Abstract

For two-dimensional (2D) arrays of metallic nanorods arranged perpendicular to a substrate several methods have been proposed to determine the electromagnetic near-field distribution and the surface plasmon resonances, but an analytical approach to explain all optical features on the nanometer length scale has been missing to date. To fill this gap, we demonstrate here that the field distribution in such arrays can be understood on the basis of surface plasmon polaritons (SPPs) that propagate along the nanorods and form standing waves. Notably, SPPs couple laterally through their optical near fields, giving rise to collective surface plasmon (CSP) effects. Using the dispersion relation of such CSPs, we deduce the condition of standing-wave formation, which enables us to successfully predict several features, such as eigenmodes and resonances. As one such property and potential application, we show both theoretically and in an experiment that CSP propagation allows for polarization conversion and optical filtering in 2D nanorod arrays. Hence, these arrays are promising candidates for manipulating the light polarization on the nanometer length scale.

© 2008 Optical Society of America

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2008 (7)

A.-G. Kussow, A. Akyurtlu, and N. Angkawisittpan, "Optically isotropic negative index of refraction metamaterial," Phys. Status Solidi B 245, 992-997 (2008).
[CrossRef]

M.-K. Kwon, J.-Y. Kim, B.-H. Kim, I.-K. Park, C.-Y. Cho, C. C. Byeon, and S.-J. Park, "Surface-plasmonenhanced light-emitting diodes," Adv. Mater. 20, 1253-1257 (2008).
[CrossRef]

P. Evans, R. Kullock, W. Hendren, R. Atkinson, R. Pollard, and L. M. Eng, "Optical transmission properties and electric field distribution of interacting 2d silver nanorod arrays." Adv. Funct. Mater. 18, 1075-1079 (2008).
[CrossRef]

G. W. Bryant, F. J. G. de Abajo, and J. Aizpurua, "Mapping the plasmon resonances of metallic nanoantennas." Nano. Lett. 8, 631-636 (2008).
[CrossRef] [PubMed]

W. Dickson, P. R. Evans, G. A. Wurtz, W. Hendren, R. Atkinson, R. J. Pollard, and A. V. Zayats, "Towards nonlinear plasmonic devices based on metallic nanorods." J. Microsc. 229, 415-420 (2008).
[CrossRef] [PubMed]

M. Stewart, C. Anderton, L. Thompson, J. Maria, S. Gray, J. Rogers, and R. Nuzzo, "Nanostructured plasmonic sensors," Chem. Rev. 108, 494-521 (2008).
[CrossRef] [PubMed]

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 coupling regime," Opt. Express 16, 7460-7470 (2008).
[CrossRef] [PubMed]

2007 (5)

H. Haick, "Chemical sensors based on molecularly modified metallic nanoparticles," J. Phys. D 40, 7173-7186 (2007).
[CrossRef]

C. G. Poulton,M. A. Schmidt, G. J. Pearce, G. Kakarantzas, and P. S. Russell, "Numerical study of guided modes in arrays of metallic nanowires," Opt. Lett. 32, 1647-1649 (2007).
[CrossRef] [PubMed]

B. McMillan, L. Berlouis, F. Cruickshank, and P. Brevet, "Reflectance and electrolyte electroreflectance from gold nanorod arrays embedded in a porous alumina matrix," J. Electroanal. Chem. 599, 177-182 (2007).
[CrossRef]

S. Lee, Z. Guan, H. Xu, and M. Moskovits, "Surface-enhanced raman spectroscopy and nanogeometry: The plasmonic origin of SERS," J. Phys. Chem. C 111, 17985-17988 (2007).
[CrossRef]

G. Wurtz, P. Evans, W. Hendren, R. Atkinson, W. Dickson, R. Pollard, W. Harrison, C. Bower, and A. Zayats, "Molecular plasmonics with tunable exciton-plasmon coupling strength in j-aggregate hybridized Au nanorod assemblies," Nano. Lett. 7, 1297-1303 (2007).
[CrossRef] [PubMed]

2005 (4)

H. A. Atwater, S. Maier, A. Polman, J. A. Dionne, and L. Sweatlock, "The new "p-n junction": Plasmonics enables photonic access to the nanoworld," MRS Bull. 30, 385-389 (2005).
[CrossRef]

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nat. Photon. 438, 335-338 (2005).

