Abstract

Metal nanoparticle arrays have proved useful for different applications due to their ability to enhance electromagnetic fields within a few tens of nanometers. This field enhancement results from the excitation of various plasmonic modes at certain resonance frequencies. In this article, we have studied an array of metallic nanocylinders placed on a thin metallic film. A simple analytical model is proposed to explain the existence of the different types of modes that can be excited in such a structure. Owing to the cylinder array, the structure can support localized surface plasmon (LSP) modes. The LSP mode couples to the propagating surface plasmon (PSP) mode of the thin film to give rise to the hybrid lattice plasmon (HLP) mode and anti-crossing phenomenon. Due to the periodicity of the array, the Bragg modes (BM) are also excited in the structure. We have calculated analytically the resonance frequencies of the BM, LSP and the corresponding HLP, and have verified the calculations by rigorous numerical methods. Experimental results obtained in the Kretschmann configuration also validate the proposed analytical model. The dependency of the resonance frequencies of these modes on the structural parameters such as cylinder diameter, height and the periodicity of the array is shown. Such a detailed study can offer insights on the physical phenomenon that governs the excitation of various plasmonic modes in the system. It is also useful to optimize the structure as per required for the different applications, where such types of structures are used.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]

2015 (6)

S. Chen, L. Y. Meng, J. W. Hu, and Z. L. Yang, “Fano interference between higher localized and propagating surface plasmon modes in nanovoid arrays,” Plasmonics 10(1), 71–76 (2015).
[Crossref]

M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015).
[Crossref]

Y. Chang and Y. Jiang, “Multiple surface plasmon polaritons modes on thin silver film controlled by a two-dimensional lattice of silver nanodimers,” J. Nanopart. Res. 17(1), 1–8 (2015).
[Crossref]

V. Yannopapas, “Periodic arrays of film-coupled cubic nanoantennas as tunable plasmonic metasurfaces,” Photonics 2(1), 270–278 (2015).
[Crossref]

S. H. Shams Mousavi, A. A. Eftekhar, A. H. Atabaki, and A. Adibi, “Band-edge bilayer plasmonic nanostructure for surface enhanced Raman spectroscopy,” ACS Photonics 10, 500487 (2015).
[Crossref]

R. Giannini, C. V. Hafner, and J. F. Löffler, “Scaling behavior of individual nanoparticle plasmon resonances,” J. Phys. Chem. C 119(11), 6138–6147 (2015).
[Crossref]

2014 (7)

M. Sarkar, M. Chamtouri, J. Moreau, M. Besbes, and M. Canva, “Introducing 2D confined propagating plasmons for surface plasmon resonance sensing using arrays of metallic ribbons,” Sensor Actuat. Biol. Chem. 191, 115–121 (2014).

D. M. Solís, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzán, and F. J. García de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8(8), 7559–7570 (2014).
[Crossref] [PubMed]

T. Špringer, M. L. Ermini, B. Špačková, J. Jabloňků, and J. Homola, “Enhancing sensitivity of surface plasmon resonance biosensors by functionalized gold nanoparticles: Size matters,” Anal. Chem. 86(20), 10350–10356 (2014).
[Crossref] [PubMed]

M. Chamtouri, A. Dhawan, M. Besbes, J. Moreau, H. Ghalila, T. Vo-Dinh, and M. Canva, “Enhanced SPR Sensitivity with nano-micro-ribbon grating-an exhaustive simulation mapping,” Plasmonics 9(1), 79–92 (2014).
[Crossref]

A. Sereda, J. Moreau, M. Canva, and E. Maillart, “High performance multi-spectral interrogation for surface plasmon resonance imaging sensors,” Biosens. Bioelectron. 54, 175–180 (2014).
[Crossref] [PubMed]

F. Zhou, Y. Liu, and W. Cai, “Huge local electric field enhancement in hybrid plasmonic arrays,” Opt. Lett. 39(5), 1302–1305 (2014).
[Crossref] [PubMed]

M. Chamtouri, M. Sarkar, J. Moreau, M. Besbes, H. Ghalila, and M. Canva, “Field enhancement and target localization impact on the biosensitivity of nanostructured plasmonic sensors,” J. Opt. Soc. Am. B 31(5), 1223–1231 (2014).
[Crossref]

