Abstract

In this study, we report the investigation of both near- and far-field electromagnetic characteristics of two-dimensional silver nanorod arrays embedded in anodic aluminum oxide with the use of a high-accuracy three-dimensional Legendre pseudospectral time-domain scheme. The simulated far-field scattering spectra agree with the experimental observations. We show that enhanced electric field is created between adjacent nanorods and, most importantly, far-field scattered light wave is mainly contributed from surface magnetic field, instead of the surface enhanced electric field. The identified near-field to far-field connection produces an important implication in the development of efficient surface-enhanced Raman scattering substrates.

© 2009 Optical Society of America

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    [CrossRef]
  3. T.-T. Liu, Y.-H. Lin, C.-S. Hung, T.-J. Liu, Y. Chen, Y.-C. Huang, T.-H. Tsai, H.-H. Wang, D.-W. Wang, J.-K. Wang, Y.-L. Wang, and C.-H. Lin, "A high speed detection platform based on surface-enhanced Raman scattering for monitoring antibiotic-induced chemical changes in bacteria cell wall," PloS One (in press).
  4. S. Biring, H.-H. Wang, J.-K. Wang, and Y.-L. Wang, "Light scattering from 2D arrays of monodispersed Ag nanoparticles separated by tunable nano-gaps: spectral evolution and analytical analysis of plasmonic coupling," Opt. Express 16,15312-15324 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  16. X. Ji, W. Cai, and P. Zhang, "High-order DGTD methods for dispersive Maxwell’s equations and modelling of silver nanowire couping," Int. J. Numer. Meth. Engng. 69, 308-325 (2007).
    [CrossRef]
  17. C.-H. Teng, B.-Y. Lin, H.-C. Chang, H.-C. Hsu, C.-N. Lin, and K.-A. Feng, "A Legendre Pseudospectral Penalty Scheme for Solving Time-Domain Maxwell’s Equations," J. Sci. Comput. 36,351-390 (2008).
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  21. M. H. Carpenter and C. A. Kennedy, "Fourth order 2N-storage Runge-Kutta scheme," NASA-TM-109112 (1994).
  22. M. H. Carpenter and D. Gottlieb and S. Abarbanel, and W. S. Don, "The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error," SIAM J. Sci. Comp. 16,1241-1252 (1995).
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  23. S. Abarbenel and D. Gottlieb, "On the construction and analysis of absorbing layer in CEM," Appl. Numer. Math. 27,331-340 (1998).
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  29. E. Hao and G. C. Schatz, "Electromagnetic fields around silver nanoparticles and dimmers," J. Chem. Phys. 120, 357-366 (2004).
    [CrossRef] [PubMed]
  30. L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles," Phys. Rev. B 71, 235408:1-7 (2006).
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    [CrossRef]
  32. T. Setälä, M. Kaivola, and A. T. Friberg, "Evanescent and propagating electromagnetic fields in scattering from point-dipole structures," J. Opt. Soc. Am. A 18, 678-688 (2001).
    [CrossRef]
  33. E. Wolf and J. T. Foley, "Do evanescent waves contribute to the far field?" Opt. Lett. 23, 16-18 (1998).
    [CrossRef]

2008 (5)

J. Zhao, A. O. Pinchuk, J. M. McMahon, A. Li, L. K. Ausman, A. L. Atkinson, and G. C. Schatz, "Methods for describing the electromagnetic properties of silver and gold Nanoparticles," Acc. Chem. Res. 41, 1710-1720 (2008).
[CrossRef] [PubMed]

C.-H. Teng, B.-Y. Lin, H.-C. Chang, H.-C. Hsu, C.-N. Lin, and K.-A. Feng, "A Legendre Pseudospectral Penalty Scheme for Solving Time-Domain Maxwell’s Equations," J. Sci. Comput. 36,351-390 (2008).
[CrossRef]

M. Pelton, J. Aizpurua, and G. Bryant, "Metal-nanoparticle plasmonics," Laser & Photon. Rev. 2, 136-159 (2008).
[CrossRef]

Y. C. Chang, J. Y. Chu, T. J. Wang, M. W. Lin, J. T. Yeh, and J.-K. Wang, "Fourier analysis of surface plasmon waves launched from single nanohole and nanohole arrays: unraveling tip-induced effects," Opt. Express 16, 740-747 (2008).
[CrossRef] [PubMed]

S. Biring, H.-H. Wang, J.-K. Wang, and Y.-L. Wang, "Light scattering from 2D arrays of monodispersed Ag nanoparticles separated by tunable nano-gaps: spectral evolution and analytical analysis of plasmonic coupling," Opt. Express 16,15312-15324 (2008).
[CrossRef] [PubMed]

2007 (2)

T. Yamaguchi and T. Hinata, "Optical near-field analysis of spherical metals: application of the FDTD method combined with the ADE method," Opt. Express 15, 11481-11491 (2007).
[CrossRef] [PubMed]

X. Ji, W. Cai, and P. Zhang, "High-order DGTD methods for dispersive Maxwell’s equations and modelling of silver nanowire couping," Int. J. Numer. Meth. Engng. 69, 308-325 (2007).
[CrossRef]

2006 (2)

H. H. Wang, C. Y. Liu, S. B. Wu, N. W. Liu, C. Y. Peng, T. H. Chan, C. F. Hsu, J. K. Wang, and Y. L. Wang, "Highly Raman-enhancing substrates based on silver nanoparticle arrays with tunable sub-10 nm gaps," Adv. Mater. 18, 491-495 (2006), and references therein.
[CrossRef]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles," Phys. Rev. B 71, 235408:1-7 (2006).

