Abstract

We report on the calculation of the fundamental plasmon waveguide modes in linear periodic chains of finite silver nanorods, aligned perpendicular to the chain. The results of rigorous full-electrodynamic calculations by the layer-multiple-scattering method are discussed in conjunction with the results of the widely used coupled-dipole model and a critical evaluation of the latter is provided. More specifically, it is shown that both diameter and height of the nanorods must be much smaller than the interparticle distance; otherwise, for relatively long nanorods close to each other, the coupled-dipole model can fail completely to predict the waveguide dispersion diagram. Moreover, the model systematically underestimates the effect of dissipative losses and cannot describe the effect of a supporting substrate, which is always present in realistic cases and induces considerable changes in the waveguide dispersion diagram.

© 2012 Optical Society of America

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    [CrossRef]

2011

A. Alù, P. A. Belov, and N. Engheta, “Coupling and guided propagation along parallel chains of plasmonic nanoparticles,” New J. Phys. 13, 033026 (2011).
[CrossRef]

Y. Hadad and B. Z. Steinberg, “Green’s function theory for infinite and semi-infinite particle chains,” Phys. Rev. B 84, 125402 (2011).
[CrossRef]

I. B. Udagedara, I. D. Rukhlenko, and M. Premaratne, “Complex–ω approach versus complex-k approach in description of gain-assisted surface plasmon-polariton propagation along linear chains of metallic nanospheres,” Phys. Rev. B 83, 115451 (2011).
[CrossRef]

S. Habouti, M. Mátéfi-Tempfli, C.-H. Solterbeck, M. Es-Souni, S. Mátéfi-Tempfli, and M. Es-Souni, “Self-standing corrugated Ag and Au-nanorods for plasmonic applications,” J. Mater. Chem. 21, 6269–6273 (2011).
[CrossRef]

M. Guasoni and M. Conforti, “Complex dispersion relation of a double chain of lossy metal nanoparticles,” J. Opt. Soc. Am. B 28, 1019–1025 (2011).
[CrossRef]

K. H. Fung, R. C. H. Tang, and C. T. Chan, “Analytical properties of the plasmon decay profile in a periodic metal-nanoparticle chain,” Opt. Lett. 36, 2206–2208 (2011).
[CrossRef]

S. Campione, S. Steshenko, and F. Capolino, “Complex bound and leaky modes in chains of plasmonic nanospheres,” Opt. Express 19, 18345–18363 (2011).
[CrossRef]

I. B. Udagedara, I. D. Rukhlenko, and M. Premaratne, “Surface plasmon-polariton propagation in piecewise linear chains of composite nanospheres: the role of optical gain and chain layout,” Opt. Express 19, 19973–19986 (2011).
[CrossRef]

M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express 19, 22029–22106 (2011).
[CrossRef]

2010

M. Conforti and M. Guasoni, “Dispersive properties of linear chains of lossy metal nanoparticles,” J. Opt. Soc. Am. B 27, 1576–1582 (2010).
[CrossRef]

R. Kullock, S. Grafström, P. R. Evans, R. J. Pollard, and L. M. Eng, “Metallic nanorod arrays: negative refraction and optical properties explained by retarded dipolar interactions,” J. Opt. Soc. Am. B 27, 1819–1827 (2010).
[CrossRef]

C. Tserkezis, N. Stefanou, and N. Papanikolaou, “Extraordinary refractive properties of photonic crystals of metallic nanorods,” J. Opt. Soc. Am. B 27, 2620–2627 (2010).
[CrossRef]

M. Fleischer, D. Zhang, K. Braun, S. Jäger, R. Ehlich, M. Häffner, C. Stanciu, J. K. H. Hörber, A. J. Meixner, and D. P. Kern, “Tailoring gold nanostructures for near-field optical applications,” Nanotechnology 21, 065301 (2010).
[CrossRef]

D. J. Lipomi, M. A. Kats, P. Kim, S. H. Kang, J. Aizenberg, F. Capasso, and G. M. Whitesides, “Fabrication and replication of arrays of single- or multicomponent nanostructures by replica molding and mechanical sectioning,” ACS Nano 4, 4017–4026 (2010).
[CrossRef]

Y.-F. Chau, H.-H. Yeh, C.-Y. Liu, and D. P. Tsai, “The optical properties in a chain waveguide of an array of silver nanoshell with dielectric holes,” Opt. Commun. 283, 3189–3193 (2010).
[CrossRef]

2009

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterial for biosensing,” Nat. Mater. 8, 867–871 (2009).
[CrossRef]

G. Gantzounis, “Plasmon modes in axisymmetric metallic nanoparticles: a group theory analysis,” J. Phys. Chem. C 113, 21560–21565 (2009).
[CrossRef]

A. F. Koenderink, “Plasmon nanoparticle array waveguides for single photon and single plasmon sources,” Nano Lett. 9, 4228–4233 (2009).