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

K. Aslan, J. R. Lakowicz, and C. D. Geddes, "Plasmon light scattering in biology and medicine: new sensing approaches, visions and perspectives," Curr. Opin. Chem. Biol. 9, 538-544 (2005).
[CrossRef] [PubMed]

2004 (1)

R.-L. Zong, J. Zhou, Q. Li, B. Du, B. Li, M. Fu, X.-W. Qi, L.-T. Li, and S. Buddhudu, "Synthesis and optical properties of silver nanowire arrays embedded in anodic alumina membrane," J. Phys. Chem. B 108, 16713-16716 (2004).
[CrossRef]

1999 (1)

S. Link, M. B. Mohamed, and M. A. El-Sayed, "Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant," J. Phys. Chem. B 103, 3073-3077 (1999).
[CrossRef]

1972 (1)

P. Johnson and R. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

1908 (1)

G. Mie, "Beitrage zur Optik truber Medien, speziell kolloidaler Metallosungen," Ann. Phys. 25, 377-445 (1908).
[CrossRef]

Aizpurua, J.

G. W. Bryant, F. J. G. de Abajo, and J. Aizpurua, "Mapping the plasmon resonances of metallic nanoantennas." Nano. Lett. 8, 631-636 (2008).
[CrossRef] [PubMed]

Akyurtlu, A.

A.-G. Kussow, A. Akyurtlu, and N. Angkawisittpan, "Optically isotropic negative index of refraction metamaterial," Phys. Status Solidi B 245, 992-997 (2008).
[CrossRef]

Anderton, C.

M. Stewart, C. Anderton, L. Thompson, J. Maria, S. Gray, J. Rogers, and R. Nuzzo, "Nanostructured plasmonic sensors," Chem. Rev. 108, 494-521 (2008).
[CrossRef] [PubMed]

Angkawisittpan, N.

A.-G. Kussow, A. Akyurtlu, and N. Angkawisittpan, "Optically isotropic negative index of refraction metamaterial," Phys. Status Solidi B 245, 992-997 (2008).
[CrossRef]

Aslan, K.

K. Aslan, J. R. Lakowicz, and C. D. Geddes, "Plasmon light scattering in biology and medicine: new sensing approaches, visions and perspectives," Curr. Opin. Chem. Biol. 9, 538-544 (2005).
[CrossRef] [PubMed]

Atkinson, R.

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 coupling regime," Opt. Express 16, 7460-7470 (2008).
[CrossRef] [PubMed]

W. Dickson, P. R. Evans, G. A. Wurtz, W. Hendren, R. Atkinson, R. J. Pollard, and A. V. Zayats, "Towards nonlinear plasmonic devices based on metallic nanorods." J. Microsc. 229, 415-420 (2008).
[CrossRef] [PubMed]

P. Evans, R. Kullock, W. Hendren, R. Atkinson, R. Pollard, and L. M. Eng, "Optical transmission properties and electric field distribution of interacting 2d silver nanorod arrays." Adv. Funct. Mater. 18, 1075-1079 (2008).
[CrossRef]

G. Wurtz, P. Evans, W. Hendren, R. Atkinson, W. Dickson, R. Pollard, W. Harrison, C. Bower, and A. Zayats, "Molecular plasmonics with tunable exciton-plasmon coupling strength in j-aggregate hybridized Au nanorod assemblies," Nano. Lett. 7, 1297-1303 (2007).
[CrossRef] [PubMed]

Atwater, H. A.

H. A. Atwater, S. Maier, A. Polman, J. A. Dionne, and L. Sweatlock, "The new "p-n junction": Plasmonics enables photonic access to the nanoworld," MRS Bull. 30, 385-389 (2005).
[CrossRef]

Berlouis, L.

B. McMillan, L. Berlouis, F. Cruickshank, and P. Brevet, "Reflectance and electrolyte electroreflectance from gold nanorod arrays embedded in a porous alumina matrix," J. Electroanal. Chem. 599, 177-182 (2007).
[CrossRef]

Bower, C.

