Abstract

In this work, we present a numerical analysis of the surface electric field of a metallic nanoparticle (either 2D or 3D) interacting with a flat substrate underneath. The influence of the distance to the substrate, particle size, the surrounding media and the substrate optical properties is analyzed as a function of the incident wavelength. We show that these are crucial factors that change the field distribution associated to the dipolar behavior of the particle. A useful parameter for illustrating the changes in the angular distribution is θmax, the angle at which the maximum of the surface electric field is located.

© 2008 Optical Society of America

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  1. M. Kreuzer, R. Quidant, J. P. Salvador, M. P. Marco, and G. Badenes, "Colloidal-based localized surface plasmon biosensor for the quantitative determination of stanozolol," Anal. Bioanal. Chem. DOI 10.1007/s00216-008-2022-z.
    [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

2008

A. Agrawal, R. Deo, G.D. Wang, M. D. Wang, and S. Nie, "Nanometer-scale mapping and single-molecule detection with color-coded nanoparticle probes," PNAS 105, 3298-3303 (2008).
[CrossRef] [PubMed]

2007

R. Jensen, J. Shermand, and S. Emory, "Single Nanoparticle Based Optical pH Probe," Appl. Spectrosc. 61, 832-838 (2007).
[CrossRef] [PubMed]

N. Engheta, "Circuits with Light at Nanoscales: Optical Nanocircuits Inspired by Metamaterials," Science 317, 1698-1702 (2007).
[CrossRef] [PubMed]

J. Nelayah, M. Kociak, O. Stéphan, F. García de Abajo, M. Tencé. L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, "Mapping surface plasmons on a single metallica nanoparticle," Nature Phys. 3, 348-353 (2007).
[CrossRef]

K. G. Lee, H. W Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and S. Kim, "Vector field microscopic imaging of light," Nature Phot. 1, 53-56 (2007).
[CrossRef]

X. Wei, X. Luo, X. Dong, and C. Du, "Localized surface Plasmon Nanolithography with Ultrahigh Resolution," Opt. Express 15, 14177-14183 (2007).
[CrossRef] [PubMed]

2006

2005

L. Sherry, S.-H. Chang, G. Schatz, and R. Van Duyne,"Localized Surface Plasmon Resonance Spectroscopy of Single Silver Nanocubes," Nanolett. 5, 2034-2038 (2005).
[CrossRef]

2004

H. Mertens, J. Verhoeven, A. Polman, and F. D. Tichelaar, "Infrared surface plasmons in two-dimensional silver nanoparticles arrays in silicon,"Appl. Phys. Lett. 85, 1317 (2004).
[CrossRef]

T. Kalkbrenner, U. Håkanson, and V. Sandoghdar, "Tomographic Plasmon Spectroscopy of a Single Gold Nanoparticle," Nanolett. 4, 2309-2314 (2004).
[CrossRef]

2002

1999

J. L. de la Peña, F. González, J. M. Saiz, F. Moreno, and P. J. Valle, "Sizing particles on substrates. A general method for oblique incidence," J.Appl. Phys. 85,432 (1999).
[CrossRef]

J. L. de la Peña, J. M. Saiz, G. Videen, F. González, P. J. Valle, and F. Moreno, "Scattering from particles on substrates: visibility factor and polydispersity," Opt. Lett. 24,1451-1453 (1999).
[CrossRef]

1998

T. Kalr, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, "Surface-Plasmon Resonances in Single Metallic Nanoparticles," Phys. Rev. Lett. 80, 4249-4252 (1998).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Agrawal, A.

A. Agrawal, R. Deo, G.D. Wang, M. D. Wang, and S. Nie, "Nanometer-scale mapping and single-molecule detection with color-coded nanoparticle probes," PNAS 105, 3298-3303 (2008).
[CrossRef] [PubMed]

Arias-González, J. R.

Badenes, G.

M. Kreuzer, R. Quidant, J. P. Salvador, M. P. Marco, and G. Badenes, "Colloidal-based localized surface plasmon biosensor for the quantitative determination of stanozolol," Anal. Bioanal. Chem. DOI 10.1007/s00216-008-2022-z.
[PubMed]

Cao, Y. C.

Y. C. Cao, R. Jin, and C. A. Mirkin," Nanoparticles with Raman Spectroscopic Fingerprints for DNA and RNA Detection," Science 297, 1536-1540 (2002).
[CrossRef] [PubMed]

Chang, S.-H.

L. Sherry, S.-H. Chang, G. Schatz, and R. Van Duyne,"Localized Surface Plasmon Resonance Spectroscopy of Single Silver Nanocubes," Nanolett. 5, 2034-2038 (2005).
[CrossRef]

Choi, S. B.