2005 (3)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98,011101-011110 (2005).
[CrossRef]

D. W. Thompson, "Optical characterization of porous alumina from vacuum ultraviolet to midinfrared," J. Appl. Phys. 97, 113511:1-9 (2005).
[CrossRef]

2004 (1)

E. Hao and G. C. Schatz, "Electromagnetic fields around silver nanoparticles and dimmers," J. Chem. Phys. 120, 357-366 (2004).
[CrossRef] [PubMed]

2001 (2)

T. Setälä, M. Kaivola, and A. T. Friberg, "Evanescent and propagating electromagnetic fields in scattering from point-dipole structures," J. Opt. Soc. Am. A 18, 678-688 (2001).
[CrossRef]

J. L. Young and R. O. Nelson, "A summary and systematic analysis of FDTD algorithms for linearly dispersive media," IEEE Antennas Propag. Mag. 43,61-77 (2001).
[CrossRef]

2000 (2)

S. R. Rengarajan and Y. Rahmat-Samii, "The field equivalence principle illustration of the establishment of the non-intuitive null fields," IEEE Antennas Propagat. Mag.,  42, 122-128 (2000).
[CrossRef]

R. M. Stöckle, Y. D. Suh, V. Deckert, and R. Zenobi, "Nanoscale chemical analysis by tip-enhanced Raman spectroscopy," Chem. Phys. Lett. 318, 131-136 (2000).
[CrossRef]

1999 (1)

S. Abarbenel and D. Gottlieb, and J. S. Hesthaven, "Well-posed perfectly matched layers for advective acoustics," J. Comput. Phys. 154,266-283 (1999).
[CrossRef]

1998 (2)

S. Abarbenel and D. Gottlieb, "On the construction and analysis of absorbing layer in CEM," Appl. Numer. Math. 27,331-340 (1998).
[CrossRef]

E. Wolf and J. T. Foley, "Do evanescent waves contribute to the far field?" Opt. Lett. 23, 16-18 (1998).
[CrossRef]

1995 (1)

M. H. Carpenter and D. Gottlieb and S. Abarbanel, and W. S. Don, "The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error," SIAM J. Sci. Comp. 16,1241-1252 (1995).
[CrossRef]

1994 (1)

1991 (1)

S. S. Zivanovic, K. S. Yee, and K. K. Mei, "A subgridding method for the time-domain finite-difference method to solve Maxwell’s equations," IEEE Trans. Microwave Theory Tech. 39, 471-479 (1991).
[CrossRef]

1972 (1)

H. O. Kreiss and J. Oliger, "Comparison of accurate methods for the integration of hyperbolic equations.Tellus,"  24, 199-215 (1972).

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]

1908 (1)

G. Mie, "Contributions to the optics of turbid media, especially colloidal metal solutions," Ann. Phys. 25, 377-445, (1908).
[CrossRef]

Abarbanel, S.

M. H. Carpenter and D. Gottlieb and S. Abarbanel, and W. S. Don, "The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error," SIAM J. Sci. Comp. 16,1241-1252 (1995).
[CrossRef]

Abarbenel, S.

S. Abarbenel and D. Gottlieb, and J. S. Hesthaven, "Well-posed perfectly matched layers for advective acoustics," J. Comput. Phys. 154,266-283 (1999).
[CrossRef]

S. Abarbenel and D. Gottlieb, "On the construction and analysis of absorbing layer in CEM," Appl. Numer. Math. 27,331-340 (1998).
[CrossRef]

Aizpurua, J.

M. Pelton, J. Aizpurua, and G. Bryant, "Metal-nanoparticle plasmonics," Laser & Photon. Rev. 2, 136-159 (2008).
[CrossRef]

Atkinson, A. L.

J. Zhao, A. O. Pinchuk, J. M. McMahon, A. Li, L. K. Ausman, A. L. Atkinson, and G. C. Schatz, "Methods for describing the electromagnetic properties of silver and gold Nanoparticles," Acc. Chem. Res. 41, 1710-1720 (2008).
[CrossRef] [PubMed]

Atwater, H. A.

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles," Phys. Rev. B 71, 235408:1-7 (2006).

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98,011101-011110 (2005).
[CrossRef]

Ausman, L. K.

J. Zhao, A. O. Pinchuk, J. M. McMahon, A. Li, L. K. Ausman, A. L. Atkinson, and G. C. Schatz, "Methods for describing the electromagnetic properties of silver and gold Nanoparticles," Acc. Chem. Res. 41, 1710-1720 (2008).
[CrossRef] [PubMed]

Biring, S.

Bryant, G.

M. Pelton, J. Aizpurua, and G. Bryant, "Metal-nanoparticle plasmonics," Laser & Photon. Rev. 2, 136-159 (2008).
[CrossRef]

Cai, W.

X. Ji, W. Cai, and P. Zhang, "High-order DGTD methods for dispersive Maxwell’s equations and modelling of silver nanowire couping," Int. J. Numer. Meth. Engng. 69, 308-325 (2007).
[CrossRef]

Carpenter, M. H.

M. H. Carpenter and D. Gottlieb and S. Abarbanel, and W. S. Don, "The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error," SIAM J. Sci. Comp. 16,1241-1252 (1995).
[CrossRef]

M. H. Carpenter and C. A. Kennedy, "Fourth order 2N-storage Runge-Kutta scheme," NASA-TM-109112 (1994).

Chan, T. H.

