Abstract

We report numerical analysis of the coupling of localized surface plasmons to the modes of U-shaped cavities. The coupling results in intense resonance for which the electric field is strongly enhanced on the cavity surfaces. As a result, an optical vortex in the power flow is formed in the cavities and a sharp and strong resonance dip is observed in the reflectance spectrum. High sensitivity of the dip wavelength to change in the refractive index of the surrounding medium is reported. The high sensitivity is realized with a small number of cavities, thus enabling miniaturization of detectors based on U-shaped cavities.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  28. E. Maeda, Y. Lee, Y. Kobayashi, A. Taino, M. Koizumi, S. Fujikawa, and J. J. Delaunay, “Sensitivity to refractive index of high-aspect-ratio nanofins with optical vortex,” Nanotechnology23(50), 505502 (2012).
    [CrossRef] [PubMed]
  29. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt.37(22), 5271–5283 (1998).
    [CrossRef] [PubMed]
  30. L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett.5(10), 2034–2038 (2005).
    [CrossRef] [PubMed]
  31. J. Becker, A. Trügler, A. Jakab, U. Hohenester, and C. Sönnichsen, “The optimal aspect ratio of gold nanorods for plasmonic bio-sensing,” Plasmonics5(2), 161–167 (2010).
    [CrossRef]
  32. D. C. Cullen, R. G. W. Brown, and C. R. Lowe, “Detection of immuno-complex formation via surface plasmon resonance on gold-coated diffraction gratings,” Biosensors3(4), 211–225 (1987).
    [CrossRef] [PubMed]
  33. N. J. Geddes, A. S. Martin, F. Caruso, R. S. Urquhart, D. N. Furlong, J. R. Sambles, K. A. Than, and J. A. Edgar, “Immobilisation of IgG onto gold surfaces and its interaction with anti-IgG studied by surface plasmon resonance,” J. Immunol. Methods175(2), 149–160 (1994).
    [CrossRef] [PubMed]
  34. C. Preininger, H. Clausen-Schaumann, A. Ahluwalia, and D. de Rossi, “Characterization of IgG Langmuir-Blodgett films immobilized on functionalized polymers,” Talanta52(5), 921–930 (2000).
    [CrossRef] [PubMed]
  35. J. Vörös, “The density and refractive index of adsorbing protein layers,” Biophys. J.87(1), 553–561 (2004).
    [CrossRef] [PubMed]
  36. H. Huang, X. Liu, B. Liao, and P. K. Chu, “A localized surface plasmon resonance biosensor based on integrated controllable Au2S/AuAgS-coated gold nanorods composite,” Plasmonics6(1), 1–9 (2011).
    [CrossRef]
  37. C.-Y. Hsu, J.-W. Huang, and K.-J. Lin, “High sensitivity and selectivity of human antibody attachment at the interstices between substrate-bound gold nanoparticles,” Chem. Commun. (Camb.)47(3), 872–874 (2010).
    [CrossRef] [PubMed]

2012 (1)

E. Maeda, Y. Lee, Y. Kobayashi, A. Taino, M. Koizumi, S. Fujikawa, and J. J. Delaunay, “Sensitivity to refractive index of high-aspect-ratio nanofins with optical vortex,” Nanotechnology23(50), 505502 (2012).
[CrossRef] [PubMed]

2011 (6)

J. Ye and P. Van Dorpe, “Improvement of figure of merit for gold nanobar array plasmonic sensors,” Plasmonics6(4), 665–671 (2011).
[CrossRef]

N. Verellen, P. Van Dorpe, C. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon line shaping using nanocrosses for high sensitivity localized surface plasmon resonance sensing,” Nano Lett.11(2), 391–397 (2011).
[CrossRef] [PubMed]

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett.11(4), 1657–1663 (2011).
[CrossRef] [PubMed]

R. Ameling, D. Dregely, and H. Giessen, “Strong coupling of localized and surface plasmons to microcavity modes,” Opt. Lett.36(12), 2218–2220 (2011).
[CrossRef] [PubMed]

K. M. Mayer and J. H. Hafner, “Localized surface plasmon resonance sensors,” Chem. Rev.111(6), 3828–3857 (2011).
[CrossRef] [PubMed]

H. Huang, X. Liu, B. Liao, and P. K. Chu, “A localized surface plasmon resonance biosensor based on integrated controllable Au2S/AuAgS-coated gold nanorods composite,” Plasmonics6(1), 1–9 (2011).
[CrossRef]

2010 (4)

C.-Y. Hsu, J.-W. Huang, and K.-J. Lin, “High sensitivity and selectivity of human antibody attachment at the interstices between substrate-bound gold nanoparticles,” Chem. Commun. (Camb.)47(3), 872–874 (2010).
[CrossRef] [PubMed]