A. Alù and N. Engheta, “Guided propagation along quadrupolar chains of plasmonic nanoparticles,” Phys. Rev. B 79, 235412 (2009).
[CrossRef]

N. Stefanou, G. Gantzounis, and C. Tserkezis, “Multiple-scattering calculations for plasmonic nanostructures,” Int. J. Nanotechnol. 6, 137–163 (2009).

C. Tserkezis, N. Papanikolaou, E. Almpanis, and N. Stefanou, “Tailoring plasmons with metallic nanorod arrays,” Phys. Rev. B 80, 125124 (2009).
[CrossRef]

2008

G. A. Wurtz, W. Dickson, D. O’Connor, R. Atkinson, W. Hendren, P. Evans, R. Pollard, and A. V. Zayats, “Guided plasmonic modes in nanorod assemblies: strong electromagnetic couping regime,” Opt. Express 16, 7460–7470 (2008).
[CrossRef]

T. Yang and K. B. Crozier, “Dispersion and extinction of surface plasmons in an array of gold nanoparticle chains: influence of the air/glass interface,” Opt. Express 16, 8570–8580 (2008).
[CrossRef]

R. Kullock, W. R. Hendren, A. Hille, S. Grafström, P. R. Evans, R. J. Pollard, R. Atkinson, and L. M. Eng, “Polarization conversion through collective surface plasmons in metallic nanorod arrays,” Opt. Express 16, 21671–21681 (2008).
[CrossRef]

S. Kawata, A. Ono, and P. Verma, “Subwavelength colour imaging with a metallic nanolens,” Nat. Photon. 2, 438–442 (2008).
[CrossRef]

W. T. Lu and S. Sridhar, “Superlens imaging theory for anisotropic nanostructured metamaterials with broadband all-angle negative refraction,” Phys. Rev. B 77, 233101 (2008).
[CrossRef]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

D. P. Lyvers, J.-M. Moon, A. V. Kildishev, V. M. Shalaev, and A. Wei, “Gold nanorod arrays as plasmonic cavity resonators,” ACS Nano 2, 2569–2576 (2008).
[CrossRef]

K. H. Fung and C. T. Chan, “A computational study of the optical response of strongly coupled metal nanoparticle chains,” Opt. Commun. 281, 855–864 (2008).
[CrossRef]

E. R. Encina and E. A. Coronado, “Plasmonic nanoantennas: angular scattering properties of multipole resonances in noble metal nanorods,” J. Phys. Chem. C 112, 9586–9594 (2008).
[CrossRef]

2007

B. N. Khlebtsov and N. G. Khlebtsov, “Multipole plasmons on metal nanorods: scaling properties and dependence on particle size, shape, orientation, and dielectric environment,” J. Phys. Chem. C 111, 11516–11527 (2007).
[CrossRef]

W. Dickson, G. A. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. V. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: a metamaterial with tuneable optical properties,” Phys. Rev. B 76, 115411 (2007).
[CrossRef]

A. F. Koenderink, R. deWaele, J. C. Prangsma, and A. Polman, “Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides,” Phys. Rev. B 76, 201403(R) (2007).
[CrossRef]

F. M. Wang, H. Liu, T. Li, S. M. Wang, S. N. Zhu, J. Zhu, and W. Cao, “Highly confined energy propagation in a gap waveguide composed of two coupled nanorod chains,” Appl. Phys. Lett. 91, 133107 (2007).
[CrossRef]

K. H. Fung and C. T. Chan, “Plasmonic modes in periodic metal nanoparticle chains: a direct dynamic eigenmode analysis,” Opt. Lett. 32, 973–975 (2007).
[CrossRef]