H. H. Wang, C. Y. Liu, S. B. Wu, N. W. Liu, C. Y. Peng, T. H. Chan, C. F. Hsu, J. K. Wang, and Y. L. Wang, "Highly Raman-enhancing substrates based on silver nanoparticle arrays with tunable sub-10 nm gaps," Adv. Mater. 18, 491-495 (2006), and references therein.
[CrossRef]

Chang, H.-C.

C.-H. Teng, B.-Y. Lin, H.-C. Chang, H.-C. Hsu, C.-N. Lin, and K.-A. Feng, "A Legendre Pseudospectral Penalty Scheme for Solving Time-Domain Maxwell’s Equations," J. Sci. Comput. 36,351-390 (2008).
[CrossRef]

Chang, Y. C.

Chen, Y.

T.-T. Liu, Y.-H. Lin, C.-S. Hung, T.-J. Liu, Y. Chen, Y.-C. Huang, T.-H. Tsai, H.-H. Wang, D.-W. Wang, J.-K. Wang, Y.-L. Wang, and C.-H. Lin, "A high speed detection platform based on surface-enhanced Raman scattering for monitoring antibiotic-induced chemical changes in bacteria cell wall," PloS One (in press).

Chu, J. Y.

Deckert, V.

R. M. Stöckle, Y. D. Suh, V. Deckert, and R. Zenobi, "Nanoscale chemical analysis by tip-enhanced Raman spectroscopy," Chem. Phys. Lett. 318, 131-136 (2000).
[CrossRef]

Don, W. S.

M. H. Carpenter and D. Gottlieb and S. Abarbanel, and W. S. Don, "The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error," SIAM J. Sci. Comp. 16,1241-1252 (1995).
[CrossRef]

Draine, B. T.

Feng, K.-A.

C.-H. Teng, B.-Y. Lin, H.-C. Chang, H.-C. Hsu, C.-N. Lin, and K.-A. Feng, "A Legendre Pseudospectral Penalty Scheme for Solving Time-Domain Maxwell’s Equations," J. Sci. Comput. 36,351-390 (2008).
[CrossRef]

Flatau, P. J.

Foley, J. T.

Fort, E.

E. Fort and S. Grésillon, "Surface enhanced fluorescence," J. Phys. D 41, 013001:1-31 (2008).
[CrossRef]

Friberg, A. T.

Gottlieb, D.

S. Abarbenel and D. Gottlieb, and J. S. Hesthaven, "Well-posed perfectly matched layers for advective acoustics," J. Comput. Phys. 154,266-283 (1999).
[CrossRef]

S. Abarbenel and D. Gottlieb, "On the construction and analysis of absorbing layer in CEM," Appl. Numer. Math. 27,331-340 (1998).
[CrossRef]

M. H. Carpenter and D. Gottlieb and S. Abarbanel, and W. S. Don, "The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error," SIAM J. Sci. Comp. 16,1241-1252 (1995).
[CrossRef]

Grésillon, S.

E. Fort and S. Grésillon, "Surface enhanced fluorescence," J. Phys. D 41, 013001:1-31 (2008).
[CrossRef]

Hao, E.

E. Hao and G. C. Schatz, "Electromagnetic fields around silver nanoparticles and dimmers," J. Chem. Phys. 120, 357-366 (2004).
[CrossRef] [PubMed]

Hesthaven, J. S.

S. Abarbenel and D. Gottlieb, and J. S. Hesthaven, "Well-posed perfectly matched layers for advective acoustics," J. Comput. Phys. 154,266-283 (1999).
[CrossRef]

Hinata, T.

Hsu, C. F.

H. H. Wang, C. Y. Liu, S. B. Wu, N. W. Liu, C. Y. Peng, T. H. Chan, C. F. Hsu, J. K. Wang, and Y. L. Wang, "Highly Raman-enhancing substrates based on silver nanoparticle arrays with tunable sub-10 nm gaps," Adv. Mater. 18, 491-495 (2006), and references therein.
[CrossRef]

Hsu, H.-C.

C.-H. Teng, B.-Y. Lin, H.-C. Chang, H.-C. Hsu, C.-N. Lin, and K.-A. Feng, "A Legendre Pseudospectral Penalty Scheme for Solving Time-Domain Maxwell’s Equations," J. Sci. Comput. 36,351-390 (2008).
[CrossRef]

Huang, Y.-C.

T.-T. Liu, Y.-H. Lin, C.-S. Hung, T.-J. Liu, Y. Chen, Y.-C. Huang, T.-H. Tsai, H.-H. Wang, D.-W. Wang, J.-K. Wang, Y.-L. Wang, and C.-H. Lin, "A high speed detection platform based on surface-enhanced Raman scattering for monitoring antibiotic-induced chemical changes in bacteria cell wall," PloS One (in press).

Hung, C.-S.

T.-T. Liu, Y.-H. Lin, C.-S. Hung, T.-J. Liu, Y. Chen, Y.-C. Huang, T.-H. Tsai, H.-H. Wang, D.-W. Wang, J.-K. Wang, Y.-L. Wang, and C.-H. Lin, "A high speed detection platform based on surface-enhanced Raman scattering for monitoring antibiotic-induced chemical changes in bacteria cell wall," PloS One (in press).

Ji, X.

X. Ji, W. Cai, and P. Zhang, "High-order DGTD methods for dispersive Maxwell’s equations and modelling of silver nanowire couping," Int. J. Numer. Meth. Engng. 69, 308-325 (2007).
[CrossRef]

Kaivola, M.

Kennedy, C. A.