G. Wurtz, P. Evans, W. Hendren, R. Atkinson, W. Dickson, R. Pollard, W. Harrison, C. Bower, and A. Zayats, "Molecular plasmonics with tunable exciton-plasmon coupling strength in j-aggregate hybridized Au nanorod assemblies," Nano. Lett. 7, 1297-1303 (2007).
[CrossRef] [PubMed]

Brevet, P.

B. McMillan, L. Berlouis, F. Cruickshank, and P. Brevet, "Reflectance and electrolyte electroreflectance from gold nanorod arrays embedded in a porous alumina matrix," J. Electroanal. Chem. 599, 177-182 (2007).
[CrossRef]

Bryant, G. W.

G. W. Bryant, F. J. G. de Abajo, and J. Aizpurua, "Mapping the plasmon resonances of metallic nanoantennas." Nano. Lett. 8, 631-636 (2008).
[CrossRef] [PubMed]

Buddhudu, S.

R.-L. Zong, J. Zhou, Q. Li, B. Du, B. Li, M. Fu, X.-W. Qi, L.-T. Li, and S. Buddhudu, "Synthesis and optical properties of silver nanowire arrays embedded in anodic alumina membrane," J. Phys. Chem. B 108, 16713-16716 (2004).
[CrossRef]

Byeon, C. C.

M.-K. Kwon, J.-Y. Kim, B.-H. Kim, I.-K. Park, C.-Y. Cho, C. C. Byeon, and S.-J. Park, "Surface-plasmonenhanced light-emitting diodes," Adv. Mater. 20, 1253-1257 (2008).
[CrossRef]

Cai, W.

Chettiar, U. K.

Cho, C.-Y.

M.-K. Kwon, J.-Y. Kim, B.-H. Kim, I.-K. Park, C.-Y. Cho, C. C. Byeon, and S.-J. Park, "Surface-plasmonenhanced light-emitting diodes," Adv. Mater. 20, 1253-1257 (2008).
[CrossRef]

Christy, R.

P. Johnson and R. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Cruickshank, F.

B. McMillan, L. Berlouis, F. Cruickshank, and P. Brevet, "Reflectance and electrolyte electroreflectance from gold nanorod arrays embedded in a porous alumina matrix," J. Electroanal. Chem. 599, 177-182 (2007).
[CrossRef]

de Abajo, F. J. G.

G. W. Bryant, F. J. G. de Abajo, and J. Aizpurua, "Mapping the plasmon resonances of metallic nanoantennas." Nano. Lett. 8, 631-636 (2008).
[CrossRef] [PubMed]

Dickson, W.

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 coupling regime," Opt. Express 16, 7460-7470 (2008).
[CrossRef] [PubMed]

W. Dickson, P. R. Evans, G. A. Wurtz, W. Hendren, R. Atkinson, R. J. Pollard, and A. V. Zayats, "Towards nonlinear plasmonic devices based on metallic nanorods." J. Microsc. 229, 415-420 (2008).
[CrossRef] [PubMed]

G. Wurtz, P. Evans, W. Hendren, R. Atkinson, W. Dickson, R. Pollard, W. Harrison, C. Bower, and A. Zayats, "Molecular plasmonics with tunable exciton-plasmon coupling strength in j-aggregate hybridized Au nanorod assemblies," Nano. Lett. 7, 1297-1303 (2007).
[CrossRef] [PubMed]

Dionne, J. A.

H. A. Atwater, S. Maier, A. Polman, J. A. Dionne, and L. Sweatlock, "The new "p-n junction": Plasmonics enables photonic access to the nanoworld," MRS Bull. 30, 385-389 (2005).
[CrossRef]

Drachev, V. P.

Du, B.

R.-L. Zong, J. Zhou, Q. Li, B. Du, B. Li, M. Fu, X.-W. Qi, L.-T. Li, and S. Buddhudu, "Synthesis and optical properties of silver nanowire arrays embedded in anodic alumina membrane," J. Phys. Chem. B 108, 16713-16716 (2004).
[CrossRef]

El-Sayed, M. A.

S. Link, M. B. Mohamed, and M. A. El-Sayed, "Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant," J. Phys. Chem. B 103, 3073-3077 (1999).
[CrossRef]

Eng, L. M.

P. Evans, R. Kullock, W. Hendren, R. Atkinson, R. Pollard, and L. M. Eng, "Optical transmission properties and electric field distribution of interacting 2d silver nanorod arrays." Adv. Funct. Mater. 18, 1075-1079 (2008).
[CrossRef]

Evans, P.

