Abstract

Metal nanoparticles are efficient resonant plasmonic scatterers for light, and, if placed on top of a high-index substrate, can efficiently couple light into the substrate. This coupling, however, strongly depends on particle shape and surrounding environment. We study the effect of particle shape and substrate refractive index on the plasmonic resonances of silver nanoparticles and we systematically relate this to the efficiency of light scattering into a substrate. The light coupling spectra are dominated by Fano resonances for the corresponding dipolar and quadrupolar scattering modes. Varying the particle shape from spherical to cylindrical leads to large shifts in the Fano resonance for the dipolar mode, reducing the light incoupling integrated over the AM1.5 spectral range. Using a dielectric spacer layer, good light coupling is achieved for cylinders in the near-infrared. An asymmetric environment around the particles turns quadrupolar resonances into efficient radiators as well.

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  1. G. Mie, “Beitrge zur Optik trber Medien, speziell kolloidaler Metallsungen,” Ann. Phys. 330(3), 377–445 (1908).
    [CrossRef]
  2. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).
  3. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
    [CrossRef] [PubMed]
  4. H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69(16), 2327–2329 (1996).
    [CrossRef]
  5. H. R. Stuart and D. G. Hall, “Island size effects in nanoparticle-enhanced photodetectors,” Appl. Phys. Lett. 73(26), 3815–3817 (1998).
    [CrossRef]
  6. D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
    [CrossRef]
  7. D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89(9), 093103 (2006).
    [CrossRef]
  8. P. Matheu, S. H. Lim, D. Derkacs, C. McPheeters, and E. T. Yu, “Metal and dielectric nanoparticle scattering for improved optical absorption in photovoltaic devices,” Appl. Phys. Lett. 93(11), 113108 (2008).
    [CrossRef]
  9. K. R. Catchpole and A. Polman, “Design principle for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008)
    [CrossRef]
  10. K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008).
    [CrossRef] [PubMed]
  11. 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), 106309 (2007).
    [CrossRef]
  12. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
    [CrossRef] [PubMed]
  13. C. Hägglund, M. Zch, 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]
  14. Lumerical FDTD Solutions ( www.lumerical.com ).
  15. http://www.lumerical.com/fdtd_online_helpprevious_help/user_guide_tfsf_sources.php .
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    [CrossRef]
  19. F. J. Beck, A. Polman, and K. R. Catchpole, “Tunable light trapping for solar cells using localized surface plasmons,” J. Appl. Phys. 105(11), 114310 (2009).
    [CrossRef]
  20. G. Xu, M. Tazawa, P. Jin, S. Nakao, and K. Yoshimura, “Wavelength tuning of surface plasmon resonance using dielectric layers,” Appl. Phys. Lett. 82(22), 3811–3813 (2003).
    [CrossRef]

2010

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

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef] [PubMed]

2009

F. J. Beck, A. Polman, and K. R. Catchpole, “Tunable light trapping for solar cells using localized surface plasmons,” J. Appl. Phys. 105(11), 114310 (2009).
[CrossRef]

2008

C. Hägglund, M. Zch, 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, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008).
[CrossRef] [PubMed]

P. Matheu, S. H. Lim, D. Derkacs, C. McPheeters, and E. T. Yu, “Metal and dielectric nanoparticle scattering for improved optical absorption in photovoltaic devices,” Appl. Phys. Lett. 93(11), 113108 (2008).
[CrossRef]

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

2007

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), 106309 (2007).
[CrossRef]

2006

D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89(9), 093103 (2006).
[CrossRef]

2005

D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
[CrossRef]

2003

G. Xu, M. Tazawa, P. Jin, S. Nakao, and K. Yoshimura, “Wavelength tuning of surface plasmon resonance using dielectric layers,” Appl. Phys. Lett. 82(22), 3811–3813 (2003).
[CrossRef]

2000

1998

H. R. Stuart and D. G. Hall, “Island size effects in nanoparticle-enhanced photodetectors,” Appl. Phys. Lett. 73(26), 3815–3817 (1998).
[CrossRef]

1996

H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69(16), 2327–2329 (1996).
[CrossRef]

1908

G. Mie, “Beitrge zur Optik trber Medien, speziell kolloidaler Metallsungen,” Ann. Phys. 330(3), 377–445 (1908).
[CrossRef]

Atwater, H. A.

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

Beck, F. J.

F. J. Beck, A. Polman, and K. R. Catchpole, “Tunable light trapping for solar cells using localized surface plasmons,” J. Appl. Phys. 105(11), 114310 (2009).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

Catchpole, K. R.

F. J. Beck, A. Polman, and K. R. Catchpole, “Tunable light trapping for solar cells using localized surface plasmons,” J. Appl. Phys. 105(11), 114310 (2009).
[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 principle for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008)
[CrossRef]

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef] [PubMed]

Derkacs, D.