Y.-F. Chau, H.-H. Yeh, and D. P. Tsai, “Surface plasmon resonances effects on different patterns of solid-silver and silver-shell nanocylindrical pairs,” J. Electromagn. Waves Appl.24(8-9), 1005–1014 (2010).
[CrossRef]

R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett.97(25), 253116 (2010).
[CrossRef]

J. Becker, A. Trügler, A. Jakab, U. Hohenester, and C. Sönnichsen, “The optimal aspect ratio of gold nanorods for plasmonic bio-sensing,” Plasmonics5(2), 161–167 (2010).
[CrossRef]

2009 (3)

2008 (5)

C. L. Nehl and J. H. Hafner, “Shape-dependent plasmon resonances of gold nanoparticles,” J. Mater. Chem.18(21), 2415–2419 (2008).
[CrossRef]

G. J. Nusz, S. M. Marinakos, A. C. Curry, A. Dahlin, F. Höök, A. Wax, and A. Chilkoti, “Label-free plasmonic detection of biomolecular binding by a single gold nanorod,” Anal. Chem.80(4), 984–989 (2008).
[CrossRef] [PubMed]

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir24(10), 5233–5237 (2008).
[CrossRef] [PubMed]

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett.100(6), 066408 (2008).
[CrossRef] [PubMed]

2007 (4)

C. Yu and J. Irudayaraj, “Multiplex biosensor using gold nanorods,” Anal. Chem.79(2), 572–579 (2007).
[CrossRef] [PubMed]

B. J. Wiley, Y. Chen, J. M. McLellan, Y. Xiong, Z.-Y. Li, D. Ginger, and Y. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett.7(4), 1032–1036 (2007).
[CrossRef] [PubMed]

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics1(11), 641–648 (2007).
[CrossRef]

C. Yu and J. Irudayaraj, “Quantitative evaluation of sensitivity and selectivity of multiplex nanoSPR biosensor assays,” Biophys. J.93(10), 3684–3692 (2007).
[CrossRef] [PubMed]

2006 (2)

C. J. Orendorff, T. K. Sau, and C. J. Murphy, “Shape-dependent plasmon-resonant gold nanoparticles,” Small2(5), 636–639 (2006).
[CrossRef] [PubMed]

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: A hybrid plasmonic nanostructure,” Nano Lett.6(4), 827–832 (2006).
[CrossRef] [PubMed]

2005 (1)

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett.5(10), 2034–2038 (2005).
[CrossRef] [PubMed]

2004 (2)

J. Vörös, “The density and refractive index of adsorbing protein layers,” Biophys. J.87(1), 553–561 (2004).
[CrossRef] [PubMed]

N. Nath and A. Chilkoti, “Label-free biosensing by surface plasmon resonance of nanoparticles on glass: optimization of nanoparticle size,” Anal. Chem.76(18), 5370–5378 (2004).
[CrossRef] [PubMed]

2003 (1)

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B107(3), 668–677 (2003).
[CrossRef]

2002 (1)

A. J. Haes and R. P. Van Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc.124(35), 10596–10604 (2002).
[CrossRef] [PubMed]

2000 (1)

C. Preininger, H. Clausen-Schaumann, A. Ahluwalia, and D. de Rossi, “Characterization of IgG Langmuir-Blodgett films immobilized on functionalized polymers,” Talanta52(5), 921–930 (2000).
[CrossRef] [PubMed]

1999 (1)

S. Link and M. A. El-Sayed, “Spectral properties and relaxation dynamics of surface plasmon electronic oscillations in gold and silver nanodots and nanorods,” J. Phys. Chem. B103(40), 8410–8426 (1999).
[CrossRef]

1998 (2)

L. S. Jung, C. T. Campbell, T. M. Chinowsky, M. N. Mar, and S. S. Yee, “Quantitative interpretation of the response of surface plasmon resonance sensors to adsorbed films,” Langmuir14(19), 5636–5648 (1998).
[CrossRef]

A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt.37(22), 5271–5283 (1998).
[CrossRef] [PubMed]

1994 (2)

N. J. Geddes, A. S. Martin, F. Caruso, R. S. Urquhart, D. N. Furlong, J. R. Sambles, K. A. Than, and J. A. Edgar, “Immobilisation of IgG onto gold surfaces and its interaction with anti-IgG studied by surface plasmon resonance,” J. Immunol. Methods175(2), 149–160 (1994).
[CrossRef] [PubMed]

S. Underwood and P. Mulvaney, “Effect of the solution refractive index on the color of gold colloids,” Langmuir10(10), 3427–3430 (1994).
[CrossRef]

1987 (1)

D. C. Cullen, R. G. W. Brown, and C. R. Lowe, “Detection of immuno-complex formation via surface plasmon resonance on gold-coated diffraction gratings,” Biosensors3(4), 211–225 (1987).
[CrossRef] [PubMed]

Ahluwalia, A.