P. Evans, R. Kullock, W. Hendren, R. Atkinson, R. Pollard, and L. M. Eng, "Optical transmission properties and electric field distribution of interacting 2d silver nanorod arrays." Adv. Funct. Mater. 18, 1075-1079 (2008).
[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 coupling regime," Opt. Express 16, 7460-7470 (2008).
[CrossRef] [PubMed]

G. Wurtz, P. Evans, W. Hendren, R. Atkinson, W. Dickson, R. Pollard, W. Harrison, C. Bower, and A. Zayats, "Molecular plasmonics with tunable exciton-plasmon coupling strength in j-aggregate hybridized Au nanorod assemblies," Nano. Lett. 7, 1297-1303 (2007).
[CrossRef] [PubMed]

Evans, P. R.

W. Dickson, P. R. Evans, G. A. Wurtz, W. Hendren, R. Atkinson, R. J. Pollard, and A. V. Zayats, "Towards nonlinear plasmonic devices based on metallic nanorods." J. Microsc. 229, 415-420 (2008).
[CrossRef] [PubMed]

Firsov, A. A.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nat. Photon. 438, 335-338 (2005).

Fu, M.

R.-L. Zong, J. Zhou, Q. Li, B. Du, B. Li, M. Fu, X.-W. Qi, L.-T. Li, and S. Buddhudu, "Synthesis and optical properties of silver nanowire arrays embedded in anodic alumina membrane," J. Phys. Chem. B 108, 16713-16716 (2004).
[CrossRef]

Geddes, C. D.

K. Aslan, J. R. Lakowicz, and C. D. Geddes, "Plasmon light scattering in biology and medicine: new sensing approaches, visions and perspectives," Curr. Opin. Chem. Biol. 9, 538-544 (2005).
[CrossRef] [PubMed]

Geim, A. K.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nat. Photon. 438, 335-338 (2005).

Gleeson, H. F.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nat. Photon. 438, 335-338 (2005).

Gray, S.

M. Stewart, C. Anderton, L. Thompson, J. Maria, S. Gray, J. Rogers, and R. Nuzzo, "Nanostructured plasmonic sensors," Chem. Rev. 108, 494-521 (2008).
[CrossRef] [PubMed]

Grigorenko, A. N.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nat. Photon. 438, 335-338 (2005).

Guan, Z.

S. Lee, Z. Guan, H. Xu, and M. Moskovits, "Surface-enhanced raman spectroscopy and nanogeometry: The plasmonic origin of SERS," J. Phys. Chem. C 111, 17985-17988 (2007).
[CrossRef]

Haick, H.

H. Haick, "Chemical sensors based on molecularly modified metallic nanoparticles," J. Phys. D 40, 7173-7186 (2007).
[CrossRef]

Harrison, W.

G. Wurtz, P. Evans, W. Hendren, R. Atkinson, W. Dickson, R. Pollard, W. Harrison, C. Bower, and A. Zayats, "Molecular plasmonics with tunable exciton-plasmon coupling strength in j-aggregate hybridized Au nanorod assemblies," Nano. Lett. 7, 1297-1303 (2007).
[CrossRef] [PubMed]

Hendren, W.

W. Dickson, P. R. Evans, G. A. Wurtz, W. Hendren, R. Atkinson, R. J. Pollard, and A. V. Zayats, "Towards nonlinear plasmonic devices based on metallic nanorods." J. Microsc. 229, 415-420 (2008).
[CrossRef] [PubMed]

P. Evans, R. Kullock, W. Hendren, R. Atkinson, R. Pollard, and L. M. Eng, "Optical transmission properties and electric field distribution of interacting 2d silver nanorod arrays." Adv. Funct. Mater. 18, 1075-1079 (2008).
[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 coupling regime," Opt. Express 16, 7460-7470 (2008).
[CrossRef] [PubMed]

G. Wurtz, P. Evans, W. Hendren, R. Atkinson, W. Dickson, R. Pollard, W. Harrison, C. Bower, and A. Zayats, "Molecular plasmonics with tunable exciton-plasmon coupling strength in j-aggregate hybridized Au nanorod assemblies," Nano. Lett. 7, 1297-1303 (2007).
[CrossRef] [PubMed]

Johnson, P.