M. H. Carpenter and C. A. Kennedy, "Fourth order 2N-storage Runge-Kutta scheme," NASA-TM-109112 (1994).

Kreiss, H. O.

H. O. Kreiss and J. Oliger, "Comparison of accurate methods for the integration of hyperbolic equations.Tellus,"  24, 199-215 (1972).

Li, A.

J. Zhao, A. O. Pinchuk, J. M. McMahon, A. Li, L. K. Ausman, A. L. Atkinson, and G. C. Schatz, "Methods for describing the electromagnetic properties of silver and gold Nanoparticles," Acc. Chem. Res. 41, 1710-1720 (2008).
[CrossRef] [PubMed]

Lin, B.-Y.

C.-H. Teng, B.-Y. Lin, H.-C. Chang, H.-C. Hsu, C.-N. Lin, and K.-A. Feng, "A Legendre Pseudospectral Penalty Scheme for Solving Time-Domain Maxwell’s Equations," J. Sci. Comput. 36,351-390 (2008).
[CrossRef]

Lin, C.-H.

T.-T. Liu, Y.-H. Lin, C.-S. Hung, T.-J. Liu, Y. Chen, Y.-C. Huang, T.-H. Tsai, H.-H. Wang, D.-W. Wang, J.-K. Wang, Y.-L. Wang, and C.-H. Lin, "A high speed detection platform based on surface-enhanced Raman scattering for monitoring antibiotic-induced chemical changes in bacteria cell wall," PloS One (in press).

Lin, C.-N.

C.-H. Teng, B.-Y. Lin, H.-C. Chang, H.-C. Hsu, C.-N. Lin, and K.-A. Feng, "A Legendre Pseudospectral Penalty Scheme for Solving Time-Domain Maxwell’s Equations," J. Sci. Comput. 36,351-390 (2008).
[CrossRef]

Lin, M. W.

Lin, Y.-H.

T.-T. Liu, Y.-H. Lin, C.-S. Hung, T.-J. Liu, Y. Chen, Y.-C. Huang, T.-H. Tsai, H.-H. Wang, D.-W. Wang, J.-K. Wang, Y.-L. Wang, and C.-H. Lin, "A high speed detection platform based on surface-enhanced Raman scattering for monitoring antibiotic-induced chemical changes in bacteria cell wall," PloS One (in press).

Liu, C. Y.

H. H. Wang, C. Y. Liu, S. B. Wu, N. W. Liu, C. Y. Peng, T. H. Chan, C. F. Hsu, J. K. Wang, and Y. L. Wang, "Highly Raman-enhancing substrates based on silver nanoparticle arrays with tunable sub-10 nm gaps," Adv. Mater. 18, 491-495 (2006), and references therein.
[CrossRef]

Liu, N. W.

H. H. Wang, C. Y. Liu, S. B. Wu, N. W. Liu, C. Y. Peng, T. H. Chan, C. F. Hsu, J. K. Wang, and Y. L. Wang, "Highly Raman-enhancing substrates based on silver nanoparticle arrays with tunable sub-10 nm gaps," Adv. Mater. 18, 491-495 (2006), and references therein.
[CrossRef]

Liu, T.-J.

T.-T. Liu, Y.-H. Lin, C.-S. Hung, T.-J. Liu, Y. Chen, Y.-C. Huang, T.-H. Tsai, H.-H. Wang, D.-W. Wang, J.-K. Wang, Y.-L. Wang, and C.-H. Lin, "A high speed detection platform based on surface-enhanced Raman scattering for monitoring antibiotic-induced chemical changes in bacteria cell wall," PloS One (in press).

Liu, T.-T.

T.-T. Liu, Y.-H. Lin, C.-S. Hung, T.-J. Liu, Y. Chen, Y.-C. Huang, T.-H. Tsai, H.-H. Wang, D.-W. Wang, J.-K. Wang, Y.-L. Wang, and C.-H. Lin, "A high speed detection platform based on surface-enhanced Raman scattering for monitoring antibiotic-induced chemical changes in bacteria cell wall," PloS One (in press).

Maier, S. A.

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles," Phys. Rev. B 71, 235408:1-7 (2006).

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98,011101-011110 (2005).
[CrossRef]

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

McMahon, J. M.

J. Zhao, A. O. Pinchuk, J. M. McMahon, A. Li, L. K. Ausman, A. L. Atkinson, and G. C. Schatz, "Methods for describing the electromagnetic properties of silver and gold Nanoparticles," Acc. Chem. Res. 41, 1710-1720 (2008).
[CrossRef] [PubMed]

Mei, K. K.

S. S. Zivanovic, K. S. Yee, and K. K. Mei, "A subgridding method for the time-domain finite-difference method to solve Maxwell’s equations," IEEE Trans. Microwave Theory Tech. 39, 471-479 (1991).
[CrossRef]

Mie, G.

G. Mie, "Contributions to the optics of turbid media, especially colloidal metal solutions," Ann. Phys. 25, 377-445, (1908).
[CrossRef]

Nelson, R. O.

J. L. Young and R. O. Nelson, "A summary and systematic analysis of FDTD algorithms for linearly dispersive media," IEEE Antennas Propag. Mag. 43,61-77 (2001).
[CrossRef]

Oliger, J.

H. O. Kreiss and J. Oliger, "Comparison of accurate methods for the integration of hyperbolic equations.Tellus,"  24, 199-215 (1972).

Pelton, M.

M. Pelton, J. Aizpurua, and G. Bryant, "Metal-nanoparticle plasmonics," Laser & Photon. Rev. 2, 136-159 (2008).
[CrossRef]

Peng, C. Y.