C. Preininger, H. Clausen-Schaumann, A. Ahluwalia, and D. de Rossi, “Characterization of IgG Langmuir-Blodgett films immobilized on functionalized polymers,” Talanta52(5), 921–930 (2000).
[CrossRef] [PubMed]

Ameling, R.

R. Ameling, D. Dregely, and H. Giessen, “Strong coupling of localized and surface plasmons to microcavity modes,” Opt. Lett.36(12), 2218–2220 (2011).
[CrossRef] [PubMed]

R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett.97(25), 253116 (2010).
[CrossRef]

Anderton, C. R.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

Angelomé, P. C.

B. Sepúlveda, P. C. Angelomé, L. M. Lechuga, and L. M. Liz-Marzán, “LSPR-based nanobiosensors,” Nano Today4(3), 244–251 (2009).
[CrossRef]

Bao, K.

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett.11(4), 1657–1663 (2011).
[CrossRef] [PubMed]

Barbara, A.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett.100(6), 066408 (2008).
[CrossRef] [PubMed]

Becker, J.

J. Becker, A. Trügler, A. Jakab, U. Hohenester, and C. Sönnichsen, “The optimal aspect ratio of gold nanorods for plasmonic bio-sensing,” Plasmonics5(2), 161–167 (2010).
[CrossRef]

Brandl, D. W.

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: A hybrid plasmonic nanostructure,” Nano Lett.6(4), 827–832 (2006).
[CrossRef] [PubMed]

Braun, P. V.

R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett.97(25), 253116 (2010).
[CrossRef]

Brown, R. G. W.

D. C. Cullen, R. G. W. Brown, and C. R. Lowe, “Detection of immuno-complex formation via surface plasmon resonance on gold-coated diffraction gratings,” Biosensors3(4), 211–225 (1987).
[CrossRef] [PubMed]

Byun, K. M.

Campbell, C. T.

L. S. Jung, C. T. Campbell, T. M. Chinowsky, M. N. Mar, and S. S. Yee, “Quantitative interpretation of the response of surface plasmon resonance sensors to adsorbed films,” Langmuir14(19), 5636–5648 (1998).
[CrossRef]

Caruso, F.

N. J. Geddes, A. S. Martin, F. Caruso, R. S. Urquhart, D. N. Furlong, J. R. Sambles, K. A. Than, and J. A. Edgar, “Immobilisation of IgG onto gold surfaces and its interaction with anti-IgG studied by surface plasmon resonance,” J. Immunol. Methods175(2), 149–160 (1994).
[CrossRef] [PubMed]

Chang, S.-H.

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett.5(10), 2034–2038 (2005).
[CrossRef] [PubMed]

Chau, Y.-F.

Y.-F. Chau, H.-H. Yeh, and D. P. Tsai, “Surface plasmon resonances effects on different patterns of solid-silver and silver-shell nanocylindrical pairs,” J. Electromagn. Waves Appl.24(8-9), 1005–1014 (2010).
[CrossRef]

Chen, H.

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir24(10), 5233–5237 (2008).
[CrossRef] [PubMed]

Chen, Y.

B. J. Wiley, Y. Chen, J. M. McLellan, Y. Xiong, Z.-Y. Li, D. Ginger, and Y. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett.7(4), 1032–1036 (2007).
[CrossRef] [PubMed]

Chilkoti, A.

G. J. Nusz, S. M. Marinakos, A. C. Curry, A. Dahlin, F. Höök, A. Wax, and A. Chilkoti, “Label-free plasmonic detection of biomolecular binding by a single gold nanorod,” Anal. Chem.80(4), 984–989 (2008).
[CrossRef] [PubMed]

N. Nath and A. Chilkoti, “Label-free biosensing by surface plasmon resonance of nanoparticles on glass: optimization of nanoparticle size,” Anal. Chem.76(18), 5370–5378 (2004).
[CrossRef] [PubMed]

Chinowsky, T. M.

L. S. Jung, C. T. Campbell, T. M. Chinowsky, M. N. Mar, and S. S. Yee, “Quantitative interpretation of the response of surface plasmon resonance sensors to adsorbed films,” Langmuir14(19), 5636–5648 (1998).
[CrossRef]

Chu, P. K.

H. Huang, X. Liu, B. Liao, and P. K. Chu, “A localized surface plasmon resonance biosensor based on integrated controllable Au2S/AuAgS-coated gold nanorods composite,” Plasmonics6(1), 1–9 (2011).
[CrossRef]

Clausen-Schaumann, H.

C. Preininger, H. Clausen-Schaumann, A. Ahluwalia, and D. de Rossi, “Characterization of IgG Langmuir-Blodgett films immobilized on functionalized polymers,” Talanta52(5), 921–930 (2000).
[CrossRef] [PubMed]

Coronado, E.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B107(3), 668–677 (2003).
[CrossRef]

Cullen, D. C.