P. Johnson and R. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Kakarantzas, G.

Khrushchev, I. Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nat. Photon. 438, 335-338 (2005).

Kildishev, A. V.

Kim, B.-H.

M.-K. Kwon, J.-Y. Kim, B.-H. Kim, I.-K. Park, C.-Y. Cho, C. C. Byeon, and S.-J. Park, "Surface-plasmonenhanced light-emitting diodes," Adv. Mater. 20, 1253-1257 (2008).
[CrossRef]

Kim, J.-Y.

M.-K. Kwon, J.-Y. Kim, B.-H. Kim, I.-K. Park, C.-Y. Cho, C. C. Byeon, and S.-J. Park, "Surface-plasmonenhanced light-emitting diodes," Adv. Mater. 20, 1253-1257 (2008).
[CrossRef]

Kullock, R.

P. Evans, R. Kullock, W. Hendren, R. Atkinson, R. Pollard, and L. M. Eng, "Optical transmission properties and electric field distribution of interacting 2d silver nanorod arrays." Adv. Funct. Mater. 18, 1075-1079 (2008).
[CrossRef]

Kussow, A.-G.

A.-G. Kussow, A. Akyurtlu, and N. Angkawisittpan, "Optically isotropic negative index of refraction metamaterial," Phys. Status Solidi B 245, 992-997 (2008).
[CrossRef]

Kwon, M.-K.

M.-K. Kwon, J.-Y. Kim, B.-H. Kim, I.-K. Park, C.-Y. Cho, C. C. Byeon, and S.-J. Park, "Surface-plasmonenhanced light-emitting diodes," Adv. Mater. 20, 1253-1257 (2008).
[CrossRef]

Lakowicz, J. R.

K. Aslan, J. R. Lakowicz, and C. D. Geddes, "Plasmon light scattering in biology and medicine: new sensing approaches, visions and perspectives," Curr. Opin. Chem. Biol. 9, 538-544 (2005).
[CrossRef] [PubMed]

Lee, S.

S. Lee, Z. Guan, H. Xu, and M. Moskovits, "Surface-enhanced raman spectroscopy and nanogeometry: The plasmonic origin of SERS," J. Phys. Chem. C 111, 17985-17988 (2007).
[CrossRef]

Li, B.

R.-L. Zong, J. Zhou, Q. Li, B. Du, B. Li, M. Fu, X.-W. Qi, L.-T. Li, and S. Buddhudu, "Synthesis and optical properties of silver nanowire arrays embedded in anodic alumina membrane," J. Phys. Chem. B 108, 16713-16716 (2004).
[CrossRef]

Li, L.-T.

R.-L. Zong, J. Zhou, Q. Li, B. Du, B. Li, M. Fu, X.-W. Qi, L.-T. Li, and S. Buddhudu, "Synthesis and optical properties of silver nanowire arrays embedded in anodic alumina membrane," J. Phys. Chem. B 108, 16713-16716 (2004).
[CrossRef]

Li, Q.

R.-L. Zong, J. Zhou, Q. Li, B. Du, B. Li, M. Fu, X.-W. Qi, L.-T. Li, and S. Buddhudu, "Synthesis and optical properties of silver nanowire arrays embedded in anodic alumina membrane," J. Phys. Chem. B 108, 16713-16716 (2004).
[CrossRef]

Link, S.

S. Link, M. B. Mohamed, and M. A. El-Sayed, "Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant," J. Phys. Chem. B 103, 3073-3077 (1999).
[CrossRef]

Maier, S.

H. A. Atwater, S. Maier, A. Polman, J. A. Dionne, and L. Sweatlock, "The new "p-n junction": Plasmonics enables photonic access to the nanoworld," MRS Bull. 30, 385-389 (2005).
[CrossRef]

Maria, J.

M. Stewart, C. Anderton, L. Thompson, J. Maria, S. Gray, J. Rogers, and R. Nuzzo, "Nanostructured plasmonic sensors," Chem. Rev. 108, 494-521 (2008).
[CrossRef] [PubMed]

McMillan, B.

