Abstract

We provide a new physical interpretation of scattering from plasmonic nanoparticles on high-index substrates. We demonstrate the excitation of different types of resonant modes on disk-shaped, Ag nanoparticles. At short wavelengths, the resonances are localised at the top of the particle, while at longer wavelengths they are localised at the Ag/substrate interface. We attribute the long wavelength resonances to geometric resonances of surface plasmon polaritons (SPPs) at the Ag/substrate interface. We show that particles that support resonant SPP modes have enhanced scattering cross-sections when placed directly on a high-index substrate; up to 7.5 times larger than that of a dipole scatterer with an equivalent free-space resonance. This has implications for designing scattering nanostructures for light trapping solar cells.

© 2011 OSA

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2010

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[CrossRef] [PubMed]

F. J. Beck, S. Mokkapati, A. Polman, and K. R. Catchpole, “Asymmetry in photocurrent enhancement by plasmonic nanoparticle arrays located on the front or on the rear of solar cells,” Appl. Phys. Lett. 96(3), 033113 (2010).
[CrossRef]

Z. Ouyang, S. Pillai, F. J. Beck, O. Kunz, S. Varlamov, K. R. Catchpole, P. Campbell, and M. A. Green, “Effective light trapping in polycrystalline silicon thin-film solar cells by means of rear localized surface plasmons,” Appl. Phys. Lett. 96(26), 261109 (2010).
[CrossRef]

A. Centeno, J. Breeze, B. Ahmed, H. Reehal, and N. Alford, “Scattering of light into silicon by spherical and hemispherical silver nanoparticles,” Opt. Lett. 35(1), 76–78 (2010).
[CrossRef] [PubMed]

2009

Y. A. Akimov, W. S. Koh, and K. Ostrikov, “Enhancement of optical absorption in thin-film solar cells through the excitation of higher-order nanoparticle plasmon modes,” Opt. Express 17(12), 10195–10205 (2009).
[CrossRef] [PubMed]

Y. A. Akimov, K. Ostrikov, and E. P. Li, “Surface Plasmon Enhancement of Optical Absorption in Thin- Film Silicon Solar Cells,” Plasmonics 4(2), 107–113 (2009).
[CrossRef]

T. L. Temple, G. D. K. Mahanama, H. S. Reehal, and D. M. Bagnall, “Influence of localized surface plasmon excitation in silver nanoparticles on the performance of silicon solar cells,” Sol. Energy Mater. Sol. Cells 93(11), 1978–1985 (2009).
[CrossRef]

E. Cubukcu and F. Capasso, “Optical nanorod antennas as dispersive one-dimensional Fabry-Perot resonantors for surface plasmons,” Appl. Phys. Lett. 95(20), 201101 (2009).
[CrossRef]

2008

K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008).
[CrossRef] [PubMed]

J. A. Dionne, E. Verhagen, A. Polman, and H. A. Atwater, “Are negative index materials achievable with surface plasmon waveguides? A case study of three plasmonic geometries,” Opt. Express 16(23), 19001–19017 (2008).
[CrossRef]

C. Hägglund, Z. Zach, G. Petersson, and B. Kasemo, “Electromagnetic coupling of light into a silicon solar cell by nanodisk plasmons,” Appl. Phys. Lett. 92(5), 053110 (2008).
[CrossRef]

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
[CrossRef]

2007

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

S. H. Lim, W. Mar, P. Matheu, D. Derkacs, and E. T. Yu, “Photocurrent spectroscopy of optical absorption enhancement in silicon photodiodes via scattering from surface plasmon polaritons in gold nanoparticles,” J. Appl. Phys. 101(10), 104309 (2007).
[CrossRef]

2006

K. R. Catchpole and S. Pillai, “Absorption enhancement due to scattering by dipoles into silicon waveguides,” J. Appl. Phys. 100(4), 044504–044508 (2006).
[CrossRef]

2002

2001

2000

1998

H. R. Stuart and D. G. Hall, “Enhanced dipole-dipole interaction between elementary radiators near a surface,” Phys. Rev. Lett. 80(25), 5663–5666 (1998).
[CrossRef]

1995

M. J. Keevers and M. A. Green, “Absorption edge of silicon from solar cell spectral response measurements,” Appl. Phys. Lett. 66(2), 174–176 (1995).
[CrossRef]

1986

P. A. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Phys. Scr. 137A, 209–--242 (1986).

1972

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

1919

H. Weyl, “Ausbreitung eiektromagnetischer, Wellen uber einem ebenen Leiter,” Ann. Phys. 4(21), 481–500 (1919).
[CrossRef]

1908

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25(3), 377–445 (1908).
[CrossRef]

Ahmed, B.