2006

D. S. Citrin, “Plasmon-polariton transport in metal-nanoparticle chains embedded in a gain medium,” Opt. Lett. 31, 98–100 (2006).
[CrossRef]

G. Gantzounis and N. Stefanou, “Layer-multiple-scattering method for photonic crystals of nonspherical particles,” Phys. Rev. B 73, 035115 (2006).
[CrossRef]

G. Gantzounis and N. Stefanou, “Cavity-plasmon waveguides: multiple scattering calculations of dispersion in weakly coupled dielectric nanocavities in a metallic host material,” Phys. Rev. B 74, 085102 (2006).
[CrossRef]

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).

A. Alù and N. Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev. B 74, 205436 (2006).
[CrossRef]

Y. Liu, J. Fan, Y.-P. Zhao, S. Shanmukh, and R. A. Dluhy, “Angle dependent surface enhanced Raman scattering obtained from an Ag nanorod array substrate,” Appl. Phys. Lett. 89, 173134 (2006).
[CrossRef]

R. Atkinson, W. R. Hendren, G. A. Wurtz, W. Dickson, A. V. Zayats, P. Evans, and R. J. Pollard, “Anisotropic optical properties of arrays of gold nanorods embedded in alumina,” Phys. Rev. B 73, 235402 (2006).
[CrossRef]

S. W. Prescott and P. Mulvaney, “Gold nanorod extinction spectra,” J. Appl. Phys. 99, 123504 (2006).
[CrossRef]

2005

K.-S. Lee and M. A. El-Sayed, “Dependence of the enhanced optical scattering efficiency relative to that of absorption for gold metal nanorods on aspect ratio, size, end-cap shape, and medium refractive index,” J. Phys. Chem. B 109, 20331–20338 (2005).
[CrossRef]

J. Venermo and A. Sihvola, “Dielectric polarizability of circular cylinder,” J. Electrost. 63, 101–117 (2005).
[CrossRef]

C. R. Simovski, A. J. Viitanen, and S. A. Tretyakov, “Resonator mode in chains of silver spheres and its possible application,” Phys. Rev. E 72, 066606 (2005).
[CrossRef]

2004

S. Y. Park and D. Stroud, “Surface-plasmon dispersion relations in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B 69, 125418 (2004).
[CrossRef]

D. S. Citrin, “Coherent excitation transport in metal-nanoparticle chains,” Nano Lett. 4, 1561–1565 (2004).
[CrossRef]

W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70, 125429 (2004).
[CrossRef]

R. Quidant, C. Girard, J.-C. Weeber, and A. Dereux, “Tailoring the transmittance of integrated optical waveguides with short metallic nanoparticle chains,” Phys. Rev. B 69, 085407 (2004).
[CrossRef]

2003

S. K. Gray and T. Kupka, “Propagation of light in metallic nanowire arrays: finite-difference time-domain studies of silver cylinders,” Phys. Rev. B 68, 045415 (2003).
[CrossRef]

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[CrossRef]

2002

S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, “Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy,” Phys. Rev. B 65, 193408 (2002).
[CrossRef]

S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: estimation of waveguide loss,” Appl. Phys. Lett. 81, 1714–1716 (2002).
[CrossRef]

2001

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics–A route to nanoscale optical devices,” Adv. Mater. 13, 1501–1505 (2001).
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1998

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W. Dickson, G. A. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. V. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: a metamaterial with tuneable optical properties,” Phys. Rev. B 76, 115411 (2007).
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A. F. Koenderink, R. deWaele, J. C. Prangsma, and A. Polman, “Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides,” Phys. Rev. B 76, 201403(R) (2007).
[CrossRef]

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).

Krenn, J. R.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticles,” Opt. Lett. 23, 1331–1333 (1998).
[CrossRef]

Kullock, R.

Kupka, T.

S. K. Gray and T. Kupka, “Propagation of light in metallic nanowire arrays: finite-difference time-domain studies of silver cylinders,” Phys. Rev. B 68, 045415 (2003).
[CrossRef]

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Lacroute, Y.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

Lee, K.-S.