K. G. Lee, H. W Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and S. Kim, "Vector field microscopic imaging of light," Nature Phot. 1, 53-56 (2007).
[CrossRef]

Choi, W. J.

K. G. Lee, H. W Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and S. Kim, "Vector field microscopic imaging of light," Nature Phot. 1, 53-56 (2007).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

de la Peña, J. L.

J. L. de la Peña, F. González, J. M. Saiz, F. Moreno, and P. J. Valle, "Sizing particles on substrates. A general method for oblique incidence," J.Appl. Phys. 85,432 (1999).
[CrossRef]

J. L. de la Peña, J. M. Saiz, G. Videen, F. González, P. J. Valle, and F. Moreno, "Scattering from particles on substrates: visibility factor and polydispersity," Opt. Lett. 24,1451-1453 (1999).
[CrossRef]

Deo, R.

A. Agrawal, R. Deo, G.D. Wang, M. D. Wang, and S. Nie, "Nanometer-scale mapping and single-molecule detection with color-coded nanoparticle probes," PNAS 105, 3298-3303 (2008).
[CrossRef] [PubMed]

Dong, X.

Du, C.

Emory, S.

Engheta, N.

N. Engheta, "Circuits with Light at Nanoscales: Optical Nanocircuits Inspired by Metamaterials," Science 317, 1698-1702 (2007).
[CrossRef] [PubMed]

Feldmann, J.

T. Kalr, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, "Surface-Plasmon Resonances in Single Metallic Nanoparticles," Phys. Rev. Lett. 80, 4249-4252 (1998).
[CrossRef]

García de Abajo, F.

J. Nelayah, M. Kociak, O. Stéphan, F. García de Abajo, M. Tencé. L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, "Mapping surface plasmons on a single metallica nanoparticle," Nature Phys. 3, 348-353 (2007).
[CrossRef]

González, F.

Grosse, S.

T. Kalr, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, "Surface-Plasmon Resonances in Single Metallic Nanoparticles," Phys. Rev. Lett. 80, 4249-4252 (1998).
[CrossRef]

Håkanson, U.

T. Kalkbrenner, U. Håkanson, and V. Sandoghdar, "Tomographic Plasmon Spectroscopy of a Single Gold Nanoparticle," Nanolett. 4, 2309-2314 (2004).
[CrossRef]

Jensen, R.

Jin, R.

Y. C. Cao, R. Jin, and C. A. Mirkin," Nanoparticles with Raman Spectroscopic Fingerprints for DNA and RNA Detection," Science 297, 1536-1540 (2002).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Kalkbrenner, T.

T. Kalkbrenner, U. Håkanson, and V. Sandoghdar, "Tomographic Plasmon Spectroscopy of a Single Gold Nanoparticle," Nanolett. 4, 2309-2314 (2004).
[CrossRef]

Kalr, T.

T. Kalr, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, "Surface-Plasmon Resonances in Single Metallic Nanoparticles," Phys. Rev. Lett. 80, 4249-4252 (1998).
[CrossRef]

Kihm, H. W

K. G. Lee, H. W Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and S. Kim, "Vector field microscopic imaging of light," Nature Phot. 1, 53-56 (2007).
[CrossRef]

Kihm, J. E.

K. G. Lee, H. W Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and S. Kim, "Vector field microscopic imaging of light," Nature Phot. 1, 53-56 (2007).
[CrossRef]

Kim, H.

K. G. Lee, H. W Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and S. Kim, "Vector field microscopic imaging of light," Nature Phot. 1, 53-56 (2007).
[CrossRef]

Kim, J.

K. G. Lee, H. W Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and S. Kim, "Vector field microscopic imaging of light," Nature Phot. 1, 53-56 (2007).
[CrossRef]

Kim, S.

K. G. Lee, H. W Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and S. Kim, "Vector field microscopic imaging of light," Nature Phot. 1, 53-56 (2007).
[CrossRef]

Kociak, M.

J. Nelayah, M. Kociak, O. Stéphan, F. García de Abajo, M. Tencé. L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, "Mapping surface plasmons on a single metallica nanoparticle," Nature Phys. 3, 348-353 (2007).
[CrossRef]

Kreuzer, M.

M. Kreuzer, R. Quidant, J. P. Salvador, M. P. Marco, and G. Badenes, "Colloidal-based localized surface plasmon biosensor for the quantitative determination of stanozolol," Anal. Bioanal. Chem. DOI 10.1007/s00216-008-2022-z.
[PubMed]

Lee, B.

K. G. Lee, H. W Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and S. Kim, "Vector field microscopic imaging of light," Nature Phot. 1, 53-56 (2007).
[CrossRef]

Lee, K. G.

K. G. Lee, H. W Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and S. Kim, "Vector field microscopic imaging of light," Nature Phot. 1, 53-56 (2007).
[CrossRef]

Lévêque, G.

Lienau, C.