D. C. Cullen, R. G. W. Brown, and C. R. Lowe, “Detection of immuno-complex formation via surface plasmon resonance on gold-coated diffraction gratings,” Biosensors3(4), 211–225 (1987).
[CrossRef] [PubMed]

Curry, A. C.

G. J. Nusz, S. M. Marinakos, A. C. Curry, A. Dahlin, F. Höök, A. Wax, and A. Chilkoti, “Label-free plasmonic detection of biomolecular binding by a single gold nanorod,” Anal. Chem.80(4), 984–989 (2008).
[CrossRef] [PubMed]

Dahlin, A.

G. J. Nusz, S. M. Marinakos, A. C. Curry, A. Dahlin, F. Höök, A. Wax, and A. Chilkoti, “Label-free plasmonic detection of biomolecular binding by a single gold nanorod,” Anal. Chem.80(4), 984–989 (2008).
[CrossRef] [PubMed]

de Rossi, D.

C. Preininger, H. Clausen-Schaumann, A. Ahluwalia, and D. de Rossi, “Characterization of IgG Langmuir-Blodgett films immobilized on functionalized polymers,” Talanta52(5), 921–930 (2000).
[CrossRef] [PubMed]

Delaunay, J. J.

E. Maeda, Y. Lee, Y. Kobayashi, A. Taino, M. Koizumi, S. Fujikawa, and J. J. Delaunay, “Sensitivity to refractive index of high-aspect-ratio nanofins with optical vortex,” Nanotechnology23(50), 505502 (2012).
[CrossRef] [PubMed]

Djurisic, A. B.

Dregely, D.

Edgar, J. A.

N. J. Geddes, A. S. Martin, F. Caruso, R. S. Urquhart, D. N. Furlong, J. R. Sambles, K. A. Than, and J. A. Edgar, “Immobilisation of IgG onto gold surfaces and its interaction with anti-IgG studied by surface plasmon resonance,” J. Immunol. Methods175(2), 149–160 (1994).
[CrossRef] [PubMed]

Elazar, J. M.

El-Sayed, M. A.

S. Link and M. A. El-Sayed, “Spectral properties and relaxation dynamics of surface plasmon electronic oscillations in gold and silver nanodots and nanorods,” J. Phys. Chem. B103(40), 8410–8426 (1999).
[CrossRef]

Fujikawa, S.

E. Maeda, Y. Lee, Y. Kobayashi, A. Taino, M. Koizumi, S. Fujikawa, and J. J. Delaunay, “Sensitivity to refractive index of high-aspect-ratio nanofins with optical vortex,” Nanotechnology23(50), 505502 (2012).
[CrossRef] [PubMed]

Furlong, D. N.

N. J. Geddes, A. S. Martin, F. Caruso, R. S. Urquhart, D. N. Furlong, J. R. Sambles, K. A. Than, and J. A. Edgar, “Immobilisation of IgG onto gold surfaces and its interaction with anti-IgG studied by surface plasmon resonance,” J. Immunol. Methods175(2), 149–160 (1994).
[CrossRef] [PubMed]

Gadsdon, M. R.

Geddes, N. J.

N. J. Geddes, A. S. Martin, F. Caruso, R. S. Urquhart, D. N. Furlong, J. R. Sambles, K. A. Than, and J. A. Edgar, “Immobilisation of IgG onto gold surfaces and its interaction with anti-IgG studied by surface plasmon resonance,” J. Immunol. Methods175(2), 149–160 (1994).
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R. Ameling, D. Dregely, and H. Giessen, “Strong coupling of localized and surface plasmons to microcavity modes,” Opt. Lett.36(12), 2218–2220 (2011).
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R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett.97(25), 253116 (2010).
[CrossRef]

Ginger, D.

B. J. Wiley, Y. Chen, J. M. McLellan, Y. Xiong, Z.-Y. Li, D. Ginger, and Y. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett.7(4), 1032–1036 (2007).
[CrossRef] [PubMed]

Gray, S. K.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
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Haes, A. J.

A. J. Haes and R. P. Van Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc.124(35), 10596–10604 (2002).
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K. M. Mayer and J. H. Hafner, “Localized surface plasmon resonance sensors,” Chem. Rev.111(6), 3828–3857 (2011).
[CrossRef] [PubMed]

C. L. Nehl and J. H. Hafner, “Shape-dependent plasmon resonances of gold nanoparticles,” J. Mater. Chem.18(21), 2415–2419 (2008).
[CrossRef]

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S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett.11(4), 1657–1663 (2011).
[CrossRef] [PubMed]

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics1(11), 641–648 (2007).
[CrossRef]

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: A hybrid plasmonic nanostructure,” Nano Lett.6(4), 827–832 (2006).
[CrossRef] [PubMed]

Hentschel, M.