K.-S. Lee and M. A. El-Sayed, “Dependence of the enhanced optical scattering efficiency relative to that of absorption for gold metal nanorods on aspect ratio, size, end-cap shape, and medium refractive index,” J. Phys. Chem. B 109, 20331–20338 (2005).
[CrossRef]

Leitner, A.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticles,” Opt. Lett. 23, 1331–1333 (1998).
[CrossRef]

Lewin, L.

L. Lewin, Polylogarithms and Associated Functions (Elsevier, 1981).

Li, T.

F. M. Wang, H. Liu, T. Li, S. M. Wang, S. N. Zhu, J. Zhu, and W. Cao, “Highly confined energy propagation in a gap waveguide composed of two coupled nanorod chains,” Appl. Phys. Lett. 91, 133107 (2007).
[CrossRef]

Lipomi, D. J.

D. J. Lipomi, M. A. Kats, P. Kim, S. H. Kang, J. Aizenberg, F. Capasso, and G. M. Whitesides, “Fabrication and replication of arrays of single- or multicomponent nanostructures by replica molding and mechanical sectioning,” ACS Nano 4, 4017–4026 (2010).
[CrossRef]

Liu, C.-Y.

Y.-F. Chau, H.-H. Yeh, C.-Y. Liu, and D. P. Tsai, “The optical properties in a chain waveguide of an array of silver nanoshell with dielectric holes,” Opt. Commun. 283, 3189–3193 (2010).
[CrossRef]

Liu, H.

F. M. Wang, H. Liu, T. Li, S. M. Wang, S. N. Zhu, J. Zhu, and W. Cao, “Highly confined energy propagation in a gap waveguide composed of two coupled nanorod chains,” Appl. Phys. Lett. 91, 133107 (2007).
[CrossRef]

Liu, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Y. Liu, J. Fan, Y.-P. Zhao, S. Shanmukh, and R. A. Dluhy, “Angle dependent surface enhanced Raman scattering obtained from an Ag nanorod array substrate,” Appl. Phys. Lett. 89, 173134 (2006).
[CrossRef]

Liu, Z.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Lu, W. T.

W. T. Lu and S. Sridhar, “Superlens imaging theory for anisotropic nanostructured metamaterials with broadband all-angle negative refraction,” Phys. Rev. B 77, 233101 (2008).
[CrossRef]

Lyvers, D. P.

D. P. Lyvers, J.-M. Moon, A. V. Kildishev, V. M. Shalaev, and A. Wei, “Gold nanorod arrays as plasmonic cavity resonators,” ACS Nano 2, 2569–2576 (2008).
[CrossRef]

Maier, S. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[CrossRef]

S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: estimation of waveguide loss,” Appl. Phys. Lett. 81, 1714–1716 (2002).
[CrossRef]

S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, “Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy,” Phys. Rev. B 65, 193408 (2002).
[CrossRef]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics–A route to nanoscale optical devices,” Adv. Mater. 13, 1501–1505 (2001).
[CrossRef]

Mátéfi-Tempfli, M.

S. Habouti, M. Mátéfi-Tempfli, C.-H. Solterbeck, M. Es-Souni, S. Mátéfi-Tempfli, and M. Es-Souni, “Self-standing corrugated Ag and Au-nanorods for plasmonic applications,” J. Mater. Chem. 21, 6269–6273 (2011).
[CrossRef]

Mátéfi-Tempfli, S.

S. Habouti, M. Mátéfi-Tempfli, C.-H. Solterbeck, M. Es-Souni, S. Mátéfi-Tempfli, and M. Es-Souni, “Self-standing corrugated Ag and Au-nanorods for plasmonic applications,” J. Mater. Chem. 21, 6269–6273 (2011).
[CrossRef]

Meixner, A. J.

M. Fleischer, D. Zhang, K. Braun, S. Jäger, R. Ehlich, M. Häffner, C. Stanciu, J. K. H. Hörber, A. J. Meixner, and D. P. Kern, “Tailoring gold nanostructures for near-field optical applications,” Nanotechnology 21, 065301 (2010).
[CrossRef]

Meltzer, S.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[CrossRef]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics–A route to nanoscale optical devices,” Adv. Mater. 13, 1501–1505 (2001).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Modinos, A.