2013 (5)

D. Barchiesi, S. Kessentini, N. Guillot, M. L. de la Chapelle, and T. Grosges, “Localized surface plasmon resonance in arrays of nano-gold cylinders: inverse problem and propagation of uncertainties,” Opt. Express 21(2), 2245–2262 (2013).
[Crossref] [PubMed]

A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of fano resonances in coupled plasmonic systems,” ACS Nano 7(5), 4527–4536 (2013).
[Crossref] [PubMed]

K. Lodewijks, J. Ryken, W. Van Roy, G. Borghs, L. Lagae, and P. Van Dorpe, “Tuning the Fano resonance between localized and propagating surface plasmon resonances for refractive index sensing applications,” Plasmonics 8(3), 1379–1385 (2013).
[Crossref]

C. Forestiere, L. Dal Negro, and G. Miano, “Theory of coupled plasmon modes and Fano-like resonances in subwavelength metal structures,” Phys. Rev. B 88(15), 155411 (2013).
[Crossref]

J. B. Lassiter, F. McGuire, J. J. Mock, C. Ciracì, R. T. Hill, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Plasmonic waveguide modes of film-coupled metallic nanocubes,” Nano Lett. 13(12), 5866–5872 (2013).
[Crossref] [PubMed]

2012 (4)

Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by fano resonances,” ACS Nano 6(2), 1830–1838 (2012).
[Crossref] [PubMed]

D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, K. Appavoo, R. F. Haglund, J. B. Pendry, and S. A. Maier, “Revealing plasmonic gap modes in particle-on-film systems using dark-field spectroscopy,” ACS Nano 6(2), 1380–1386 (2012).
[Crossref] [PubMed]

A. T. M. A. Rahman, P. Majewski, and K. Vasilev, “Extraordinary optical transmission: coupling of the Wood-Rayleigh anomaly and the Fabry-Perot resonance,” Opt. Lett. 37(10), 1742–1744 (2012).
[Crossref] [PubMed]

X. L. Wang, P. Gogol, E. Cambril, and B. Palpant, “Near- and far-field effects on the plasmon coupling in gold nanoparticle arrays,” J. Phys. Chem. C 116(46), 24741–24747 (2012).
[Crossref]

2010 (7)

M. Nakkach, A. Duval, B. Ea-Kim, J. Moreau, and M. Canva, “Angulo-spectral surface plasmon resonance imaging of nanofabricated grating surfaces,” Opt. Lett. 35(13), 2209–2211 (2010).
[Crossref] [PubMed]

A. Hohenau and J. R. Krenn, “Plasmonic modes of gold nano-particle arrays on thin gold films,” Phys. Status Solidi 4(10), 256–258 (2010).
[Crossref]

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(9), 707–715 (2010).
[Crossref] [PubMed]

L. Novotny, “Strong coupling, energy splitting, and level crossings: A classical perspective,” Am. J. Phys. 78(11), 1199–1202 (2010).
[Crossref]

T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10(7), 2618–2625 (2010).
[Crossref] [PubMed]

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

K. C. Vernon, A. M. Funston, C. Novo, D. E. Gómez, P. Mulvaney, and T. J. Davis, “Influence of particle-substrate interaction on localized plasmon resonances,” Nano Lett. 10(6), 2080–2086 (2010).
[Crossref] [PubMed]

2009 (4)

2008 (3)

J. P. Hugonin, M. Besbes, and P. Lalanne, “Hybridization of electromagnetic numerical methods through the G-matrix algorithm,” Opt. Lett. 33(14), 1590–1592 (2008).
[Crossref] [PubMed]

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
[Crossref] [PubMed]

P. G. Etchegoin and E. C. Le Ru, “A perspective on single molecule SERS: current status and future challenges,” Phys. Chem. Chem. Phys. 10(40), 6079–6089 (2008).
[Crossref] [PubMed]

2007 (3)

J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
[Crossref]

N. Papanikolaou, “Optical properties of metallic nanoparticle arrays on a thin metallic film,” Phys. Rev. B 75(23), 235426 (2007).
[Crossref]