Akimov, Y. A.

Y. A. Akimov, W. S. Koh, and K. Ostrikov, “Enhancement of optical absorption in thin-film solar cells through the excitation of higher-order nanoparticle plasmon modes,” Opt. Express 17(12), 10195–10205 (2009).
[CrossRef] [PubMed]

Y. A. Akimov, K. Ostrikov, and E. P. Li, “Surface Plasmon Enhancement of Optical Absorption in Thin- Film Silicon Solar Cells,” Plasmonics 4(2), 107–113 (2009).
[CrossRef]

Alford, N.

Atwater, H. A.

Bagnall, D. M.

T. L. Temple, G. D. K. Mahanama, H. S. Reehal, and D. M. Bagnall, “Influence of localized surface plasmon excitation in silver nanoparticles on the performance of silicon solar cells,” Sol. Energy Mater. Sol. Cells 93(11), 1978–1985 (2009).
[CrossRef]

Beck, F. J.

F. J. Beck, S. Mokkapati, A. Polman, and K. R. Catchpole, “Asymmetry in photocurrent enhancement by plasmonic nanoparticle arrays located on the front or on the rear of solar cells,” Appl. Phys. Lett. 96(3), 033113 (2010).
[CrossRef]

Z. Ouyang, S. Pillai, F. J. Beck, O. Kunz, S. Varlamov, K. R. Catchpole, P. Campbell, and M. A. Green, “Effective light trapping in polycrystalline silicon thin-film solar cells by means of rear localized surface plasmons,” Appl. Phys. Lett. 96(26), 261109 (2010).
[CrossRef]

Bobbert, P. A.

P. A. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Phys. Scr. 137A, 209–--242 (1986).

Breeze, J.

Campbell, P.

Z. Ouyang, S. Pillai, F. J. Beck, O. Kunz, S. Varlamov, K. R. Catchpole, P. Campbell, and M. A. Green, “Effective light trapping in polycrystalline silicon thin-film solar cells by means of rear localized surface plasmons,” Appl. Phys. Lett. 96(26), 261109 (2010).
[CrossRef]

Capasso, F.

E. Cubukcu and F. Capasso, “Optical nanorod antennas as dispersive one-dimensional Fabry-Perot resonantors for surface plasmons,” Appl. Phys. Lett. 95(20), 201101 (2009).
[CrossRef]

Catchpole, K. R.

Z. Ouyang, S. Pillai, F. J. Beck, O. Kunz, S. Varlamov, K. R. Catchpole, P. Campbell, and M. A. Green, “Effective light trapping in polycrystalline silicon thin-film solar cells by means of rear localized surface plasmons,” Appl. Phys. Lett. 96(26), 261109 (2010).
[CrossRef]

F. J. Beck, S. Mokkapati, A. Polman, and K. R. Catchpole, “Asymmetry in photocurrent enhancement by plasmonic nanoparticle arrays located on the front or on the rear of solar cells,” Appl. Phys. Lett. 96(3), 033113 (2010).
[CrossRef]

K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008).
[CrossRef] [PubMed]

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

K. R. Catchpole and S. Pillai, “Absorption enhancement due to scattering by dipoles into silicon waveguides,” J. Appl. Phys. 100(4), 044504–044508 (2006).
[CrossRef]

Centeno, A.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Cubukcu, E.

E. Cubukcu and F. Capasso, “Optical nanorod antennas as dispersive one-dimensional Fabry-Perot resonantors for surface plasmons,” Appl. Phys. Lett. 95(20), 201101 (2009).
[CrossRef]

Derkacs, D.

S. H. Lim, W. Mar, P. Matheu, D. Derkacs, and E. T. Yu, “Photocurrent spectroscopy of optical absorption enhancement in silicon photodiodes via scattering from surface plasmon polaritons in gold nanoparticles,” J. Appl. Phys. 101(10), 104309 (2007).
[CrossRef]

Dionne, J. A.

Green, M. A.

Z. Ouyang, S. Pillai, F. J. Beck, O. Kunz, S. Varlamov, K. R. Catchpole, P. Campbell, and M. A. Green, “Effective light trapping in polycrystalline silicon thin-film solar cells by means of rear localized surface plasmons,” Appl. Phys. Lett. 96(26), 261109 (2010).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

M. J. Keevers and M. A. Green, “Absorption edge of silicon from solar cell spectral response measurements,” Appl. Phys. Lett. 66(2), 174–176 (1995).
[CrossRef]

Hägglund, C.