N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM2: a new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132, 189–196 (2000).
[CrossRef]

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[CrossRef]

N. Stefanou and A. Modinos, “Optical properties of thin discontinuous metal films,” J. Phys. Condens. Matter 3, 8149–8157 (1991).
[CrossRef]

N. Stefanou and A. Modinos, “Scattering of light by a two-dimensional array of spherical particles on a substrate,” J. Phys. Condens. Matter 3, 8135–8148 (1991).
[CrossRef]

Moon, J.-M.

D. P. Lyvers, J.-M. Moon, A. V. Kildishev, V. M. Shalaev, and A. Wei, “Gold nanorod arrays as plasmonic cavity resonators,” ACS Nano 2, 2569–2576 (2008).
[CrossRef]

Mulvaney, P.

S. W. Prescott and P. Mulvaney, “Gold nanorod extinction spectra,” J. Appl. Phys. 99, 123504 (2006).
[CrossRef]

O’Connor, D.

G. A. Wurtz, W. Dickson, D. O’Connor, R. Atkinson, W. Hendren, P. Evans, R. Pollard, and A. V. Zayats, “Guided plasmonic modes in nanorod assemblies: strong electromagnetic couping regime,” Opt. Express 16, 7460–7470 (2008).
[CrossRef]

W. Dickson, G. A. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. V. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: a metamaterial with tuneable optical properties,” Phys. Rev. B 76, 115411 (2007).
[CrossRef]

Ono, A.

S. Kawata, A. Ono, and P. Verma, “Subwavelength colour imaging with a metallic nanolens,” Nat. Photon. 2, 438–442 (2008).
[CrossRef]

Papanikolaou, N.

C. Tserkezis, N. Stefanou, and N. Papanikolaou, “Extraordinary refractive properties of photonic crystals of metallic nanorods,” J. Opt. Soc. Am. B 27, 2620–2627 (2010).
[CrossRef]

C. Tserkezis, N. Papanikolaou, E. Almpanis, and N. Stefanou, “Tailoring plasmons with metallic nanorod arrays,” Phys. Rev. B 80, 125124 (2009).
[CrossRef]

Park, S. Y.

S. Y. Park and D. Stroud, “Surface-plasmon dispersion relations in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B 69, 125418 (2004).
[CrossRef]

Pastkovsky, S.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterial for biosensing,” Nat. Mater. 8, 867–871 (2009).
[CrossRef]

Podolskiy, V. A.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterial for biosensing,” Nat. Mater. 8, 867–871 (2009).
[CrossRef]

Pollard, R.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterial for biosensing,” Nat. Mater. 8, 867–871 (2009).
[CrossRef]

G. A. Wurtz, W. Dickson, D. O’Connor, R. Atkinson, W. Hendren, P. Evans, R. Pollard, and A. V. Zayats, “Guided plasmonic modes in nanorod assemblies: strong electromagnetic couping regime,” Opt. Express 16, 7460–7470 (2008).
[CrossRef]

W. Dickson, G. A. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. V. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: a metamaterial with tuneable optical properties,” Phys. Rev. B 76, 115411 (2007).
[CrossRef]

Pollard, R. J.

Polman, A.

A. F. Koenderink, R. deWaele, J. C. Prangsma, and A. Polman, “Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides,” Phys. Rev. B 76, 201403(R) (2007).
[CrossRef]

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).

Prangsma, J. C.

A. F. Koenderink, R. deWaele, J. C. Prangsma, and A. Polman, “Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides,” Phys. Rev. B 76, 201403(R) (2007).
[CrossRef]

Premaratne, M.

I. B. Udagedara, I. D. Rukhlenko, and M. Premaratne, “Surface plasmon-polariton propagation in piecewise linear chains of composite nanospheres: the role of optical gain and chain layout,” Opt. Express 19, 19973–19986 (2011).
[CrossRef]

I. B. Udagedara, I. D. Rukhlenko, and M. Premaratne, “Complex–ω approach versus complex-k approach in description of gain-assisted surface plasmon-polariton propagation along linear chains of metallic nanospheres,” Phys. Rev. B 83, 115451 (2011).
[CrossRef]

Prescott, S. W.

S. W. Prescott and P. Mulvaney, “Gold nanorod extinction spectra,” J. Appl. Phys. 99, 123504 (2006).
[CrossRef]

Quidant, R.