P. Matheu, S. H. Lim, D. Derkacs, C. McPheeters, and E. T. Yu, “Metal and dielectric nanoparticle scattering for improved optical absorption in photovoltaic devices,” Appl. Phys. Lett. 93(11), 113108 (2008).
[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), 106309 (2007).
[CrossRef]

D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89(9), 093103 (2006).
[CrossRef]

Feng, B.

D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
[CrossRef]

Giessen, H.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef] [PubMed]

Hägglund, C.

C. Hägglund, M. Zch, 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]

Halas, N. J.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef] [PubMed]

Hall, D. G.

H. R. Stuart and D. G. Hall, “Island size effects in nanoparticle-enhanced photodetectors,” Appl. Phys. Lett. 73(26), 3815–3817 (1998).
[CrossRef]

H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69(16), 2327–2329 (1996).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

Jin, P.

G. Xu, M. Tazawa, P. Jin, S. Nakao, and K. Yoshimura, “Wavelength tuning of surface plasmon resonance using dielectric layers,” Appl. Phys. Lett. 82(22), 3811–3813 (2003).
[CrossRef]

Kasemo, B.

C. Hägglund, M. Zch, 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]

Kreibig, U.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

Lim, S. H.

P. Matheu, S. H. Lim, D. Derkacs, C. McPheeters, and E. T. Yu, “Metal and dielectric nanoparticle scattering for improved optical absorption in photovoltaic devices,” Appl. Phys. Lett. 93(11), 113108 (2008).
[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), 106309 (2007).
[CrossRef]

D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89(9), 093103 (2006).
[CrossRef]

Luk’yanchuk, B.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef] [PubMed]

Maier, S. A.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef] [PubMed]

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), 106309 (2007).
[CrossRef]

D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89(9), 093103 (2006).
[CrossRef]

Matheu, P.

P. Matheu, S. H. Lim, D. Derkacs, C. McPheeters, and E. T. Yu, “Metal and dielectric nanoparticle scattering for improved optical absorption in photovoltaic devices,” Appl. Phys. Lett. 93(11), 113108 (2008).
[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), 106309 (2007).
[CrossRef]

D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89(9), 093103 (2006).
[CrossRef]

McPheeters, C.

P. Matheu, S. H. Lim, D. Derkacs, C. McPheeters, and E. T. Yu, “Metal and dielectric nanoparticle scattering for improved optical absorption in photovoltaic devices,” Appl. Phys. Lett. 93(11), 113108 (2008).
[CrossRef]

Mertz, J.

Mie, G.

G. Mie, “Beitrge zur Optik trber Medien, speziell kolloidaler Metallsungen,” Ann. Phys. 330(3), 377–445 (1908).
[CrossRef]

Nakao, S.

G. Xu, M. Tazawa, P. Jin, S. Nakao, and K. Yoshimura, “Wavelength tuning of surface plasmon resonance using dielectric layers,” Appl. Phys. Lett. 82(22), 3811–3813 (2003).
[CrossRef]

Nordlander, P.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef] [PubMed]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

Petersson, G.

C. Hägglund, M. Zch, 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]

Polman, A.

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

F. J. Beck, A. Polman, and K. R. Catchpole, “Tunable light trapping for solar cells using localized surface plasmons,” J. Appl. Phys. 105(11), 114310 (2009).
[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 principle for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008)
[CrossRef]

Schaadt, D. M.

D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
[CrossRef]

Stuart, H. R.

H. R. Stuart and D. G. Hall, “Island size effects in nanoparticle-enhanced photodetectors,” Appl. Phys. Lett. 73(26), 3815–3817 (1998).
[CrossRef]

H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69(16), 2327–2329 (1996).
[CrossRef]

Tazawa, M.

G. Xu, M. Tazawa, P. Jin, S. Nakao, and K. Yoshimura, “Wavelength tuning of surface plasmon resonance using dielectric layers,” Appl. Phys. Lett. 82(22), 3811–3813 (2003).
[CrossRef]

Vollmer, M.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

Xu, G.

G. Xu, M. Tazawa, P. Jin, S. Nakao, and K. Yoshimura, “Wavelength tuning of surface plasmon resonance using dielectric layers,” Appl. Phys. Lett. 82(22), 3811–3813 (2003).
[CrossRef]

Yoshimura, K.

G. Xu, M. Tazawa, P. Jin, S. Nakao, and K. Yoshimura, “Wavelength tuning of surface plasmon resonance using dielectric layers,” Appl. Phys. Lett. 82(22), 3811–3813 (2003).
[CrossRef]

Yu, E. T.

P. Matheu, S. H. Lim, D. Derkacs, C. McPheeters, and E. T. Yu, “Metal and dielectric nanoparticle scattering for improved optical absorption in photovoltaic devices,” Appl. Phys. Lett. 93(11), 113108 (2008).
[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), 106309 (2007).
[CrossRef]

D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89(9), 093103 (2006).
[CrossRef]

D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
[CrossRef]

Zch, M.