K. G. Lee, H. W Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and S. Kim, "Vector field microscopic imaging of light," Nature Phot. 1, 53-56 (2007).
[CrossRef]

Luo, X.

Marco, M. P.

M. Kreuzer, R. Quidant, J. P. Salvador, M. P. Marco, and G. Badenes, "Colloidal-based localized surface plasmon biosensor for the quantitative determination of stanozolol," Anal. Bioanal. Chem. DOI 10.1007/s00216-008-2022-z.
[PubMed]

Martin, O. J. F.

Mertens, H.

H. Mertens, J. Verhoeven, A. Polman, and F. D. Tichelaar, "Infrared surface plasmons in two-dimensional silver nanoparticles arrays in silicon,"Appl. Phys. Lett. 85, 1317 (2004).
[CrossRef]

Mirkin, C. A.

Y. C. Cao, R. Jin, and C. A. Mirkin," Nanoparticles with Raman Spectroscopic Fingerprints for DNA and RNA Detection," Science 297, 1536-1540 (2002).
[CrossRef] [PubMed]

Moreno, F.

Nelayah, J.

J. Nelayah, M. Kociak, O. Stéphan, F. García de Abajo, M. Tencé. L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, "Mapping surface plasmons on a single metallica nanoparticle," Nature Phys. 3, 348-353 (2007).
[CrossRef]

Nie, S.

A. Agrawal, R. Deo, G.D. Wang, M. D. Wang, and S. Nie, "Nanometer-scale mapping and single-molecule detection with color-coded nanoparticle probes," PNAS 105, 3298-3303 (2008).
[CrossRef] [PubMed]

Nieto-Vesperinas, M.

Park, D. J.

K. G. Lee, H. W Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and S. Kim, "Vector field microscopic imaging of light," Nature Phot. 1, 53-56 (2007).
[CrossRef]

Park, Q. H.

K. G. Lee, H. W Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and S. Kim, "Vector field microscopic imaging of light," Nature Phot. 1, 53-56 (2007).
[CrossRef]

Perner, M.

T. Kalr, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, "Surface-Plasmon Resonances in Single Metallic Nanoparticles," Phys. Rev. Lett. 80, 4249-4252 (1998).
[CrossRef]

Polman, A.

H. Mertens, J. Verhoeven, A. Polman, and F. D. Tichelaar, "Infrared surface plasmons in two-dimensional silver nanoparticles arrays in silicon,"Appl. Phys. Lett. 85, 1317 (2004).
[CrossRef]

Quidant, R.

M. Kreuzer, R. Quidant, J. P. Salvador, M. P. Marco, and G. Badenes, "Colloidal-based localized surface plasmon biosensor for the quantitative determination of stanozolol," Anal. Bioanal. Chem. DOI 10.1007/s00216-008-2022-z.
[PubMed]

Ropers, C.

K. G. Lee, H. W Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and S. Kim, "Vector field microscopic imaging of light," Nature Phot. 1, 53-56 (2007).
[CrossRef]

Saiz, J. M.

Salvador, J. P.

M. Kreuzer, R. Quidant, J. P. Salvador, M. P. Marco, and G. Badenes, "Colloidal-based localized surface plasmon biosensor for the quantitative determination of stanozolol," Anal. Bioanal. Chem. DOI 10.1007/s00216-008-2022-z.
[PubMed]

Sandoghdar, V.

T. Kalkbrenner, U. Håkanson, and V. Sandoghdar, "Tomographic Plasmon Spectroscopy of a Single Gold Nanoparticle," Nanolett. 4, 2309-2314 (2004).
[CrossRef]

Schatz, G.

L. Sherry, S.-H. Chang, G. Schatz, and R. Van Duyne,"Localized Surface Plasmon Resonance Spectroscopy of Single Silver Nanocubes," Nanolett. 5, 2034-2038 (2005).
[CrossRef]

Shermand, J.

Sherry, L.

L. Sherry, S.-H. Chang, G. Schatz, and R. Van Duyne,"Localized Surface Plasmon Resonance Spectroscopy of Single Silver Nanocubes," Nanolett. 5, 2034-2038 (2005).
[CrossRef]

Spirkl, W.

T. Kalr, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, "Surface-Plasmon Resonances in Single Metallic Nanoparticles," Phys. Rev. Lett. 80, 4249-4252 (1998).
[CrossRef]

Stéphan, O.

J. Nelayah, M. Kociak, O. Stéphan, F. García de Abajo, M. Tencé. L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, "Mapping surface plasmons on a single metallica nanoparticle," Nature Phys. 3, 348-353 (2007).
[CrossRef]

Tencé, M.

J. Nelayah, M. Kociak, O. Stéphan, F. García de Abajo, M. Tencé. L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, "Mapping surface plasmons on a single metallica nanoparticle," Nature Phys. 3, 348-353 (2007).
[CrossRef]

Tichelaar, F. D.

