. P. Skinner, and S. L. Johns, “Shielding effectiveness of three dimensional gratings using the periodic FDTD technique and CPML absorbing boundary condition,” in IEEE/ACES International Conference on Wireless Communications and Applied Computational Electromagnetics (IEEE, 2005), pp. 128–131.

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media,” Microwave Opt. Technol. Lett. 27, 334–339(2000).
[Crossref]

J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, “Time-domain analysis of periodic structures at oblique incidence: orthogonal and nonorthogonal FDTD implementations,” IEEE Trans. Microwave Theory Tech. 46, 420–427(1998).
[Crossref]

Schatz, G. C.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, “Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography,” Nano Lett. 5, 1065–1070 (2005).
[Crossref] [PubMed]

S. Zou and G. C. Schatz, “Silver nanoparticle array structures that produce giant enhancements in electromagnetic fields,” Chem. Phys. Lett. 403, 62–67 (2005).
[Crossref]

E. Hao and G. C. Schatz, “Electromagnetic fields around silver nanoparticles and dimmers,” J. Chem. Phys. 120, 357–366(2004).
[Crossref] [PubMed]

S. Zou and G. C. Schatz, “Narrow plasmonic/photonic extinction and scattering line shapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121, 12606–12612(2004).
[Crossref] [PubMed]

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[Crossref] [PubMed]

C. L. Haynes, A. D. McFarland, L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: the importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107, 7337–7342 (2003).
[Crossref]

Schider, G.

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
[Crossref] [PubMed]

Schneider, M.

R. J. Luebbers, K. S. Kunz, M. Schneider, and F. Hunsberger, “A finite-difference time-domain near zone to far zone transformation,” IEEE Trans. Antennas Propag. 39, 429–433 (1991).
[Crossref]

Schonbrun, E.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93, 181108 (2008).
[Crossref]

Shin, R. T.

M. E. Veysoglu, R. T. Shin, and J. A. Kong, “A finite-difference time-domain analysis of wave scattering from periodic structures: oblique incidence case,” J. Electromagn. Waves Appl. 7, 1595–1607 (1993).
[Crossref]

Skinner, J. P.

J. A. Roden, J. P. Skinner, and S. L. Johns, “Shielding effectiveness of three dimensional gratings using the periodic FDTD technique and CPML absorbing boundary condition,” in IEEE/ACES International Conference on Wireless Communications and Applied Computational Electromagnetics (IEEE, 2005), pp. 128–131.

Soleimani, M.

S. M. Amjadi and M. Soleimani, “Design of band-pass waveguide filter using frequency selective surfaces loaded with surface mount capacitors based on split-field update FDTD method,” Prog. Electromagn. Res. B 3, 271–281 (2008).
[Crossref]

Spears, K. G.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, “Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography,” Nano Lett. 5, 1065–1070 (2005).
[Crossref] [PubMed]

Taflove, A.

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

Valuev, I.

Van Duyne, R. P.

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, “Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography,” Nano Lett. 5, 1065–1070 (2005).
[Crossref] [PubMed]

C. L. Haynes, A. D. McFarland, L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: the importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107, 7337–7342 (2003).
[Crossref]

Verghese, S.

B. Wu, E. Yang, J. A. Kong, J. A. Oswald, K. A. McIntosh, L. Mahoney, and S. Verghese, “Analysis of photonic crystal filters by the finite-difference time-domain technique,” Microwave Opt. Technol. Lett. 27, 81–87 (2000).
[Crossref]

Veysoglu, M. E.

M. E. Veysoglu, R. T. Shin, and J. A. Kong, “A finite-difference time-domain analysis of wave scattering from periodic structures: oblique incidence case,” J. Electromagn. Waves Appl. 7, 1595–1607 (1993).
[Crossref]

Vial, A.

A. Vial, A. Grimault, D. Macías, D. Barchiesi, and M. L. 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]

Walker, L. R.

J. R. Ren, O. P. Gandhi, L. R. Walker, J. Fraschilla, and C. R. Boerman, “Floquet-based FDTD analysis of two-dimensional phased array antennas,” IEEE Microwave Guided Wave Lett. 4, 109–111 (1994).
[Crossref]

Wokaun, A.

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1980).
[PubMed]

Wu, B.

B. Wu, E. Yang, J. A. Kong, J. A. Oswald, K. A. McIntosh, L. Mahoney, and S. Verghese, “Analysis of photonic crystal filters by the finite-difference time-domain technique,” Microwave Opt. Technol. Lett. 27, 81–87 (2000).
[Crossref]

Wurtz, G. A.