C. Hägglund, M. Zch, 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]

Zheludev, N. I.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef] [PubMed]

Ann. Phys.

G. Mie, “Beitrge zur Optik trber Medien, speziell kolloidaler Metallsungen,” Ann. Phys. 330(3), 377–445 (1908).
[CrossRef]

Appl. Phys. Lett.

C. Hägglund, M. Zch, 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]

H. R. Stuart and D. G. Hall, “Absorption enhancement in silicon-on-insulator waveguides using metal island films,” Appl. Phys. Lett. 69(16), 2327–2329 (1996).
[CrossRef]

H. R. Stuart and D. G. Hall, “Island size effects in nanoparticle-enhanced photodetectors,” Appl. Phys. Lett. 73(26), 3815–3817 (1998).
[CrossRef]

D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005).
[CrossRef]

D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89(9), 093103 (2006).
[CrossRef]

P. Matheu, S. H. Lim, D. Derkacs, C. McPheeters, and E. T. Yu, “Metal and dielectric nanoparticle scattering for improved optical absorption in photovoltaic devices,” Appl. Phys. Lett. 93(11), 113108 (2008).
[CrossRef]

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

G. Xu, M. Tazawa, P. Jin, S. Nakao, and K. Yoshimura, “Wavelength tuning of surface plasmon resonance using dielectric layers,” Appl. Phys. Lett. 82(22), 3811–3813 (2003).
[CrossRef]

J. Appl. Phys.

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), 106309 (2007).
[CrossRef]

F. J. Beck, A. Polman, and K. R. Catchpole, “Tunable light trapping for solar cells using localized surface plasmons,” J. Appl. Phys. 105(11), 114310 (2009).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Mater.

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

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef] [PubMed]

Opt. Express

Other

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

Lumerical FDTD Solutions ( www.lumerical.com ).

http://www.lumerical.com/fdtd_online_helpprevious_help/user_guide_tfsf_sources.php .

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

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Figures (6)

Fig. 1
Fig. 1

Normalized scattering cross section spectra (a), and normalized transmittance (b) for particles of three different shapes on top of a crystalline Si substrate. The dipole resonance is strongly red-shifted when particle shape is changed from a sphere (green), to a 10 nm round edge cylinder (red), to a sharp edge cylinder (blue). The normalized transmittance spectrum shows a reduction below each resonance, due to the Fano effect. The inset in (a) shows the simulation geometry. Data are calculated for a box size of 1×1×0.8 μm 3. The peak resonance wavelengths are indicated by the dashed vertical lines.

Fig. 2
Fig. 2

Normalized scattering cross section (NSCS) spectra (gray scale) for a Ag sphere in air as a function of particle size (a), for a 150 nm diameter Ag sphere as a function of different surrounding refractive index (b), and for a nanoparticle in air as a function of the round edge parameter h (c). Panels (a) and (b) are calculated using Mie theory; panel (c) is the result of FDTD calculations. A redshift of the resonances is observed as the particle size or the surrounding refractive index increase and when the shape is changed from a sphere to a cylinder. Dipolar (D), quadrupolar (Q) and octupolar (O) resonances are indicated.

Fig. 3
Fig. 3

Normalized scattering cross section spectra (NSCS, gray scale) for a sphere (a), a 10 nm round edge cylinder (b) and for a sharp cylinder (c), all with an in-plane diameter of 150 nm, as a function of the substrate refractive index. A redshift of the dipolar resonance is observed as the substrate index increases. This effect is very large for cylindrical particles. The quadrupolar resonance is only slightly affected by the presence of the substrate.

Fig. 4
Fig. 4

Scattered electric field intensity distribution for the dipolar (a) and quadrupolar (b) resonance in air and for the dipolar (c) and quadrupolar (d) resonance for a 150 nm diameter cylinder on a n=3 substrate. The presence of the substrate strongly modifies the field distribution of the particle at resonance. The field distribution due to the dipolar resonance is located at the interface with the substrate, whereas the quadrupolar resonance field is located at the particle-air interface.

Fig. 5
Fig. 5

Transmission enhancement factor, calculated by integrating transmission spectra such as in Fig. 1(b) over the AM1.5 solar spectrum, normalized to a bare Si substrate, as a function of the round edge parameter. Spherical particles (75 nm round edge) show better incoupling of light than cylindrical particles (0 nm round edge). The simulation box size is 1×1×0.8 μm 3.

Fig. 6
Fig. 6

Normalized scattering cross section (a) and normalized transmittance (b) spectra for a cylindrical Ag particle on top of Si (blue) and on top of 10 nm (red), 30 nm (purple) and 50 nm (green) thick Si3N4 layer. Data in (b) are normalized to the transmission for a Si substrate with the corresponding Si3N4 layer thickness. The dipolar resonance is shifted to the blue as the Si3N4 layer thickness is increased. The normalized transmittance spectrum shows a reduction below each resonance, due to the Fano effect.

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