H. H. Wang, C. Y. Liu, S. B. Wu, N. W. Liu, C. Y. Peng, T. H. Chan, C. F. Hsu, J. K. Wang, and Y. L. Wang, "Highly Raman-enhancing substrates based on silver nanoparticle arrays with tunable sub-10 nm gaps," Adv. Mater. 18, 491-495 (2006), and references therein.
[CrossRef]

Penninkhof, J. J.

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles," Phys. Rev. B 71, 235408:1-7 (2006).

Pinchuk, A. O.

J. Zhao, A. O. Pinchuk, J. M. McMahon, A. Li, L. K. Ausman, A. L. Atkinson, and G. C. Schatz, "Methods for describing the electromagnetic properties of silver and gold Nanoparticles," Acc. Chem. Res. 41, 1710-1720 (2008).
[CrossRef] [PubMed]

Polman, A.

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles," Phys. Rev. B 71, 235408:1-7 (2006).

Rahmat-Samii, Y.

S. R. Rengarajan and Y. Rahmat-Samii, "The field equivalence principle illustration of the establishment of the non-intuitive null fields," IEEE Antennas Propagat. Mag.,  42, 122-128 (2000).
[CrossRef]

Rengarajan, S. R.

S. R. Rengarajan and Y. Rahmat-Samii, "The field equivalence principle illustration of the establishment of the non-intuitive null fields," IEEE Antennas Propagat. Mag.,  42, 122-128 (2000).
[CrossRef]

Schatz, G. C.

J. Zhao, A. O. Pinchuk, J. M. McMahon, A. Li, L. K. Ausman, A. L. Atkinson, and G. C. Schatz, "Methods for describing the electromagnetic properties of silver and gold Nanoparticles," Acc. Chem. Res. 41, 1710-1720 (2008).
[CrossRef] [PubMed]

E. Hao and G. C. Schatz, "Electromagnetic fields around silver nanoparticles and dimmers," J. Chem. Phys. 120, 357-366 (2004).
[CrossRef] [PubMed]

Setälä, T.

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

Stöckle, R. M.

R. M. Stöckle, Y. D. Suh, V. Deckert, and R. Zenobi, "Nanoscale chemical analysis by tip-enhanced Raman spectroscopy," Chem. Phys. Lett. 318, 131-136 (2000).
[CrossRef]

Suh, Y. D.

R. M. Stöckle, Y. D. Suh, V. Deckert, and R. Zenobi, "Nanoscale chemical analysis by tip-enhanced Raman spectroscopy," Chem. Phys. Lett. 318, 131-136 (2000).
[CrossRef]

Sweatlock, L. A.

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles," Phys. Rev. B 71, 235408:1-7 (2006).

Teng, C.-H.

C.-H. Teng, B.-Y. Lin, H.-C. Chang, H.-C. Hsu, C.-N. Lin, and K.-A. Feng, "A Legendre Pseudospectral Penalty Scheme for Solving Time-Domain Maxwell’s Equations," J. Sci. Comput. 36,351-390 (2008).
[CrossRef]

Thompson, D. W.

D. W. Thompson, "Optical characterization of porous alumina from vacuum ultraviolet to midinfrared," J. Appl. Phys. 97, 113511:1-9 (2005).
[CrossRef]

Tsai, T.-H.

T.-T. Liu, Y.-H. Lin, C.-S. Hung, T.-J. Liu, Y. Chen, Y.-C. Huang, T.-H. Tsai, H.-H. Wang, D.-W. Wang, J.-K. Wang, Y.-L. Wang, and C.-H. Lin, "A high speed detection platform based on surface-enhanced Raman scattering for monitoring antibiotic-induced chemical changes in bacteria cell wall," PloS One (in press).

Wang, D.-W.

T.-T. Liu, Y.-H. Lin, C.-S. Hung, T.-J. Liu, Y. Chen, Y.-C. Huang, T.-H. Tsai, H.-H. Wang, D.-W. Wang, J.-K. Wang, Y.-L. Wang, and C.-H. Lin, "A high speed detection platform based on surface-enhanced Raman scattering for monitoring antibiotic-induced chemical changes in bacteria cell wall," PloS One (in press).

Wang, H. H.

H. H. Wang, C. Y. Liu, S. B. Wu, N. W. Liu, C. Y. Peng, T. H. Chan, C. F. Hsu, J. K. Wang, and Y. L. Wang, "Highly Raman-enhancing substrates based on silver nanoparticle arrays with tunable sub-10 nm gaps," Adv. Mater. 18, 491-495 (2006), and references therein.
[CrossRef]

Wang, H.-H.

S. Biring, H.-H. Wang, J.-K. Wang, and Y.-L. Wang, "Light scattering from 2D arrays of monodispersed Ag nanoparticles separated by tunable nano-gaps: spectral evolution and analytical analysis of plasmonic coupling," Opt. Express 16,15312-15324 (2008).
[CrossRef] [PubMed]

T.-T. Liu, Y.-H. Lin, C.-S. Hung, T.-J. Liu, Y. Chen, Y.-C. Huang, T.-H. Tsai, H.-H. Wang, D.-W. Wang, J.-K. Wang, Y.-L. Wang, and C.-H. Lin, "A high speed detection platform based on surface-enhanced Raman scattering for monitoring antibiotic-induced chemical changes in bacteria cell wall," PloS One (in press).

Wang, J. K.