R. Quidant, C. Girard, J.-C. Weeber, and A. Dereux, “Tailoring the transmittance of integrated optical waveguides with short metallic nanoparticle chains,” Phys. Rev. B 69, 085407 (2004).
[CrossRef]

Quinten, M.

Requicha, A. A. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[CrossRef]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics–A route to nanoscale optical devices,” Adv. Mater. 13, 1501–1505 (2001).
[CrossRef]

Rukhlenko, I. D.

I. B. Udagedara, I. D. Rukhlenko, and M. Premaratne, “Complex–ω approach versus complex-k approach in description of gain-assisted surface plasmon-polariton propagation along linear chains of metallic nanospheres,” Phys. Rev. B 83, 115451 (2011).
[CrossRef]

I. B. Udagedara, I. D. Rukhlenko, and M. Premaratne, “Surface plasmon-polariton propagation in piecewise linear chains of composite nanospheres: the role of optical gain and chain layout,” Opt. Express 19, 19973–19986 (2011).
[CrossRef]

Schider, G.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

Shalaev, V. M.

D. P. Lyvers, J.-M. Moon, A. V. Kildishev, V. M. Shalaev, and A. Wei, “Gold nanorod arrays as plasmonic cavity resonators,” ACS Nano 2, 2569–2576 (2008).
[CrossRef]

Shanmukh, S.

Y. Liu, J. Fan, Y.-P. Zhao, S. Shanmukh, and R. A. Dluhy, “Angle dependent surface enhanced Raman scattering obtained from an Ag nanorod array substrate,” Appl. Phys. Lett. 89, 173134 (2006).
[CrossRef]

Sihvola, A.

J. Venermo and A. Sihvola, “Dielectric polarizability of circular cylinder,” J. Electrost. 63, 101–117 (2005).
[CrossRef]

Simovski, C. R.

C. R. Simovski, A. J. Viitanen, and S. A. Tretyakov, “Resonator mode in chains of silver spheres and its possible application,” Phys. Rev. E 72, 066606 (2005).
[CrossRef]

Solterbeck, C.-H.

S. Habouti, M. Mátéfi-Tempfli, C.-H. Solterbeck, M. Es-Souni, S. Mátéfi-Tempfli, and M. Es-Souni, “Self-standing corrugated Ag and Au-nanorods for plasmonic applications,” J. Mater. Chem. 21, 6269–6273 (2011).
[CrossRef]

Sridhar, S.

W. T. Lu and S. Sridhar, “Superlens imaging theory for anisotropic nanostructured metamaterials with broadband all-angle negative refraction,” Phys. Rev. B 77, 233101 (2008).
[CrossRef]

Stacy, A. M.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Stanciu, C.

M. Fleischer, D. Zhang, K. Braun, S. Jäger, R. Ehlich, M. Häffner, C. Stanciu, J. K. H. Hörber, A. J. Meixner, and D. P. Kern, “Tailoring gold nanostructures for near-field optical applications,” Nanotechnology 21, 065301 (2010).
[CrossRef]

Stefanou, N.

C. Tserkezis, N. Stefanou, and N. Papanikolaou, “Extraordinary refractive properties of photonic crystals of metallic nanorods,” J. Opt. Soc. Am. B 27, 2620–2627 (2010).
[CrossRef]

C. Tserkezis, N. Papanikolaou, E. Almpanis, and N. Stefanou, “Tailoring plasmons with metallic nanorod arrays,” Phys. Rev. B 80, 125124 (2009).
[CrossRef]

N. Stefanou, G. Gantzounis, and C. Tserkezis, “Multiple-scattering calculations for plasmonic nanostructures,” Int. J. Nanotechnol. 6, 137–163 (2009).

G. Gantzounis and N. Stefanou, “Layer-multiple-scattering method for photonic crystals of nonspherical particles,” Phys. Rev. B 73, 035115 (2006).
[CrossRef]

G. Gantzounis and N. Stefanou, “Cavity-plasmon waveguides: multiple scattering calculations of dispersion in weakly coupled dielectric nanocavities in a metallic host material,” Phys. Rev. B 74, 085102 (2006).
[CrossRef]

N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM2: a new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132, 189–196 (2000).
[CrossRef]

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[CrossRef]

N. Stefanou and A. Modinos, “Optical properties of thin discontinuous metal films,” J. Phys. Condens. Matter 3, 8149–8157 (1991).
[CrossRef]

N. Stefanou and A. Modinos, “Scattering of light by a two-dimensional array of spherical particles on a substrate,” J. Phys. Condens. Matter 3, 8135–8148 (1991).
[CrossRef]

Steinberg, B. Z.