R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett.97(25), 253116 (2010).
[CrossRef]

Hibbins, A. P.

Hohenester, U.

J. Becker, A. Trügler, A. Jakab, U. Hohenester, and C. Sönnichsen, “The optimal aspect ratio of gold nanorods for plasmonic bio-sensing,” Plasmonics5(2), 161–167 (2010).
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G. J. Nusz, S. M. Marinakos, A. C. Curry, A. Dahlin, F. Höök, A. Wax, and A. Chilkoti, “Label-free plasmonic detection of biomolecular binding by a single gold nanorod,” Anal. Chem.80(4), 984–989 (2008).
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Hsu, C.-Y.

C.-Y. Hsu, J.-W. Huang, and K.-J. Lin, “High sensitivity and selectivity of human antibody attachment at the interstices between substrate-bound gold nanoparticles,” Chem. Commun. (Camb.)47(3), 872–874 (2010).
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N. Verellen, P. Van Dorpe, C. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon line shaping using nanocrosses for high sensitivity localized surface plasmon resonance sensing,” Nano Lett.11(2), 391–397 (2011).
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H. Huang, X. Liu, B. Liao, and P. K. Chu, “A localized surface plasmon resonance biosensor based on integrated controllable Au2S/AuAgS-coated gold nanorods composite,” Plasmonics6(1), 1–9 (2011).
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C.-Y. Hsu, J.-W. Huang, and K.-J. Lin, “High sensitivity and selectivity of human antibody attachment at the interstices between substrate-bound gold nanoparticles,” Chem. Commun. (Camb.)47(3), 872–874 (2010).
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J. Becker, A. Trügler, A. Jakab, U. Hohenester, and C. Sönnichsen, “The optimal aspect ratio of gold nanorods for plasmonic bio-sensing,” Plasmonics5(2), 161–167 (2010).
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Jang, S. M.

Jung, L. S.

L. S. Jung, C. T. Campbell, T. M. Chinowsky, M. N. Mar, and S. S. Yee, “Quantitative interpretation of the response of surface plasmon resonance sensors to adsorbed films,” Langmuir14(19), 5636–5648 (1998).
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K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B107(3), 668–677 (2003).
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Kim, S. J.

Kobayashi, Y.

E. Maeda, Y. Lee, Y. Kobayashi, A. Taino, M. Koizumi, S. Fujikawa, and J. J. Delaunay, “Sensitivity to refractive index of high-aspect-ratio nanofins with optical vortex,” Nanotechnology23(50), 505502 (2012).
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E. Maeda, Y. Lee, Y. Kobayashi, A. Taino, M. Koizumi, S. Fujikawa, and J. J. Delaunay, “Sensitivity to refractive index of high-aspect-ratio nanofins with optical vortex,” Nanotechnology23(50), 505502 (2012).
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H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir24(10), 5233–5237 (2008).
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N. Verellen, P. Van Dorpe, C. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon line shaping using nanocrosses for high sensitivity localized surface plasmon resonance sensing,” Nano Lett.11(2), 391–397 (2011).
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S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics1(11), 641–648 (2007).
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R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett.97(25), 253116 (2010).
[CrossRef]

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H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: A hybrid plasmonic nanostructure,” Nano Lett.6(4), 827–832 (2006).
[CrossRef] [PubMed]

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J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett.100(6), 066408 (2008).
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B. Sepúlveda, P. C. Angelomé, L. M. Lechuga, and L. M. Liz-Marzán, “LSPR-based nanobiosensors,” Nano Today4(3), 244–251 (2009).
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E. Maeda, Y. Lee, Y. Kobayashi, A. Taino, M. Koizumi, S. Fujikawa, and J. J. Delaunay, “Sensitivity to refractive index of high-aspect-ratio nanofins with optical vortex,” Nanotechnology23(50), 505502 (2012).
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B. J. Wiley, Y. Chen, J. M. McLellan, Y. Xiong, Z.-Y. Li, D. Ginger, and Y. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett.7(4), 1032–1036 (2007).
[CrossRef] [PubMed]

Liao, B.

H. Huang, X. Liu, B. Liao, and P. K. Chu, “A localized surface plasmon resonance biosensor based on integrated controllable Au2S/AuAgS-coated gold nanorods composite,” Plasmonics6(1), 1–9 (2011).
[CrossRef]

Lin, K.-J.