C. Hägglund, Z. Zach, G. Petersson, and B. Kasemo, “Electromagnetic coupling of light into a silicon solar cell by nanodisk plasmons,” Appl. Phys. Lett. 92(5), 053110 (2008).
[CrossRef]

Hall, D. G.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kasemo, B.

C. Hägglund, Z. Zach, G. Petersson, and B. Kasemo, “Electromagnetic coupling of light into a silicon solar cell by nanodisk plasmons,” Appl. Phys. Lett. 92(5), 053110 (2008).
[CrossRef]

Keevers, M. J.

M. J. Keevers and M. A. Green, “Absorption edge of silicon from solar cell spectral response measurements,” Appl. Phys. Lett. 66(2), 174–176 (1995).
[CrossRef]

Koh, W. S.

Kunz, O.

Z. Ouyang, S. Pillai, F. J. Beck, O. Kunz, S. Varlamov, K. R. Catchpole, P. Campbell, and M. A. Green, “Effective light trapping in polycrystalline silicon thin-film solar cells by means of rear localized surface plasmons,” Appl. Phys. Lett. 96(26), 261109 (2010).
[CrossRef]

Li, E. P.

Y. A. Akimov, K. Ostrikov, and E. P. Li, “Surface Plasmon Enhancement of Optical Absorption in Thin- Film Silicon Solar Cells,” Plasmonics 4(2), 107–113 (2009).
[CrossRef]

Lim, S. H.

S. H. Lim, W. Mar, P. Matheu, D. Derkacs, and E. T. Yu, “Photocurrent spectroscopy of optical absorption enhancement in silicon photodiodes via scattering from surface plasmon polaritons in gold nanoparticles,” J. Appl. Phys. 101(10), 104309 (2007).
[CrossRef]

Mahanama, G. D. K.

T. L. Temple, G. D. K. Mahanama, H. S. Reehal, and D. M. Bagnall, “Influence of localized surface plasmon excitation in silver nanoparticles on the performance of silicon solar cells,” Sol. Energy Mater. Sol. Cells 93(11), 1978–1985 (2009).
[CrossRef]

Mar, W.

S. H. Lim, W. Mar, P. Matheu, D. Derkacs, and E. T. Yu, “Photocurrent spectroscopy of optical absorption enhancement in silicon photodiodes via scattering from surface plasmon polaritons in gold nanoparticles,” J. Appl. Phys. 101(10), 104309 (2007).
[CrossRef]

Matheu, P.

S. H. Lim, W. Mar, P. Matheu, D. Derkacs, and E. T. Yu, “Photocurrent spectroscopy of optical absorption enhancement in silicon photodiodes via scattering from surface plasmon polaritons in gold nanoparticles,” J. Appl. Phys. 101(10), 104309 (2007).
[CrossRef]

Mertz, J.

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25(3), 377–445 (1908).
[CrossRef]

Mokkapati, S.

F. J. Beck, S. Mokkapati, A. Polman, and K. R. Catchpole, “Asymmetry in photocurrent enhancement by plasmonic nanoparticle arrays located on the front or on the rear of solar cells,” Appl. Phys. Lett. 96(3), 033113 (2010).
[CrossRef]

Ostrikov, K.

Y. A. Akimov, K. Ostrikov, and E. P. Li, “Surface Plasmon Enhancement of Optical Absorption in Thin- Film Silicon Solar Cells,” Plasmonics 4(2), 107–113 (2009).
[CrossRef]

Y. A. Akimov, W. S. Koh, and K. Ostrikov, “Enhancement of optical absorption in thin-film solar cells through the excitation of higher-order nanoparticle plasmon modes,” Opt. Express 17(12), 10195–10205 (2009).
[CrossRef] [PubMed]

Ouyang, Z.

Z. Ouyang, S. Pillai, F. J. Beck, O. Kunz, S. Varlamov, K. R. Catchpole, P. Campbell, and M. A. Green, “Effective light trapping in polycrystalline silicon thin-film solar cells by means of rear localized surface plasmons,” Appl. Phys. Lett. 96(26), 261109 (2010).
[CrossRef]

Petersson, G.

C. Hägglund, Z. Zach, G. Petersson, and B. Kasemo, “Electromagnetic coupling of light into a silicon solar cell by nanodisk plasmons,” Appl. Phys. Lett. 92(5), 053110 (2008).
[CrossRef]

Pillai, S.