Y. Hadad and B. Z. Steinberg, “Green’s function theory for infinite and semi-infinite particle chains,” Phys. Rev. B 84, 125402 (2011).
[CrossRef]

Steshenko, S.

Stockman, M. I.

Stroud, D.

S. Y. Park and D. Stroud, “Surface-plasmon dispersion relations in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B 69, 125418 (2004).
[CrossRef]

Sun, C.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Tang, R. C. H.

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Tretyakov, S. A.

C. R. Simovski, A. J. Viitanen, and S. A. Tretyakov, “Resonator mode in chains of silver spheres and its possible application,” Phys. Rev. E 72, 066606 (2005).
[CrossRef]

Tsai, D. P.

Y.-F. Chau, H.-H. Yeh, C.-Y. Liu, and D. P. Tsai, “The optical properties in a chain waveguide of an array of silver nanoshell with dielectric holes,” Opt. Commun. 283, 3189–3193 (2010).
[CrossRef]

Tserkezis, C.

C. Tserkezis, N. Stefanou, and N. Papanikolaou, “Extraordinary refractive properties of photonic crystals of metallic nanorods,” J. Opt. Soc. Am. B 27, 2620–2627 (2010).
[CrossRef]

C. Tserkezis, N. Papanikolaou, E. Almpanis, and N. Stefanou, “Tailoring plasmons with metallic nanorod arrays,” Phys. Rev. B 80, 125124 (2009).
[CrossRef]

N. Stefanou, G. Gantzounis, and C. Tserkezis, “Multiple-scattering calculations for plasmonic nanostructures,” Int. J. Nanotechnol. 6, 137–163 (2009).

Udagedara, I. B.

I. B. Udagedara, I. D. Rukhlenko, and M. Premaratne, “Surface plasmon-polariton propagation in piecewise linear chains of composite nanospheres: the role of optical gain and chain layout,” Opt. Express 19, 19973–19986 (2011).
[CrossRef]

I. B. Udagedara, I. D. Rukhlenko, and M. Premaratne, “Complex–ω approach versus complex-k approach in description of gain-assisted surface plasmon-polariton propagation along linear chains of metallic nanospheres,” Phys. Rev. B 83, 115451 (2011).
[CrossRef]

Venermo, J.

J. Venermo and A. Sihvola, “Dielectric polarizability of circular cylinder,” J. Electrost. 63, 101–117 (2005).
[CrossRef]

Verma, P.

S. Kawata, A. Ono, and P. Verma, “Subwavelength colour imaging with a metallic nanolens,” Nat. Photon. 2, 438–442 (2008).
[CrossRef]

Viitanen, A. J.

C. R. Simovski, A. J. Viitanen, and S. A. Tretyakov, “Resonator mode in chains of silver spheres and its possible application,” Phys. Rev. E 72, 066606 (2005).
[CrossRef]

Wang, F. M.

F. M. Wang, H. Liu, T. Li, S. M. Wang, S. N. Zhu, J. Zhu, and W. Cao, “Highly confined energy propagation in a gap waveguide composed of two coupled nanorod chains,” Appl. Phys. Lett. 91, 133107 (2007).
[CrossRef]

Wang, S. M.

F. M. Wang, H. Liu, T. Li, S. M. Wang, S. N. Zhu, J. Zhu, and W. Cao, “Highly confined energy propagation in a gap waveguide composed of two coupled nanorod chains,” Appl. Phys. Lett. 91, 133107 (2007).
[CrossRef]

Wang, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Weber, W. H.

W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70, 125429 (2004).
[CrossRef]

Weeber, J. C.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[CrossRef]

Weeber, J.-C.

R. Quidant, C. Girard, J.-C. Weeber, and A. Dereux, “Tailoring the transmittance of integrated optical waveguides with short metallic nanoparticle chains,” Phys. Rev. B 69, 085407 (2004).
[CrossRef]

Wei, A.