H. H. Wang, C. Y. Liu, S. B. Wu, N. W. Liu, C. Y. Peng, T. H. Chan, C. F. Hsu, J. K. Wang, and Y. L. Wang, "Highly Raman-enhancing substrates based on silver nanoparticle arrays with tunable sub-10 nm gaps," Adv. Mater. 18, 491-495 (2006), and references therein.
[CrossRef]

Wang, J.-K.

Wang, T. J.

Wang, Y. L.

H. H. Wang, C. Y. Liu, S. B. Wu, N. W. Liu, C. Y. Peng, T. H. Chan, C. F. Hsu, J. K. Wang, and Y. L. Wang, "Highly Raman-enhancing substrates based on silver nanoparticle arrays with tunable sub-10 nm gaps," Adv. Mater. 18, 491-495 (2006), and references therein.
[CrossRef]

Wang, Y.-L.

S. Biring, H.-H. Wang, J.-K. Wang, and Y.-L. Wang, "Light scattering from 2D arrays of monodispersed Ag nanoparticles separated by tunable nano-gaps: spectral evolution and analytical analysis of plasmonic coupling," Opt. Express 16,15312-15324 (2008).
[CrossRef] [PubMed]

T.-T. Liu, Y.-H. Lin, C.-S. Hung, T.-J. Liu, Y. Chen, Y.-C. Huang, T.-H. Tsai, H.-H. Wang, D.-W. Wang, J.-K. Wang, Y.-L. Wang, and C.-H. Lin, "A high speed detection platform based on surface-enhanced Raman scattering for monitoring antibiotic-induced chemical changes in bacteria cell wall," PloS One (in press).

Wolf, E.

Wu, S. B.

H. H. Wang, C. Y. Liu, S. B. Wu, N. W. Liu, C. Y. Peng, T. H. Chan, C. F. Hsu, J. K. Wang, and Y. L. Wang, "Highly Raman-enhancing substrates based on silver nanoparticle arrays with tunable sub-10 nm gaps," Adv. Mater. 18, 491-495 (2006), and references therein.
[CrossRef]

Yamaguchi, T.

Yee, K. S.

S. S. Zivanovic, K. S. Yee, and K. K. Mei, "A subgridding method for the time-domain finite-difference method to solve Maxwell’s equations," IEEE Trans. Microwave Theory Tech. 39, 471-479 (1991).
[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]

Yeh, J. T.

Young, J. L.

J. L. Young and R. O. Nelson, "A summary and systematic analysis of FDTD algorithms for linearly dispersive media," IEEE Antennas Propag. Mag. 43,61-77 (2001).
[CrossRef]

Zayats, A. V.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

Zenobi, R.

R. M. Stöckle, Y. D. Suh, V. Deckert, and R. Zenobi, "Nanoscale chemical analysis by tip-enhanced Raman spectroscopy," Chem. Phys. Lett. 318, 131-136 (2000).
[CrossRef]

Zhang, P.

X. Ji, W. Cai, and P. Zhang, "High-order DGTD methods for dispersive Maxwell’s equations and modelling of silver nanowire couping," Int. J. Numer. Meth. Engng. 69, 308-325 (2007).
[CrossRef]

Zhao, J.

J. Zhao, A. O. Pinchuk, J. M. McMahon, A. Li, L. K. Ausman, A. L. Atkinson, and G. C. Schatz, "Methods for describing the electromagnetic properties of silver and gold Nanoparticles," Acc. Chem. Res. 41, 1710-1720 (2008).
[CrossRef] [PubMed]

Zivanovic, S. S.

S. S. Zivanovic, K. S. Yee, and K. K. Mei, "A subgridding method for the time-domain finite-difference method to solve Maxwell’s equations," IEEE Trans. Microwave Theory Tech. 39, 471-479 (1991).
[CrossRef]

Acc. Chem. Res. (1)

J. Zhao, A. O. Pinchuk, J. M. McMahon, A. Li, L. K. Ausman, A. L. Atkinson, and G. C. Schatz, "Methods for describing the electromagnetic properties of silver and gold Nanoparticles," Acc. Chem. Res. 41, 1710-1720 (2008).
[CrossRef] [PubMed]

Adv. Mater. (1)

H. H. Wang, C. Y. Liu, S. B. Wu, N. W. Liu, C. Y. Peng, T. H. Chan, C. F. Hsu, J. K. Wang, and Y. L. Wang, "Highly Raman-enhancing substrates based on silver nanoparticle arrays with tunable sub-10 nm gaps," Adv. Mater. 18, 491-495 (2006), and references therein.
[CrossRef]

Ann. Phys. (1)

G. Mie, "Contributions to the optics of turbid media, especially colloidal metal solutions," Ann. Phys. 25, 377-445, (1908).
[CrossRef]

Appl. Numer. Math. (1)

S. Abarbenel and D. Gottlieb, "On the construction and analysis of absorbing layer in CEM," Appl. Numer. Math. 27,331-340 (1998).
[CrossRef]

Chem. Phys. Lett. (1)

R. M. Stöckle, Y. D. Suh, V. Deckert, and R. Zenobi, "Nanoscale chemical analysis by tip-enhanced Raman spectroscopy," Chem. Phys. Lett. 318, 131-136 (2000).
[CrossRef]

IEEE Antennas Propag. Mag. (1)

J. L. Young and R. O. Nelson, "A summary and systematic analysis of FDTD algorithms for linearly dispersive media," IEEE Antennas Propag. Mag. 43,61-77 (2001).
[CrossRef]

IEEE Antennas Propagat. Mag. (1)

S. R. Rengarajan and Y. Rahmat-Samii, "The field equivalence principle illustration of the establishment of the non-intuitive null fields," IEEE Antennas Propagat. Mag.,  42, 122-128 (2000).
[CrossRef]