Z. Ouyang, S. Pillai, F. J. Beck, O. Kunz, S. Varlamov, K. R. Catchpole, P. Campbell, and M. A. Green, “Effective light trapping in polycrystalline silicon thin-film solar cells by means of rear localized surface plasmons,” Appl. Phys. Lett. 96(26), 261109 (2010).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

K. R. Catchpole and S. Pillai, “Absorption enhancement due to scattering by dipoles into silicon waveguides,” J. Appl. Phys. 100(4), 044504–044508 (2006).
[CrossRef]

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[CrossRef] [PubMed]

F. J. Beck, S. Mokkapati, A. Polman, and K. R. Catchpole, “Asymmetry in photocurrent enhancement by plasmonic nanoparticle arrays located on the front or on the rear of solar cells,” Appl. Phys. Lett. 96(3), 033113 (2010).
[CrossRef]

K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008).
[CrossRef] [PubMed]

J. A. Dionne, E. Verhagen, A. Polman, and H. A. Atwater, “Are negative index materials achievable with surface plasmon waveguides? A case study of three plasmonic geometries,” Opt. Express 16(23), 19001–19017 (2008).
[CrossRef]

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
[CrossRef]

Reehal, H.

Reehal, H. S.

T. L. Temple, G. D. K. Mahanama, H. S. Reehal, and D. M. Bagnall, “Influence of localized surface plasmon excitation in silver nanoparticles on the performance of silicon solar cells,” Sol. Energy Mater. Sol. Cells 93(11), 1978–1985 (2009).
[CrossRef]

Soller, B. J.

Stuart, H. R.

H. R. Stuart and D. G. Hall, “Enhanced dipole-dipole interaction between elementary radiators near a surface,” Phys. Rev. Lett. 80(25), 5663–5666 (1998).
[CrossRef]

Temple, T. L.

T. L. Temple, G. D. K. Mahanama, H. S. Reehal, and D. M. Bagnall, “Influence of localized surface plasmon excitation in silver nanoparticles on the performance of silicon solar cells,” Sol. Energy Mater. Sol. Cells 93(11), 1978–1985 (2009).
[CrossRef]

Trupke, T.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

Varlamov, S.

Z. Ouyang, S. Pillai, F. J. Beck, O. Kunz, S. Varlamov, K. R. Catchpole, P. Campbell, and M. A. Green, “Effective light trapping in polycrystalline silicon thin-film solar cells by means of rear localized surface plasmons,” Appl. Phys. Lett. 96(26), 261109 (2010).
[CrossRef]

Verhagen, E.

Vlieger, J.

P. A. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Phys. Scr. 137A, 209–--242 (1986).

Weyl, H.

H. Weyl, “Ausbreitung eiektromagnetischer, Wellen uber einem ebenen Leiter,” Ann. Phys. 4(21), 481–500 (1919).
[CrossRef]

Yu, E. T.

S. H. Lim, W. Mar, P. Matheu, D. Derkacs, and E. T. Yu, “Photocurrent spectroscopy of optical absorption enhancement in silicon photodiodes via scattering from surface plasmon polaritons in gold nanoparticles,” J. Appl. Phys. 101(10), 104309 (2007).
[CrossRef]

Zach, Z.

C. Hägglund, Z. Zach, G. Petersson, and B. Kasemo, “Electromagnetic coupling of light into a silicon solar cell by nanodisk plasmons,” Appl. Phys. Lett. 92(5), 053110 (2008).
[CrossRef]

Ann. Phys.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25(3), 377–445 (1908).
[CrossRef]

H. Weyl, “Ausbreitung eiektromagnetischer, Wellen uber einem ebenen Leiter,” Ann. Phys. 4(21), 481–500 (1919).
[CrossRef]

Appl. Phys. Lett.

C. Hägglund, Z. Zach, G. Petersson, and B. Kasemo, “Electromagnetic coupling of light into a silicon solar cell by nanodisk plasmons,” Appl. Phys. Lett. 92(5), 053110 (2008).
[CrossRef]

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
[CrossRef]

F. J. Beck, S. Mokkapati, A. Polman, and K. R. Catchpole, “Asymmetry in photocurrent enhancement by plasmonic nanoparticle arrays located on the front or on the rear of solar cells,” Appl. Phys. Lett. 96(3), 033113 (2010).
[CrossRef]

Z. Ouyang, S. Pillai, F. J. Beck, O. Kunz, S. Varlamov, K. R. Catchpole, P. Campbell, and M. A. Green, “Effective light trapping in polycrystalline silicon thin-film solar cells by means of rear localized surface plasmons,” Appl. Phys. Lett. 96(26), 261109 (2010).
[CrossRef]

M. J. Keevers and M. A. Green, “Absorption edge of silicon from solar cell spectral response measurements,” Appl. Phys. Lett. 66(2), 174–176 (1995).
[CrossRef]