C.-Y. Hsu, J.-W. Huang, and K.-J. Lin, “High sensitivity and selectivity of human antibody attachment at the interstices between substrate-bound gold nanoparticles,” Chem. Commun. (Camb.)47(3), 872–874 (2010).
[CrossRef] [PubMed]

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S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics1(11), 641–648 (2007).
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S. Link and M. A. El-Sayed, “Spectral properties and relaxation dynamics of surface plasmon electronic oscillations in gold and silver nanodots and nanorods,” J. Phys. Chem. B103(40), 8410–8426 (1999).
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H. Huang, X. Liu, B. Liao, and P. K. Chu, “A localized surface plasmon resonance biosensor based on integrated controllable Au2S/AuAgS-coated gold nanorods composite,” Plasmonics6(1), 1–9 (2011).
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B. Sepúlveda, P. C. Angelomé, L. M. Lechuga, and L. M. Liz-Marzán, “LSPR-based nanobiosensors,” Nano Today4(3), 244–251 (2009).
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N. Verellen, P. Van Dorpe, C. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon line shaping using nanocrosses for high sensitivity localized surface plasmon resonance sensing,” Nano Lett.11(2), 391–397 (2011).
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J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett.100(6), 066408 (2008).
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D. C. Cullen, R. G. W. Brown, and C. R. Lowe, “Detection of immuno-complex formation via surface plasmon resonance on gold-coated diffraction gratings,” Biosensors3(4), 211–225 (1987).
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E. Maeda, Y. Lee, Y. Kobayashi, A. Taino, M. Koizumi, S. Fujikawa, and J. J. Delaunay, “Sensitivity to refractive index of high-aspect-ratio nanofins with optical vortex,” Nanotechnology23(50), 505502 (2012).
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Majewski, M. L.

Mar, M. N.

L. S. Jung, C. T. Campbell, T. M. Chinowsky, M. N. Mar, and S. S. Yee, “Quantitative interpretation of the response of surface plasmon resonance sensors to adsorbed films,” Langmuir14(19), 5636–5648 (1998).
[CrossRef]

Maria, J.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
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Marinakos, S. M.

G. J. Nusz, S. M. Marinakos, A. C. Curry, A. Dahlin, F. Höök, A. Wax, and A. Chilkoti, “Label-free plasmonic detection of biomolecular binding by a single gold nanorod,” Anal. Chem.80(4), 984–989 (2008).
[CrossRef] [PubMed]

Martin, A. S.

N. J. Geddes, A. S. Martin, F. Caruso, R. S. Urquhart, D. N. Furlong, J. R. Sambles, K. A. Than, and J. A. Edgar, “Immobilisation of IgG onto gold surfaces and its interaction with anti-IgG studied by surface plasmon resonance,” J. Immunol. Methods175(2), 149–160 (1994).
[CrossRef] [PubMed]

Mayer, K. M.

K. M. Mayer and J. H. Hafner, “Localized surface plasmon resonance sensors,” Chem. Rev.111(6), 3828–3857 (2011).
[CrossRef] [PubMed]

McLellan, J. M.

B. J. Wiley, Y. Chen, J. M. McLellan, Y. Xiong, Z.-Y. Li, D. Ginger, and Y. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett.7(4), 1032–1036 (2007).
[CrossRef] [PubMed]

Mesch, M.

R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett.97(25), 253116 (2010).
[CrossRef]

Moshchalkov, V. V.

N. Verellen, P. Van Dorpe, C. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon line shaping using nanocrosses for high sensitivity localized surface plasmon resonance sensing,” Nano Lett.11(2), 391–397 (2011).
[CrossRef] [PubMed]

Mulvaney, P.

S. Underwood and P. Mulvaney, “Effect of the solution refractive index on the color of gold colloids,” Langmuir10(10), 3427–3430 (1994).
[CrossRef]

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C. J. Orendorff, T. K. Sau, and C. J. Murphy, “Shape-dependent plasmon-resonant gold nanoparticles,” Small2(5), 636–639 (2006).
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N. Nath and A. Chilkoti, “Label-free biosensing by surface plasmon resonance of nanoparticles on glass: optimization of nanoparticle size,” Anal. Chem.76(18), 5370–5378 (2004).
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C. L. Nehl and J. H. Hafner, “Shape-dependent plasmon resonances of gold nanoparticles,” J. Mater. Chem.18(21), 2415–2419 (2008).
[CrossRef]

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H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir24(10), 5233–5237 (2008).
[CrossRef] [PubMed]

Nordlander, P.

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett.11(4), 1657–1663 (2011).
[CrossRef] [PubMed]

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: A hybrid plasmonic nanostructure,” Nano Lett.6(4), 827–832 (2006).
[CrossRef] [PubMed]

Nusz, G. J.

G. J. Nusz, S. M. Marinakos, A. C. Curry, A. Dahlin, F. Höök, A. Wax, and A. Chilkoti, “Label-free plasmonic detection of biomolecular binding by a single gold nanorod,” Anal. Chem.80(4), 984–989 (2008).
[CrossRef] [PubMed]

Nuzzo, R. G.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

Orendorff, C. J.