D. P. Lyvers, J.-M. Moon, A. V. Kildishev, V. M. Shalaev, and A. Wei, “Gold nanorod arrays as plasmonic cavity resonators,” ACS Nano 2, 2569–2576 (2008).
[CrossRef]

Whitesides, G. M.

D. J. Lipomi, M. A. Kats, P. Kim, S. H. Kang, J. Aizenberg, F. Capasso, and G. M. Whitesides, “Fabrication and replication of arrays of single- or multicomponent nanostructures by replica molding and mechanical sectioning,” ACS Nano 4, 4017–4026 (2010).
[CrossRef]

Wurtz, G. A.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterial for biosensing,” Nat. Mater. 8, 867–871 (2009).
[CrossRef]

G. A. Wurtz, W. Dickson, D. O’Connor, R. Atkinson, W. Hendren, P. Evans, R. Pollard, and A. V. Zayats, “Guided plasmonic modes in nanorod assemblies: strong electromagnetic couping regime,” Opt. Express 16, 7460–7470 (2008).
[CrossRef]

W. Dickson, G. A. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. V. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: a metamaterial with tuneable optical properties,” Phys. Rev. B 76, 115411 (2007).
[CrossRef]

R. Atkinson, W. R. Hendren, G. A. Wurtz, W. Dickson, A. V. Zayats, P. Evans, and R. J. Pollard, “Anisotropic optical properties of arrays of gold nanorods embedded in alumina,” Phys. Rev. B 73, 235402 (2006).
[CrossRef]

Yang, T.

Yannopapas, V.

N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM2: a new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132, 189–196 (2000).
[CrossRef]

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[CrossRef]

Yao, J.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008).
[CrossRef]

Yeh, H.-H.

Y.-F. Chau, H.-H. Yeh, C.-Y. Liu, and D. P. Tsai, “The optical properties in a chain waveguide of an array of silver nanoshell with dielectric holes,” Opt. Commun. 283, 3189–3193 (2010).
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Figures (5)

Fig. 1.
Fig. 1.

Schematic view of the structures of linear chains of silver nanorods under consideration.

Fig. 2.
Fig. 2.

Dispersion diagram of the fundamental plasmon waveguide modes of a linear periodic chain of free-standing silver nanorods (D=20nm, H=50nm) separated by a distance ax=75nm, aligned perpendicular to the chain, as calculated by the layer-multiple-scattering method (solid curve) and by the coupled-dipole model (dotted curve). Above the light line (outside the black region), we display relevant extinction spectra, calculated by the layer-multiple-scattering method.

Fig. 3.
Fig. 3.

Upper diagram: imaginary part of the frequency for the modes depicted in Fig. 2, calculated by the layer-multiple-scattering method (solid curve) and by the coupled-dipole model (dotted curve). Lower diagram: the corresponding propagation length.

Fig. 4.
Fig. 4.

Same as Fig. 2, for nanorods with D=20nm and H=100nm, separated by a distance ax=50nm.

Fig. 5.
Fig. 5.

Upper diagram: same as Fig. 2, for nanorods with D=20nm and H=50nm, separated by a distance ax=50nm. Lower diagram: the corresponding dispersion diagram in the presence of a semi-infinite glass substrate. The dotted curve represents the dispersion curve obtained by the coupled-dipole model assuming an effective embedding medium with an average permittivity ε¯=1.56. The dashed curve shows the light line for this effective embedding medium.

Equations (8)

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E(r)=[(1iqr)3(r^·p)r^pr3+q2p(r^·p)r^r]eiqr,
α(ω)=V4πεm(ω)εε+L[εm(ω)ε],
pn=α(ω)mn[(1iq|nm|ax)pm|nm|3ax3+q2pm|nm|ax]eiq|nm|ax.
1+2α(ω)ax3m=1(1m3iqax1m2q2ax21m)cos(kxmax)eiqmax=0.
1+α(ω)ax3Σ(ω,kx)=0,
Σ(ω,kx)=[Li3(ei(qkx)ax)+Li3(ei(q+kx)ax)]iqax[Li2(ei(qkx)ax))+Li2(ei(q+kx)ax))](qax)2[Li1(ei(qkx)ax)+Li1(ei(q+kx)ax)].
det[IT(ω)Ω(ω,k)]=0,
det[IQLIIQRIII]=0.

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