IEEE Trans. Antennas Propag. (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]

IEEE Trans. Microwave Theory Tech. (1)

S. S. Zivanovic, K. S. Yee, and K. K. Mei, "A subgridding method for the time-domain finite-difference method to solve Maxwell’s equations," IEEE Trans. Microwave Theory Tech. 39, 471-479 (1991).
[CrossRef]

Int. J. Numer. Meth. Engng. (1)

X. Ji, W. Cai, and P. Zhang, "High-order DGTD methods for dispersive Maxwell’s equations and modelling of silver nanowire couping," Int. J. Numer. Meth. Engng. 69, 308-325 (2007).
[CrossRef]

J. Appl. Phys. (2)

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98,011101-011110 (2005).
[CrossRef]

D. W. Thompson, "Optical characterization of porous alumina from vacuum ultraviolet to midinfrared," J. Appl. Phys. 97, 113511:1-9 (2005).
[CrossRef]

J. Chem. Phys. (1)

E. Hao and G. C. Schatz, "Electromagnetic fields around silver nanoparticles and dimmers," J. Chem. Phys. 120, 357-366 (2004).
[CrossRef] [PubMed]

J. Comput. Phys. (1)

S. Abarbenel and D. Gottlieb, and J. S. Hesthaven, "Well-posed perfectly matched layers for advective acoustics," J. Comput. Phys. 154,266-283 (1999).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Sci. Comput. (1)

C.-H. Teng, B.-Y. Lin, H.-C. Chang, H.-C. Hsu, C.-N. Lin, and K.-A. Feng, "A Legendre Pseudospectral Penalty Scheme for Solving Time-Domain Maxwell’s Equations," J. Sci. Comput. 36,351-390 (2008).
[CrossRef]

Laser & Photon. Rev. (1)

M. Pelton, J. Aizpurua, and G. Bryant, "Metal-nanoparticle plasmonics," Laser & Photon. Rev. 2, 136-159 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rep. (1)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

Phys. Rev. B (1)

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles," Phys. Rev. B 71, 235408:1-7 (2006).

PloS One (1)

T.-T. Liu, Y.-H. Lin, C.-S. Hung, T.-J. Liu, Y. Chen, Y.-C. Huang, T.-H. Tsai, H.-H. Wang, D.-W. Wang, J.-K. Wang, Y.-L. Wang, and C.-H. Lin, "A high speed detection platform based on surface-enhanced Raman scattering for monitoring antibiotic-induced chemical changes in bacteria cell wall," PloS One (in press).

SIAM J. Sci. Comp. (1)

M. H. Carpenter and D. Gottlieb and S. Abarbanel, and W. S. Don, "The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error," SIAM J. Sci. Comp. 16,1241-1252 (1995).
[CrossRef]

Tellus (1)

H. O. Kreiss and J. Oliger, "Comparison of accurate methods for the integration of hyperbolic equations.Tellus,"  24, 199-215 (1972).

Other (6)

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method (Artech House, Boston, 2005).

D. W. Lynch and W. R. Hunter, "Silver (Ag)" in Handbook of optical constants of solids, E. D. Palik, ed. (Academic Press, Orlando, 1985), pp. 350-357.

E. Fort and S. Grésillon, "Surface enhanced fluorescence," J. Phys. D 41, 013001:1-31 (2008).
[CrossRef]

M. H. Carpenter and C. A. Kennedy, "Fourth order 2N-storage Runge-Kutta scheme," NASA-TM-109112 (1994).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999), pp. 724-726.

R. S. Elliott, Antenna theory and design (Prentice-Hall, New Jersey, 1981), pp. 114-117.

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Figures (13)

Fig. 1.
Fig. 1.

Top-view scanning electron microscopy image (a) and top-view (b) and side-view (c) schematic diagrams of Ag/AAO substrate. The blue arrow represents the electric field direction of incident light wave. PBC and PBC1~3 represent periodic boundary conditions. D and L are the diameter and length of Ag nanorods, respectively, while W is the gap between adjacent nanorods. S is the distance from the bottom of the Ag nanorod to the bottom surface of alumina. ε 0, ε 1 and ε 2 are dielectric functions of vacuum, alumina, and silver, respectively. Orange line represents the top surface of the substrate.

Fig. 2.
Fig. 2.

(a) Top-view and (b) side-view of mesh scheme of single unit cell used in calculation. The diameter and the length of the Ag nanorod are 25 and 100 nm, respectively, and the inter-nanorod gap is 25 nm.

Fig. 3.
Fig. 3.

Incident-and-scattering geometry over an array of Ag nanorods arranged in a hexagonal pattern. k i and k o are the wave vectors of incident and scattered waves, respectively. θ is scattering collection angle.

Fig. 4.
Fig. 4.

(a) Bistatic scattering cross section ( σSC ) νs. observation angle, θ, for a silver sphere with a diameter of 25 nm at ϕ = 0° and (b) errors (∣ΔσSC ∣ ) for N = 13 (red line) and 15 (green line).

Fig. 5.
Fig. 5.

Maximal (a) electric and (b) magnetic fields (∣Emaxand ∣Hmax, respectively) on the surface of a silver sphere embedded in alumina as a function of wavelength, λ. The diameter of the sphere is 25 nm. Black lines represent calculated results based on the dielectric function of silver, red lines represent that based on fitted Drude-Lorentz model, and blue lines represent the difference between them (∣ΔE∣ and ∣ΔH∣).