C. J. Orendorff, T. K. Sau, and C. J. Murphy, “Shape-dependent plasmon-resonant gold nanoparticles,” Small2(5), 636–639 (2006).
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C. Preininger, H. Clausen-Schaumann, A. Ahluwalia, and D. de Rossi, “Characterization of IgG Langmuir-Blodgett films immobilized on functionalized polymers,” Talanta52(5), 921–930 (2000).
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J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett.100(6), 066408 (2008).
[CrossRef] [PubMed]

Rakic, A. D.

Rogers, J. A.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

Sambles, J. R.

M. R. Gadsdon, I. R. Hooper, A. P. Hibbins, and J. R. Sambles, “Surface plasmon polaritons on deep, narrow-ridged rectangular gratings,” J. Opt. Soc. Am. B26(6), 1228–1237 (2009).
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N. J. Geddes, A. S. Martin, F. Caruso, R. S. Urquhart, D. N. Furlong, J. R. Sambles, K. A. Than, and J. A. Edgar, “Immobilisation of IgG onto gold surfaces and its interaction with anti-IgG studied by surface plasmon resonance,” J. Immunol. Methods175(2), 149–160 (1994).
[CrossRef] [PubMed]

Sau, T. K.

C. J. Orendorff, T. K. Sau, and C. J. Murphy, “Shape-dependent plasmon-resonant gold nanoparticles,” Small2(5), 636–639 (2006).
[CrossRef] [PubMed]

Schatz, G. C.

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett.5(10), 2034–2038 (2005).
[CrossRef] [PubMed]

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B107(3), 668–677 (2003).
[CrossRef]

Sepúlveda, B.

B. Sepúlveda, P. C. Angelomé, L. M. Lechuga, and L. M. Liz-Marzán, “LSPR-based nanobiosensors,” Nano Today4(3), 244–251 (2009).
[CrossRef]

Sherry, L. J.

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett.5(10), 2034–2038 (2005).
[CrossRef] [PubMed]

Sönnichsen, C.

J. Becker, A. Trügler, A. Jakab, U. Hohenester, and C. Sönnichsen, “The optimal aspect ratio of gold nanorods for plasmonic bio-sensing,” Plasmonics5(2), 161–167 (2010).
[CrossRef]

Stewart, M. E.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

Taino, A.

E. Maeda, Y. Lee, Y. Kobayashi, A. Taino, M. Koizumi, S. Fujikawa, and J. J. Delaunay, “Sensitivity to refractive index of high-aspect-ratio nanofins with optical vortex,” Nanotechnology23(50), 505502 (2012).
[CrossRef] [PubMed]

Than, K. A.

N. J. Geddes, A. S. Martin, F. Caruso, R. S. Urquhart, D. N. Furlong, J. R. Sambles, K. A. Than, and J. A. Edgar, “Immobilisation of IgG onto gold surfaces and its interaction with anti-IgG studied by surface plasmon resonance,” J. Immunol. Methods175(2), 149–160 (1994).
[CrossRef] [PubMed]

Thompson, L. B.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008).
[CrossRef] [PubMed]

Trügler, A.

J. Becker, A. Trügler, A. Jakab, U. Hohenester, and C. Sönnichsen, “The optimal aspect ratio of gold nanorods for plasmonic bio-sensing,” Plasmonics5(2), 161–167 (2010).
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Y.-F. Chau, H.-H. Yeh, and D. P. Tsai, “Surface plasmon resonances effects on different patterns of solid-silver and silver-shell nanocylindrical pairs,” J. Electromagn. Waves Appl.24(8-9), 1005–1014 (2010).
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S. Underwood and P. Mulvaney, “Effect of the solution refractive index on the color of gold colloids,” Langmuir10(10), 3427–3430 (1994).
[CrossRef]

Urquhart, R. S.

N. J. Geddes, A. S. Martin, F. Caruso, R. S. Urquhart, D. N. Furlong, J. R. Sambles, K. A. Than, and J. A. Edgar, “Immobilisation of IgG onto gold surfaces and its interaction with anti-IgG studied by surface plasmon resonance,” J. Immunol. Methods175(2), 149–160 (1994).
[CrossRef] [PubMed]

Van Dorpe, P.

N. Verellen, P. Van Dorpe, C. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon line shaping using nanocrosses for high sensitivity localized surface plasmon resonance sensing,” Nano Lett.11(2), 391–397 (2011).
[CrossRef] [PubMed]

J. Ye and P. Van Dorpe, “Improvement of figure of merit for gold nanobar array plasmonic sensors,” Plasmonics6(4), 665–671 (2011).
[CrossRef]

Van Duyne, R. P.

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett.5(10), 2034–2038 (2005).
[CrossRef] [PubMed]

A. J. Haes and R. P. Van Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc.124(35), 10596–10604 (2002).
[CrossRef] [PubMed]

Vandenbosch, G. A. E.