C. Noguez, “Surface plasmons on metal nanoparticles: The influence of shape and physical environment,” J. Phys. Chem. C 111(10), 3806–3819 (2007).
[Crossref]

2006 (2)

A. Mejdoubi and C. Brosseau, “Finite-element simulation of the depolarization factor of arbitrarily shaped inclusions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3 Pt 1), 031405 (2006).
[PubMed]

G. C. Schatz, M. A. Young, and R. P. Van Duyne, “Electromagnetic mechanism of SERS,” Top. Appl. Phys. 103, 19–45 (2006).
[Crossref]

2005 (2)

F. Marquier, J. Greffet, S. Collin, F. Pardo, and J. Pelouard, “Resonant transmission through a metallic film due to coupled modes,” Opt. Express 13(1), 70–76 (2005).
[Crossref] [PubMed]

J. Grand, M. L. de la Chapelle, J. L. Bijeon, P. M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72(3), 033407 (2005).
[Crossref]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

2002 (1)

A. Zehe and A. Ramirez, “The depolarization field in polarizable objects of general shape,” Rev. Mex. Fis. 48, 427–431 (2002).

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

1996 (1)

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996).
[Crossref] [PubMed]

1995 (1)

1988 (1)

H. Raether, “Surface-plasmons on smooth and rough surfaces and on gratings,” Springer Tr. Mod. Phys. 111, 1–133 (1988).

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Adam, P. M.

J. Grand, M. L. de la Chapelle, J. L. Bijeon, P. M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72(3), 033407 (2005).
[Crossref]

Adibi, A.

S. H. Shams Mousavi, A. A. Eftekhar, A. H. Atabaki, and A. Adibi, “Band-edge bilayer plasmonic nanostructure for surface enhanced Raman spectroscopy,” ACS Photonics 10, 500487 (2015).
[Crossref]

Appavoo, K.

D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, K. Appavoo, R. F. Haglund, J. B. Pendry, and S. A. Maier, “Revealing plasmonic gap modes in particle-on-film systems using dark-field spectroscopy,” ACS Nano 6(2), 1380–1386 (2012).
[Crossref] [PubMed]

Atabaki, A. H.

S. H. Shams Mousavi, A. A. Eftekhar, A. H. Atabaki, and A. Adibi, “Band-edge bilayer plasmonic nanostructure for surface enhanced Raman spectroscopy,” ACS Photonics 10, 500487 (2015).
[Crossref]

Atwater, H. A.

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

Barbillon, G.

M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015).
[Crossref]

Barchiesi, D.

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996).
[Crossref] [PubMed]

Bartenlian, B.

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A. Sereda, J. Moreau, M. Canva, and E. Maillart, “High performance multi-spectral interrogation for surface plasmon resonance imaging sensors,” Biosens. Bioelectron. 54, 175–180 (2014).
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V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
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M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015).
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M. Sarkar, M. Chamtouri, J. Moreau, M. Besbes, and M. Canva, “Introducing 2D confined propagating plasmons for surface plasmon resonance sensing using arrays of metallic ribbons,” Sensor Actuat. Biol. Chem. 191, 115–121 (2014).

M. Chamtouri, M. Sarkar, J. Moreau, M. Besbes, H. Ghalila, and M. Canva, “Field enhancement and target localization impact on the biosensitivity of nanostructured plasmonic sensors,” J. Opt. Soc. Am. B 31(5), 1223–1231 (2014).
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A. Sereda, J. Moreau, M. Canva, and E. Maillart, “High performance multi-spectral interrogation for surface plasmon resonance imaging sensors,” Biosens. Bioelectron. 54, 175–180 (2014).
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S. H. Shams Mousavi, A. A. Eftekhar, A. H. Atabaki, and A. Adibi, “Band-edge bilayer plasmonic nanostructure for surface enhanced Raman spectroscopy,” ACS Photonics 10, 500487 (2015).
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J. B. Lassiter, F. McGuire, J. J. Mock, C. Ciracì, R. T. Hill, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Plasmonic waveguide modes of film-coupled metallic nanocubes,” Nano Lett. 13(12), 5866–5872 (2013).
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D. M. Solís, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzán, and F. J. García de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8(8), 7559–7570 (2014).
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D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, K. Appavoo, R. F. Haglund, J. B. Pendry, and S. A. Maier, “Revealing plasmonic gap modes in particle-on-film systems using dark-field spectroscopy,” ACS Nano 6(2), 1380–1386 (2012).
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T. Špringer, M. L. Ermini, B. Špačková, J. Jabloňků, and J. Homola, “Enhancing sensitivity of surface plasmon resonance biosensors by functionalized gold nanoparticles: Size matters,” Anal. Chem. 86(20), 10350–10356 (2014).
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D. M. Solís, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzán, and F. J. García de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8(8), 7559–7570 (2014).
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J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
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J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
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K. C. Vernon, A. M. Funston, C. Novo, D. E. Gómez, P. Mulvaney, and T. J. Davis, “Influence of particle-substrate interaction on localized plasmon resonances,” Nano Lett. 10(6), 2080–2086 (2010).
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T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10(7), 2618–2625 (2010).
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T. J. Davis, K. C. Vernon, and D. E. Gomez, “Designing plasmonic systems using optical coupling between nanoparticles,” Phys. Rev. B 79(15), 155423 (2009).
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Vial, A.