W. R. Hendren, A. Murphy, P. Evans, D. O. Connor, G. A. Wurtz, A. V. Zayats, R. Atkinson, and R. J. Pollard, “Fabrication and optical properties of gold nanotube arrays,” J. Phys. Condens. Matter 20, 362203 (2008).
[Crossref]

Yang, E.

B. Wu, E. Yang, J. A. Kong, J. A. Oswald, K. A. McIntosh, L. Mahoney, and S. Verghese, “Analysis of photonic crystal filters by the finite-difference time-domain technique,” Microwave Opt. Technol. Lett. 27, 81–87 (2000).
[Crossref]

Yang, T.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93, 181108 (2008).
[Crossref]

Ye, J.

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77, 035440 (2008).
[Crossref]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[Crossref]

Zayats, A. V.

W. R. Hendren, A. Murphy, P. Evans, D. O. Connor, G. A. Wurtz, A. V. Zayats, R. Atkinson, and R. J. Pollard, “Fabrication and optical properties of gold nanotube arrays,” J. Phys. Condens. Matter 20, 362203 (2008).
[Crossref]

Zhao, L.

C. L. Haynes, A. D. McFarland, L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: the importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107, 7337–7342 (2003).
[Crossref]

Zou, S.

S. Zou and G. C. Schatz, “Silver nanoparticle array structures that produce giant enhancements in electromagnetic fields,” Chem. Phys. Lett. 403, 62–67 (2005).
[Crossref]

E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, “Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography,” Nano Lett. 5, 1065–1070 (2005).
[Crossref] [PubMed]

S. Zou and G. C. Schatz, “Narrow plasmonic/photonic extinction and scattering line shapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121, 12606–12612(2004).
[Crossref] [PubMed]

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93, 181108 (2008).
[Crossref]

Chem. Phys. Lett. (1)

S. Zou and G. C. Schatz, “Silver nanoparticle array structures that produce giant enhancements in electromagnetic fields,” Chem. Phys. Lett. 403, 62–67 (2005).
[Crossref]

IEEE Microwave Guided Wave Lett. (1)

J. R. Ren, O. P. Gandhi, L. R. Walker, J. Fraschilla, and C. R. Boerman, “Floquet-based FDTD analysis of two-dimensional phased array antennas,” IEEE Microwave Guided Wave Lett. 4, 109–111 (1994).
[Crossref]

IEEE Trans. Antennas Propag. (5)

A. Aminian and Y. Rahmat-Samii, “Spectral FDTD: a novel technique for the analysis of oblique incident plane wave on periodic structures,” IEEE Trans. Antennas Propag. 54, 1818–1825(2006).
[Crossref]

R. J. Luebbers, K. S. Kunz, M. Schneider, and F. Hunsberger, “A finite-difference time-domain near zone to far zone transformation,” IEEE Trans. Antennas Propag. 39, 429–433 (1991).
[Crossref]

P. Harms, R. Mittra, and W. Ko, “Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for FSS structures,” IEEE Trans. Antennas Propag. 42, 1317–1324 (1994).
[Crossref]

S. D. Gedney, “An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[Crossref]

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, “Time-domain analysis of periodic structures at oblique incidence: orthogonal and nonorthogonal FDTD implementations,” IEEE Trans. Microwave Theory Tech. 46, 420–427(1998).
[Crossref]

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

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Phys. Rev. E (2)

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Figures (8)

Fig. 1
Fig. 1

Cross section of one unit cell, incidence wave at arbitrary angle (θ) injected into the structure through the TF/SF planes. Scattered-field regions, PML, and NTFFT planes are marked.

Fig. 2
Fig. 2

Cross section of one unit cell and auxiliary grid for injecting an incidence wave through TF/SF.

Fig. 3
Fig. 3

Reflection (for TE polarization) of Au film ( 40 nm thick) suspended in air, comparison between numerical results of the SF-FDTD method using the Drude model for Au dispersion and analytical results. (a) Fixed wavelength λ = 800 nm , incidence angles from normal to 70 ° , stepped by 10 ° . (b) Incidence angle of 40 ° and wavelength varying from 650 to 1200 nm .

Fig. 4
Fig. 4

Reflection (for TM polarization) of Au film ( 40 nm thick) suspended in air, comparison between numerical results of the SF-FDTD method using the Drude model for Au dispersion and analytical results. (a) Fixed wavelength λ = 800 nm , incidence angles from normal to 70 ° , stepped by 10 ° . (b) Incidence angle of 40 ° and wavelength varying from 650 to 1200 nm .