N. Verellen, P. Van Dorpe, C. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon line shaping using nanocrosses for high sensitivity localized surface plasmon resonance sensing,” Nano Lett.11(2), 391–397 (2011).
[CrossRef] [PubMed]

Verellen, N.

N. Verellen, P. Van Dorpe, C. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon line shaping using nanocrosses for high sensitivity localized surface plasmon resonance sensing,” Nano Lett.11(2), 391–397 (2011).
[CrossRef] [PubMed]

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J. Vörös, “The density and refractive index of adsorbing protein layers,” Biophys. J.87(1), 553–561 (2004).
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Wang, H.

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: A hybrid plasmonic nanostructure,” Nano Lett.6(4), 827–832 (2006).
[CrossRef] [PubMed]

Wang, J.

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir24(10), 5233–5237 (2008).
[CrossRef] [PubMed]

Wax, A.

G. J. Nusz, S. M. Marinakos, A. C. Curry, A. Dahlin, F. Höök, A. Wax, and A. Chilkoti, “Label-free plasmonic detection of biomolecular binding by a single gold nanorod,” Anal. Chem.80(4), 984–989 (2008).
[CrossRef] [PubMed]

Wiley, B. J.

B. J. Wiley, Y. Chen, J. M. McLellan, Y. Xiong, Z.-Y. Li, D. Ginger, and Y. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett.7(4), 1032–1036 (2007).
[CrossRef] [PubMed]

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett.5(10), 2034–2038 (2005).
[CrossRef] [PubMed]

Xia, Y.

B. J. Wiley, Y. Chen, J. M. McLellan, Y. Xiong, Z.-Y. Li, D. Ginger, and Y. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett.7(4), 1032–1036 (2007).
[CrossRef] [PubMed]

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett.5(10), 2034–2038 (2005).
[CrossRef] [PubMed]

Xiong, Y.

B. J. Wiley, Y. Chen, J. M. McLellan, Y. Xiong, Z.-Y. Li, D. Ginger, and Y. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett.7(4), 1032–1036 (2007).
[CrossRef] [PubMed]

Xu, H.

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett.11(4), 1657–1663 (2011).
[CrossRef] [PubMed]

Yang, Z.

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir24(10), 5233–5237 (2008).
[CrossRef] [PubMed]

Ye, J.

J. Ye and P. Van Dorpe, “Improvement of figure of merit for gold nanobar array plasmonic sensors,” Plasmonics6(4), 665–671 (2011).
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Figures (6)

Fig. 1
Fig. 1

(a) Schematic of the studied U-shaped cavity together with the direction and polarization of the incident light. The parameters are the period p, the height h, the Au layer thickness t, the incident angle θ, and the refractive index of the surrounding medium n. (b) Simulated total reflectance spectrum performed with periodic boundary conditions for p = h = 1 μm, t = 50 nm, θ = 35°, and n = 1 (the total and the zero order reflectance spectra are the same in the region of the resonance dip).

Fig. 2
Fig. 2

(a) Simulated time-averaged electric field density in a cavity at the resonance wavelength of 1891 nm performed with periodic boundary conditions (the density relative to free space is shown on a log scale). The insets show high resolution images of the simulated field density. (b) Distributions of the electric field components Ex and Ez. (c) Time-averaged Poynting vector field at the resonance wavelength of 1891 nm. Optical vortices are clearly seen near the cavity center and the tops of the vertical walls. The parameters have the same values as those in Fig. 1(b).

Fig. 3
Fig. 3

(a) Reflectance variation with the incident light frequency and the cavity period p (p = h) at a fixed angle θ = 35 degrees. (b) Reflectance variation with the incident light wavelength and the incident angle θ for p = h = 1 µm. All calculations were done with t = 50 nm.

Fig. 4
Fig. 4

Time-averaged Poynting vector magnitude distribution of (a) a 5 cavity structure, (b) a 10 cavity structure, and (c) an infinite array of cavities. The parameters have the same values as those in Fig. 1(b). The resonance wavelengths were 1886 nm, 1885 nm and 1891 nm for the 5, 10, and infinite number of cavities, respectively.

Fig. 5
Fig. 5

(a) Simulated reflectance spectra of the Au U-shaped cavities for p = h = 1 μm, t = 50 nm and θ = 35 degrees. The solid and dashed curves show the results for two surrounding media of different refractive indices (n = 1.333 and 1.361). (b) Calculated S* with a maximum value reaching 25.4. (c) Calculated FOM* with a maximum value over 106.

Fig. 6
Fig. 6

FOM (open circle) and resonance wavelength (filled square) variations with the period of the U-shaped cavities when n is varied from 1.333 to 1.361. The ratio between period and height of the cavities is kept constant (p = h), θ = 35 degrees and t = 50 nm.

Tables (1)

Tables Icon

Table 1 Sensitivities and figure of merits for infinite and finite arrays of cavities

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