J. Grand, M. L. de la Chapelle, J. L. Bijeon, P. M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72(3), 033407 (2005).
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M. Chamtouri, A. Dhawan, M. Besbes, J. Moreau, H. Ghalila, T. Vo-Dinh, and M. Canva, “Enhanced SPR Sensitivity with nano-micro-ribbon grating-an exhaustive simulation mapping,” Plasmonics 9(1), 79–92 (2014).
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X. L. Wang, P. Gogol, E. Cambril, and B. Palpant, “Near- and far-field effects on the plasmon coupling in gold nanoparticle arrays,” J. Phys. Chem. C 116(46), 24741–24747 (2012).
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J. B. Lassiter, F. McGuire, J. J. Mock, C. Ciracì, R. T. Hill, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Plasmonic waveguide modes of film-coupled metallic nanocubes,” Nano Lett. 13(12), 5866–5872 (2013).
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T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
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S. Chen, L. Y. Meng, J. W. Hu, and Z. L. Yang, “Fano interference between higher localized and propagating surface plasmon modes in nanovoid arrays,” Plasmonics 10(1), 71–76 (2015).
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V. Yannopapas, “Periodic arrays of film-coupled cubic nanoantennas as tunable plasmonic metasurfaces,” Photonics 2(1), 270–278 (2015).
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G. C. Schatz, M. A. Young, and R. P. Van Duyne, “Electromagnetic mechanism of SERS,” Top. Appl. Phys. 103, 19–45 (2006).
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A. Zehe and A. Ramirez, “The depolarization field in polarizable objects of general shape,” Rev. Mex. Fis. 48, 427–431 (2002).

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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(9), 707–715 (2010).
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ACS Nano (4)

A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of fano resonances in coupled plasmonic systems,” ACS Nano 7(5), 4527–4536 (2013).
[Crossref] [PubMed]

D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, K. Appavoo, R. F. Haglund, J. B. Pendry, and S. A. Maier, “Revealing plasmonic gap modes in particle-on-film systems using dark-field spectroscopy,” ACS Nano 6(2), 1380–1386 (2012).
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D. M. Solís, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzán, and F. J. García de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8(8), 7559–7570 (2014).
[Crossref] [PubMed]

ACS Photonics (2)

S. H. Shams Mousavi, A. A. Eftekhar, A. H. Atabaki, and A. Adibi, “Band-edge bilayer plasmonic nanostructure for surface enhanced Raman spectroscopy,” ACS Photonics 10, 500487 (2015).
[Crossref]

M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015).
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Am. J. Phys. (1)

L. Novotny, “Strong coupling, energy splitting, and level crossings: A classical perspective,” Am. J. Phys. 78(11), 1199–1202 (2010).
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Anal. Chem. (1)

T. Špringer, M. L. Ermini, B. Špačková, J. Jabloňků, and J. Homola, “Enhancing sensitivity of surface plasmon resonance biosensors by functionalized gold nanoparticles: Size matters,” Anal. Chem. 86(20), 10350–10356 (2014).
[Crossref] [PubMed]

Biosens. Bioelectron. (1)