Fig. 5
Fig. 5

Reflection (for TE polarization) of Au film ( 40 nm thick) suspended in air, comparison between numerical results of the SF-FDTD method using the Drude–Lorentz model for Au dispersion and analytical results. (a) Fixed wavelength λ = 800 nm , incidence angles from normal to 70 ° , stepped by 10 ° . (b) Incidence angle of 40 ° and wavelength varying from 500 to 1200 nm .

Fig. 6
Fig. 6

Reflection (for TM polarization) of Au film ( 40 nm thick) suspended in air, comparison between numerical results of the SF-FDTD method using the Drude–Lorentz model for Au dispersion and analytical results. (a) Fixed wavelength λ = 800 nm , incidence angles from normal to 70 ° stepped by 10 ° . (b) Incidence angle of 40 ° and wavelength varying from 500 to 1200 nm .

Fig. 7
Fig. 7

Cross section of nanodisk array. Nanodisks with diameter 180 nm and height 40 nm placed in a biperiodic array with 540 nm periodicity.

Fig. 8
Fig. 8

Nanodisk array (a) near-field intensity enhancement ( | E | 2 at a point near the top edge of the nanodisk in water, normalized to | E i | 2 , the field intensity at the same point in the absence of a nanodisk). (b) Extinction cross section of one unit cell of the nanodisk array. The incidence wave is a TE polarized plane wave with varying angle 0 ° 26 ° .

Equations (73)