H. Mertens, J. Verhoeven, A. Polman, and F. D. Tichelaar, "Infrared surface plasmons in two-dimensional silver nanoparticles arrays in silicon,"Appl. Phys. Lett. 85, 1317 (2004).
[CrossRef]

Valle, P. J.

J. L. de la Peña, J. M. Saiz, G. Videen, F. González, P. J. Valle, and F. Moreno, "Scattering from particles on substrates: visibility factor and polydispersity," Opt. Lett. 24,1451-1453 (1999).
[CrossRef]

J. L. de la Peña, F. González, J. M. Saiz, F. Moreno, and P. J. Valle, "Sizing particles on substrates. A general method for oblique incidence," J.Appl. Phys. 85,432 (1999).
[CrossRef]

Van Duyne, R.

L. Sherry, S.-H. Chang, G. Schatz, and R. Van Duyne,"Localized Surface Plasmon Resonance Spectroscopy of Single Silver Nanocubes," Nanolett. 5, 2034-2038 (2005).
[CrossRef]

Verhoeven, J.

H. Mertens, J. Verhoeven, A. Polman, and F. D. Tichelaar, "Infrared surface plasmons in two-dimensional silver nanoparticles arrays in silicon,"Appl. Phys. Lett. 85, 1317 (2004).
[CrossRef]

Videen, G.

von Plessen, G.

T. Kalr, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, "Surface-Plasmon Resonances in Single Metallic Nanoparticles," Phys. Rev. Lett. 80, 4249-4252 (1998).
[CrossRef]

Wang, G.D.

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Figures (13)

Fig. 1.
Fig. 1.

Geometry of the system used in our calculations.

Fig. 2.
Fig. 2.

Angular position of the maximum of the local electric field (θ max) around an isolated silver sphere (full symbols) or an isolated silver cylinder (hollow symbols) as a function of the radius for several incident wavelengths.

Fig. 3.
Fig. 3.

Angular distribution of the local electric field at the surface of (a) an isolated silver cylinder and (b) an isolated silver sphere for three different incident wavelengths (at and around the plasmon resonance) and two different sizes. * means that that wavelength is resonant for that geometry.

Fig. 4.
Fig. 4.

Angular position of the maximum of the local electric field (θmax ) around an isolated cylinder made of silver (squares) or gold (up-triangles) and around an isolated sphere made of silver (circles) or gold (down-triangles) as a function of the incident wavelength and for the same size for all the cases.

Fig. 5.
Fig. 5.

Angular position of the maximum of the local electric field (θmax ) around an isolated cylinder for two different sizes and for a case in which the surrounding medium is denser (n=1.5) than the air.

Fig. 6.
Fig. 6.

Scheme of the geometry used for a system consisting of a metallic cylinder above a flat substrate.

Fig. 7.
Fig. 7.

Angular position of the maximum of the local electric field (θmax ) around a silver cylinder both isolated or above a flat substrate (n’=1.5) as a function of the incident wavelength and for several values of the gap between the cylinder and the substrate.

Fig. 8.
Fig. 8.

Angular position of the maximum of the local electric field (θmax ) around a silver cylinder of two different sizes above a dielectric substrate (n’=1.5) at a distance: (a) 1 nm and (b) 5 nm as a function of the incident wavelength.

Fig. 9.
Fig. 9.

Scattering diagram of a silver cylinder of R=25 nm and above a dielectric substrate (n’=1.5) at a distance d=1nm for several incident wavelengths.

Fig. 10.
Fig. 10.

Angular position of the maximum of the local electric field (θmax ) around a silver cylinder (R=25 nm) above a flat substrate at a distance d=1 nm as a function of the incident wavelength and for different combinations of the refractive index of the surrounding medium and the substrate.

Fig. 11.
Fig. 11.

Angular position of the maximum of the local electric field (θmax ) around a gold cylinder of two different sizes above a flat substrate, at a distance d=1nm, as a function of the incident wavelength and for different combinations of the refractive index of the surrounding medium and the substrate.

Fig. 12.
Fig. 12.

Distribution of the electric field around a gold cylinder of radius R=25 nm embedded in glass (n=1.5) above vacuum at distance d=1nm for three different incident wavelength: (a) λ=420 nm, (b) λ=496 nm and (c) λ=560 nm

Fig. 13.
Fig. 13.

Distribution of the electric field around a gold cylinder of radius R=25 nm embedded in water (n=1.3) above a gold substrate at distance d=1nm, (a) (b) and (c), or d=10 nm, (d) (e) and (f), for three different incident wavelength: (a) and (d) λ=320 nm, (b) and (e) λ=430 nm and (c) and (f) λ=600 nm.

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