E. Cubukcu and F. Capasso, “Optical nanorod antennas as dispersive one-dimensional Fabry-Perot resonantors for surface plasmons,” Appl. Phys. Lett. 95(20), 201101 (2009).
[CrossRef]

J. Appl. Phys.

K. R. Catchpole and S. Pillai, “Absorption enhancement due to scattering by dipoles into silicon waveguides,” J. Appl. Phys. 100(4), 044504–044508 (2006).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

S. H. Lim, W. Mar, P. Matheu, D. Derkacs, and E. T. Yu, “Photocurrent spectroscopy of optical absorption enhancement in silicon photodiodes via scattering from surface plasmon polaritons in gold nanoparticles,” J. Appl. Phys. 101(10), 104309 (2007).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nat. Mater.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. B

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Phys. Rev. Lett.

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[CrossRef]

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[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Calculated normalized scattering cross-section spectra (Q scat) of a 100 nm diameter, 50 nm tall, Ag disk on the front (crosses), or rear (solid line), of a Si substrate. The particle is either directly on the Si surface (t = 0 nm) or on thin SiO2 spacer layers of thickness, t = 5 nm and t = 20 nm. (b) The coupling efficiency (F subs) for the particles on the front of a Si substrate, calculated as the fraction of the scattered light scattered into the substrate. Data is also shown for a particle directly on the surface of a non-absorbing substrate with refractive index, n = 3.5 (dashed lines, black circles). (c-e) The electric field profiles ( |E |) calculated over a plane bisecting the nanoparticle, with light incident from the air. Data is shown at the resonance wavelengths marked in (a), where (c) R1 λ R1 = 396 nm, and R2 λ R2 = 990 nm for particles on bare Si, (d) R1 λ R1 = 396 nm, and R2 λ R2 = 671 nm for t = 5 nm, and (e) R1 λ R1 = 388 nm, and R2 λ R2 = 574 nm for particles on a 20 nm thick oxide.

Fig. 2
Fig. 2

The surface plasmon polariton wavelength corresponding to λRjsppRj)) plotted against stripe width (d). For R1, the wavelength of the SPPs excited at the air/Ag interface is shown (λsppR1)), hollow shapes), while for R2 (λsppR2)), light filled shapes) and R3 (λsppR3)), dark filled shape) the wavelength of the SPPs at the Ag/substrate interface is shown. The conditions d = 1/2 λ spp(λ R2), and d = λ spp(λ R3) are plotted for comparison.

Fig. 3
Fig. 3

Field profile of the real part of the component of the electric field vector in the direction of polarisation (Re(Ex)) calculated from 3D FDTD simulations. Data is shown for a 150 nm diameter, 50 nm tall, disk-shaped particle on a bare Si substrate with light incident from the air. The plots are shown at the free space resonance wavelengths, (a) λR1 = 368 nm, (b) λR2 = 1274 nm and (c) λR3 = 744 nm. Insets in (b) and (c) show a schematic representation of Re(Ex) at the Ag/Si interface.

Fig. 4
Fig. 4

(a) Strength of the scattering cross-section at the R2 resonance (Q scat(λ R2)) for a 100 nm diameter, disk-shaped, Ag nanoparticle, on a Si substrate, normalised to the scattering cross-section of a similar disk in free space (Q scat) for different thicknesses of SiO2, from t = 0-150 nm. (b) Strength of the scattering cross-section for a horizontally orientated dipole on a Si substrate for different thicknesses of SiO2 spacer layer, normalised to the cross-section of a dipole in free space (σ/σ ). The cross-section is calculated using the Mertz formulation [16], at wavelengths corresponding to λ R2 for the disks in part (a). For both parts of the figure, data is shown for particles on the front (circles, blue) and rear (squares, red) of the substrates. The intensity of the electric field driving the resonance (I d) normalised to the incident radiation, calculated using a simple model for a multilayered substrate described in ref [17] is also plotted (solid lines). The insets show the relative efficiency of excitation (η), calculated as the normalised scattering cross-section divided by intensity of the driving field, for front (stars, red) or rear-located scatterers (blue, solid line).

Fig. 5
Fig. 5

Magnitude of the electric field due to the resonant mode at λR2 (|EMODE|) normalized to the incident field for a 100 nm diameter, disk-shaped nanoparticle on a Si substrate. Data is shown for particles on the Si substrate with (a) t = 0 nm and λR2 = 990 nm, (b) t = 5 nm with λR2 = 671 nm, and (c) t = 20 nm with λR2 = 574 nm. The results are plotted perpendicular to the substrate, at the centre of the particle.

Equations (1)

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σ = 2 π λ m [ α m ] I d ,

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