A. Sereda, J. Moreau, M. Canva, and E. Maillart, “High performance multi-spectral interrogation for surface plasmon resonance imaging sensors,” Biosens. Bioelectron. 54, 175–180 (2014).
[Crossref] [PubMed]

Chem. Soc. Rev. (1)

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
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J. Nanopart. Res. (1)

Y. Chang and Y. Jiang, “Multiple surface plasmon polaritons modes on thin silver film controlled by a two-dimensional lattice of silver nanodimers,” J. Nanopart. Res. 17(1), 1–8 (2015).
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J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Phys. Chem. C (3)

X. L. Wang, P. Gogol, E. Cambril, and B. Palpant, “Near- and far-field effects on the plasmon coupling in gold nanoparticle arrays,” J. Phys. Chem. C 116(46), 24741–24747 (2012).
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Nano Lett. (3)

K. C. Vernon, A. M. Funston, C. Novo, D. E. Gómez, P. Mulvaney, and T. J. Davis, “Influence of particle-substrate interaction on localized plasmon resonances,” Nano Lett. 10(6), 2080–2086 (2010).
[Crossref] [PubMed]

T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10(7), 2618–2625 (2010).
[Crossref] [PubMed]

J. B. Lassiter, F. McGuire, J. J. Mock, C. Ciracì, R. T. Hill, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Plasmonic waveguide modes of film-coupled metallic nanocubes,” Nano Lett. 13(12), 5866–5872 (2013).
[Crossref] [PubMed]

Nat. Mater. (2)

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(9), 707–715 (2010).
[Crossref] [PubMed]

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

Nat. Phys. (1)

J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
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Nature (2)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
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Opt. Express (4)

Opt. Lett. (5)

Photonics (1)

V. Yannopapas, “Periodic arrays of film-coupled cubic nanoantennas as tunable plasmonic metasurfaces,” Photonics 2(1), 270–278 (2015).
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Phys. Chem. Chem. Phys. (1)

P. G. Etchegoin and E. C. Le Ru, “A perspective on single molecule SERS: current status and future challenges,” Phys. Chem. Chem. Phys. 10(40), 6079–6089 (2008).
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Phys. Rev. B (5)

N. Papanikolaou, “Optical properties of metallic nanoparticle arrays on a thin metallic film,” Phys. Rev. B 75(23), 235426 (2007).
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C. Forestiere, L. Dal Negro, and G. Miano, “Theory of coupled plasmon modes and Fano-like resonances in subwavelength metal structures,” Phys. Rev. B 88(15), 155411 (2013).
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Figures (11)