Fig. 6.
Fig. 6.

Normalized scattering intensity spectra in (a) x-polarized and (b) y-polarized excitation schemes of Ag nanorod arrays with five different inter-nanorod gaps: 5 (brown lines), 10 (red lines), 15 (orange lines), 20 (green lines) and 25 nm (blue lines).

Fig. 7.
Fig. 7.

Scattering intensity contribution of surface current densities in x-polarized excitation scheme as a function of wavelength, λ: (a) J⃗ and (b) M⃗ ; corresponding one in y-polarized excitation scheme: (c) J⃗ and (d) M⃗. Red lines represent the x-component, Green lines represent the y-component, and blue lines represent the z-component.

Fig. 8.
Fig. 8.

Surface field distribution of Ag nanorod array with W = 25 nm at λ = 626 nm in x-polarized excitation scheme: (a) electric and (b) magnetic field, and corresponding ones in y-polarized excitation scheme: (c) electric and (d) magnetic field.

Fig. 9.
Fig. 9.

Surface field distribution of Ag nanorod array with W = 25 nm at λ = 629 nm in x-polarized excitation scheme: (a) electric and (b) magnetic field, and corresponding ones in y-polarized excitation scheme: (c) electric and (d) magnetic field.

Fig. 10.
Fig. 10.

Average energy densities, ℰ, on the top surface of the Ag nanorod arrays as a function of the inter-nanorod gap, W, at resonance corresponding to surface electric (open squares) and magnetic field (filled circles) in x-polarized (a) and y-polarized (b) excitation schemes.

Fig. 11.
Fig. 11.

Scattering intensity spectra from ∣Jx ∣ on top surface of aluminum oxide, ISC (AlOx), and silver rod, ISC (Ag), in x-polarized, (a) and (b), and y-polarized excitation scheme, (c) and (d), for five different inter-nanorod gaps: 5 (brown lines), 10 (red lines), 15 (orange lines), 20 (green lines), 25 nm (blue lines).

Fig. 12.
Fig. 12.

Cross-sectional views of (a) electric and (b) magnetic fields at resonance of Ag nanorod array with W = 5 nm in x-polarized excitation scheme and corresponding ones of (c) electric and (d) magnetic fields in y-polarized excitation scheme. Orange lines represent vacuum-Ag interface; blue lines represent vacuum-AlOx interface; red lines represent Ag-AlOx interface.

Fig. A1.
Fig. A1.

Real (a) and imaginary (b) parts of relative permittivity, ε, of silver from 0.2 to 1.0 μm. Black lines represent experimental data, red lines represent the best-fit curve based on Drude-Lorentz model, and blue lines represent relative differences in percentage between them.

Equations (25)

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

εDL(ω)=ε ωp2ω(ω+i/τD) +s=1νfsωp2(ωs2ω2)Γs,
×H=ε t E +s=12tPs+J,
×E=μt H ,
·E=1εs=12·Ps,
and·H=0
tJ+τD1J=ωp2 E
and2t2Ps+ΓstPs+ωs2Ps=fsωp2 E {s=1and2} ,
Mijk(1)qijk(1)t=η=13Aη(1) qijk(1)ξηC(1) qijk(2)χ2Pijk,
Mijk(2)qijk(2)t=C(2) qijk(1) C(3) qijk(2) ,
whereqijk(1)(t)=(Ex,Ey,Ez,Hx,Hy,Hz)T (ξijk,t) ,
qijk(2)(t)=(Jx,Jy,Jz,Qx,1,Qy,1,Qz,1,Qx,2,Qy,2,Qz,2,Px,1,Py,1,Pz,1,Px,2,Py,2,Pz,2)T(ξijk,t),
Aη(1)=[0000δη3δη2000δη30δη1000δη2δη100δη3δη2000δη30δη1000δη2δη10000],
C(1)=(I3×3I3×3I3×3I3×603×303×303×303×6) , C(2)={[ωp2]3×3[f1ωp2]3×3[f2ωp2]3×306×303×303×303×306×3}T,
andC(3)=([τ1]3×303×303×303×303×303×3[Γ1]3×303×3[ω22]3×303×303×303×3[Γ2]3×303×3[ω22]3×303×3I3×303×303×303×303×303×3I3×303×303×3),
J=n̂×H
andM=n̂×E,
σSC(k,θ,ϕ)limR(4πR2PSCPIN)=k28πη0PIN(Lϕ+η0Nθ2+Lθn0Nϕ2)
withNθ=S(Jxcosθcosϕ+JycosθsinϕJzsinθ)×ejk(r̂·r̂0)Θ(k,θ,ϕ)ds,
Nϕ=S(Jxsinϕ+Jycosϕ×ejk(r̂·r̂0)Θ(k,θ,ϕ)ds,
Lθ=S (Mxcosθcosϕ+MycosθsinϕMzsinθ)×ejk(r̂·r̂0)Θ(k,θ,ϕ)ds,
andLϕ=S(Mxsinϕ+Mycosϕ)×ejk(r̂·r̂0)Θ(k,θ,ϕ)ds,
Θ(k,θ,ϕ)=limNm=NNn=NNAexp(jksinθ[(ma+nacos60°sinϕ)]),
=12s ε0 E2 ds / S ds or 12 S μ0 H2 ds / S ds ,
Ψ=j({Re[εexp(ωj)εDL(ωj)]}2+{Im[εexp(ωj)εDL(ωj)]}2),
Re[Δε]=Re[εDLεexp]/Re[εexp]   and   Im[εΔ]=Im[εDLεexp]/Im[εexp],

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