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P ˘ = Ĕ exp [ j ( k y y + k z z ) ] ,
Q ˘ = H ˘ exp [ j ( k y y + k z z ) ] .
ε r c P x t = Q z y Q y z k ¯ y c Q z t + k ¯ z c Q y t ,
ε r c P y t = Q z x + Q x z k ¯ z c Q x t ,
ε r c P z t = Q y x Q x y + k ¯ y c Q x t ,
μ r c Q x t = P z y + P y z + k ¯ y c P z t k ¯ z c P y t ,
μ r c Q y t = P z x P x z + k ¯ z c P x t ,
μ r c Q z t = P y x + P x y k ¯ y c P x t .
P x = P x a + k ¯ z ε r Q y k ¯ y ε r Q z , Q x = Q x a k ¯ z μ r P y + k ¯ y μ r P z ,
P y = P y a k ¯ z ε r Q x , Q y = Q y a + k ¯ z μ r P x ,
P z = P z a + k ¯ y ε r Q x , Q z = Q z a k ¯ y μ r P x .
ε r c P x a t = Q z y Q y z ,
ε r c P y a t = Q z x + Q x z ,
ε r c P z a t = Q y x Q x y ,
μ r c Q x a t = P z y + P y z ,
μ r c Q y a t = P z x P x z ,
μ r c Q z a t = P y x + P x y .
( 1 k ¯ y 2 μ r ε r k ¯ z 2 μ r ε r ) P x = P x a + k ¯ z ε r Q y a k ¯ y ε r Q z a , ( 1 k ¯ y 2 μ r ε r k ¯ z 2 μ r ε r ) Q x = Q x a k ¯ z μ r P y a + k ¯ y μ r P z a ,
P y = P y a k ¯ z ε r Q x , Q y = Q y a + k ¯ z μ r P x ,
P z = P z a + k ¯ y ε r Q x , Q z = Q z a k ¯ y μ r P x .
ε r c P x t = k ¯ y c Q z t + k ¯ z c Q y t ,
ε r c P y t = Q z x k ¯ z c Q x t ,
ε r c P z t = Q y x + k ¯ y c Q x t ,
μ r c Q x t = k ¯ y c P z t k ¯ z c P y t ,
μ r c Q y t = P z x + k ¯ z c P x t ,
μ r c Q z t = P y x k ¯ y c P x t .
ε r c P y a t = Q z x ,
ε r c P z a t = Q y x ,
μ r c Q y a t = P z x ,
μ r c Q z a t = P y x .
sin ( θ m ) = m λ Λ + sin ( θ i ) ,
E far field , m ( t ) = 1 Λ 0 Λ P near field ( t , x ) exp ( j 2 π m Λ x ) d x .
E far field , m TE ( t ) = 1 Λ 0 Λ [ P x , near field ( t , x ) cos ( θ m ) P z , near field ( t , x ) sin ( θ m ) ] exp ( j 2 π m Λ x ) d x ,
E far field , m TM ( t ) = 1 Λ 0 Λ P y , near field ( t , x ) exp ( j 2 π m Λ x ) d x .
J ˘ s = × H ˘ s , M ˘ s = × Ĕ s ,
N ˘ = s J ˘ s exp ( j k r . ȓ ) d s = s × H ˘ s exp ( j k r . ȓ ) d s ,
L ˘ = s M ˘ s exp ( j k r . ȓ ) d s = s × E ˘ s exp ( j k r . ȓ ) d s .
W ˘ = j exp ( j k R ) N ˘ / ( 2 λ R ) ,
U ˘ = j exp ( j k R ) L ˘ / ( 2 λ R ) ,
W ( t ) = 1 4 π R c t [ s × H s ( t + r . ȓ R c ) d s ] ,
U ( t ) = 1 4 π R c t [ s × E s ( t + r . ȓ R c ) d s ] .
E θ ( t ) η 0 W θ ( t ) U φ ( t ) ,
E ϕ ( t ) η 0 W ϕ ( t ) + U θ ( t ) ,
H θ ( t ) W φ ( t ) U θ ( t ) / η 0 ,
H φ ( t ) W θ ( t ) U φ ( t ) / η 0 .
N ˘ = s × Q ˘ s exp ( j k ( k ¯ y y + k ¯ z z r . ȓ ) ) d s ,
L ˘ = s × P ˘ s exp ( j k ( k ¯ y y + k ¯ z z r . ȓ ) ) d s .
W ( t ) = 1 4 π R c t [ s × Q s ( t + r . ȓ R c k ¯ y y + k ¯ z z c ) d s ] ,
U ( t ) = 1 4 π R c t [ s × P s ( t + r . ȓ R c k ¯ y y + k ¯ z z c ) d s ] .
W a = A S · ȇ r d A .
S = 1 2 Re { Ĕ × H ˘ * } = S i + S s + S ext ,
S i = 1 2 Re { Ĕ i × H ˘ i * } , S s = 1 2 Re { Ĕ s × H ˘ s * } ,
S ext = 1 2 Re { Ĕ i × H ˘ s * + Ĕ s × H ˘ i * } .
W i = A S i · ȇ r d A W s = A S s · ȇ r d A W ext = A S ext · ȇ r d A
Ĕ s = exp ( j k R ) j k R T ˘ ,
C ext = 4 π k 2 | Ĕ i | 2 Re { ( Ĕ i * . T ˘ ) θ = θ i } ,
ε ( ω ) = ε p = 1 P ω p 2 ω 2 j ω γ p .
J ˘ p = j ω ε 0 ( ω p 2 ω 2 j ω γ p ) Ĕ .
G ˘ p = J ˘ p exp [ j ( k y y + k z z ) ] .
ω 2 G ˘ p j ω γ p G ˘ p = j ω ε 0 ω p 2 P ˘ .
G p t + γ p G p = ε 0 ω p 2 P .
ε c P x a t + G x = Q z y Q y z ,
ε c P y a t + G y = Q z x + Q x z ,
ε c P z a t + G z = Q y x Q x y .
G p n + 1 = G p n ( γ p Δ t ) G p n + 1 / 2 + ( ε 0 ω p 2 Δ t ) P n + 1 / 2 .
P x a n + 1 ( i , j , k ) = P x a n ( i , j , k ) + 1 ε [ T y ( Q z n + 1 / 2 ( i , j , k ) Q z n + 1 / 2 ( i , j 1 , k ) ) T z ( Q y n + 1 / 2 ( i , j , k ) Q y n + 1 / 2 ( i , j , k 1 ) ) c Δ t G x n + 1 / 2 ( i , j , k ) ] ,
P y a n + 1 ( i , j , k ) = P y a n ( i , j , k ) + 1 ε [ T z ( Q x n + 1 / 2 ( i , j , k ) Q x n + 1 / 2 ( i , j , k 1 ) ) T x ( Q z n + 1 / 2 ( i , j , k ) Q z n + 1 / 2 ( i 1 , j , k ) ) c Δ t G y n + 1 / 2 ( i , j , k ) ] ,
P z a n + 1 ( i , j , k ) = P z a n ( i , j , k ) + 1 ε [ T x ( Q y n + 1 / 2 ( i , j , k ) Q y n + 1 / 2 ( i 1 , j , k ) ) T y ( Q x n + 1 / 2 ( i , j , k ) Q x n + 1 / 2 ( i , j 1 , k ) ) c Δ t G z n + 1 / 2 ( i , j , k ) ] .
ε ( ω ) = ε ω D 2 ω 2 j ω γ D Δ ε ω L 2 ω 2 j ω Γ L ω L 2 ,
P ( ω ) · P * ( ω ) = E ( ω ) · E * ( ω ) .
λ 1 st L = Λ × n air × sin ( θ ) + Λ × n L ,
n glass > n ITO > n water > n air ,
λ 1 st glass > λ 1 st   ITO > λ 1 st water > λ 1 st air .

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