Fig. 1
Fig. 1 The studied structure geometry consists of an array of metallic cylinders of diameter D and height h2 placed on a thin metallic film of height h1. The refractive index on the side of the array was taken as nw while that on the other side was ng. A sketch of the numerical method is also shown, which uses a mesh around the nanostructured region to calculate the S matrix by FEM, and then uses FMM to calculate the far-field response of the system.
Fig. 2
Fig. 2 Left, the analytically calculated polarizability α(k0) for a nanocylinder of 30 nm height and 50 nm diameter in a homogenous medium nw (in red). The same for the cylinder placed on a semi-infinite gold medium (in blue). The calculated LSP frequency for the later configuration is k0 = 8.87 µm−1. Center, the HLP mode (green) dispersion, which results from the harmonic coupling of the LSP and PSP. Right, the calculated dispersion (k0-neff) for the PSP in a gold film with plasmons propagating in the medium nw. The resonance frequencies of the LSP (blue solid) and the PSP (blue dotted) are also shown. For this scheme, the period of the array was taken as 180 nm.
Fig. 3
Fig. 3 . (a) The normalized absorption (A) dispersion map as a function of k0 and neff for h2 = 30 nm, D = 50 nm, and period Λ = 180 nm with the medium around the nanocylinders of refractive index nw. The lightline in the medium is defined as neff = nw. The proposed analytical calculation of the dispersion of different modes of the system are also shown: LSP (blue solid), PSP (blue dashed), HLP (green), and BMs (black solid and dashed). (b) Same as (a) for period Λ = 300 nm.
Fig. 4
Fig. 4 The resonance frequencies (k0) of all the modes in the structure (D = 50 nm, h2 = 30 nm) manifest as absorption maxima in the dispersion map calculated by rigorous numerical method (red dots) as a function of array period for neff = 1.42. We have superposed the analytically calculated frequencies of the modes as a function of period: LSP (blue), HLP (green), BMs calculated for kB = 2π/(Λ) (black solid and dashed) and BMs for kB = 2π/(Λ + D) (red dashed and solid).
Fig. 5
Fig. 5 (a) The resonance frequencies (k0) of HLP modes in the structure (Λ = 350 nm, D = 50 nm) manifest as absorption maxima in the dispersion map calculated by rigorous numerical method (red dots) as a function of cylinder height (h2) for neff = 1.45. We have superposed the analytically calculated frequencies of the modes as a function of h2: LSP (blue), HLP (green). (b) For D = 90 nm with the same period as previously.
Fig. 6
Fig. 6 The normalized reflectivity (R) dispersion map as a function of k0 and neff for h2 = 30 nm, D = 50 nm and period Λ = 340 nm with the medium around the nanocylinders of refractive index nw in the Kretschmann configuration. The lightline in the medium is defined as neff = nw. The analytical calculation of the dispersion of different modes of the system are also shown: LSP (blue solid), PSP (blue dashed), HLP (green) and BMs (black and red solid and dashed same as Fig. 4). (b) The transmission (T) for the same parameters.
Fig. 7
Fig. 7 (a) Scheme of the SPR imaging system used to characterize the fabricated nanostructure in the Kretschmann configuration. (b) An image of the structured chip with 3 × 6 zones as obtained by the SPR imaging system. Each zone has a size of 500 × 500 µm2 and has the same structural parameters (diameter and periodicity of cylinders) along the rows. The period is changed from 150 nm to 400 nm along the columns as shown in the figure. (c) SEM images of cylinder with a diameter of 50 nm and periods of 150 nm, 250 nm and 400 nm. (d) The experimental reflectivity (R) dispersion map as a function of k0 and neff for h2 = 30 nm, D = 50 nm and period Λ = 300 nm. The experimental reflectivity map should be compared to the numerical absorption map of Fig. 3(b), which has the same structural dimensions. The analytical calculation of the dispersion of different modes of the system is also shown.
Fig. 8
Fig. 8 (a) Normalized reflectivity spectra at θ = 71.14° for different period (Λ) of the structure. Arrows show the reflectivity minima, which correspond to the various modes excited in the structure. (b) The resonance frequencies (k0) of all the modes (minima of reflectivity) are shown as red squares as a function of array period. The error bars correspond to the minimum step of incident wavelength (10 nm) used for the experiment. We have superposed the analytically calculated frequencies of the modes as a function of period: LSP (blue), HLP (green), BMs calculated for kB = 2π/(Λ) (black solid and dashed) and BMs for kB = 2π/(Λ + D) (red dashed and solid).
Fig. 9
Fig. 9 The normalized absorption (A) dispersion maps calculated by numerical methods with varying period (Λ) as a function of k0 and neff for h2 = 30nm, D = 50nm. The analytically calculated dispersion of the various modes is also shown which fits accurately to the rigorously calculated numerical results.
Fig. 10
Fig. 10 The normalized reflectivity (R) dispersion maps calculated by numerical methods with varying h2 and D function of k0 and neff for Λ = 350nm. The analytically calculated dispersion of the various modes is also shown and the color legend is same as Fig. 9.
Fig. 11
Fig. 11 The normalized reflectivity (R) dispersion maps obtained experimentally with varying period (Λ) as a function of k0 and neff for h2 = 30nm, D = 50nm. The analytically calculated dispersion of the various modes is also shown and the color legend is same as Fig. 9.

Equations (5)

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α(ω)=const× n m 2 (ω) n d 2 n d 2 +L( n m 2 (ω) n d 2 )
n e 2 = n d 2 [ 1+ηT/1+γ 1+ηT/1γ ]
k psp:d = k 0 n d 2 n m 2 n d 2 + n m 2
ω HLP ± 2 = 1 2 [ ω 1 2 + ω 2 2 ± ( ω 1 2 ω 2 2 ) 2 +4 κ 2 ]
k BM = k psp:d ±m k B

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