B. McMillan, L. Berlouis, F. Cruickshank, and P. Brevet, "Reflectance and electrolyte electroreflectance from gold nanorod arrays embedded in a porous alumina matrix," J. Electroanal. Chem. 599, 177-182 (2007).
[CrossRef]

Mie, G.

G. Mie, "Beitrage zur Optik truber Medien, speziell kolloidaler Metallosungen," Ann. Phys. 25, 377-445 (1908).
[CrossRef]

Mohamed, M. B.

S. Link, M. B. Mohamed, and M. A. El-Sayed, "Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant," J. Phys. Chem. B 103, 3073-3077 (1999).
[CrossRef]

Moskovits, M.

S. Lee, Z. Guan, H. Xu, and M. Moskovits, "Surface-enhanced raman spectroscopy and nanogeometry: The plasmonic origin of SERS," J. Phys. Chem. C 111, 17985-17988 (2007).
[CrossRef]

Nuzzo, R.

M. Stewart, C. Anderton, L. Thompson, J. Maria, S. Gray, J. Rogers, and R. Nuzzo, "Nanostructured plasmonic sensors," Chem. Rev. 108, 494-521 (2008).
[CrossRef] [PubMed]

O’Connor, D.

Park, I.-K.

M.-K. Kwon, J.-Y. Kim, B.-H. Kim, I.-K. Park, C.-Y. Cho, C. C. Byeon, and S.-J. Park, "Surface-plasmonenhanced light-emitting diodes," Adv. Mater. 20, 1253-1257 (2008).
[CrossRef]

Park, S.-J.

M.-K. Kwon, J.-Y. Kim, B.-H. Kim, I.-K. Park, C.-Y. Cho, C. C. Byeon, and S.-J. Park, "Surface-plasmonenhanced light-emitting diodes," Adv. Mater. 20, 1253-1257 (2008).
[CrossRef]

Pearce, G. J.

Petrovic, J.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nat. Photon. 438, 335-338 (2005).

Pollard, R.

P. Evans, R. Kullock, W. Hendren, R. Atkinson, R. Pollard, and L. M. Eng, "Optical transmission properties and electric field distribution of interacting 2d silver nanorod arrays." Adv. Funct. Mater. 18, 1075-1079 (2008).
[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 coupling regime," Opt. Express 16, 7460-7470 (2008).
[CrossRef] [PubMed]

G. Wurtz, P. Evans, W. Hendren, R. Atkinson, W. Dickson, R. Pollard, W. Harrison, C. Bower, and A. Zayats, "Molecular plasmonics with tunable exciton-plasmon coupling strength in j-aggregate hybridized Au nanorod assemblies," Nano. Lett. 7, 1297-1303 (2007).
[CrossRef] [PubMed]

Pollard, R. J.

W. Dickson, P. R. Evans, G. A. Wurtz, W. Hendren, R. Atkinson, R. J. Pollard, and A. V. Zayats, "Towards nonlinear plasmonic devices based on metallic nanorods." J. Microsc. 229, 415-420 (2008).
[CrossRef] [PubMed]

Polman, A.

H. A. Atwater, S. Maier, A. Polman, J. A. Dionne, and L. Sweatlock, "The new "p-n junction": Plasmonics enables photonic access to the nanoworld," MRS Bull. 30, 385-389 (2005).
[CrossRef]

Poulton, C. G.

Qi, X.-W.

R.-L. Zong, J. Zhou, Q. Li, B. Du, B. Li, M. Fu, X.-W. Qi, L.-T. Li, and S. Buddhudu, "Synthesis and optical properties of silver nanowire arrays embedded in anodic alumina membrane," J. Phys. Chem. B 108, 16713-16716 (2004).
[CrossRef]

Rogers, J.

M. Stewart, C. Anderton, L. Thompson, J. Maria, S. Gray, J. Rogers, and R. Nuzzo, "Nanostructured plasmonic sensors," Chem. Rev. 108, 494-521 (2008).
[CrossRef] [PubMed]

Russell, P. S.

Sarychev, A. K.

Schmidt, M. A.

Shalaev, V. M.

Stewart, M.

M. Stewart, C. Anderton, L. Thompson, J. Maria, S. Gray, J. Rogers, and R. Nuzzo, "Nanostructured plasmonic sensors," Chem. Rev. 108, 494-521 (2008).
[CrossRef] [PubMed]

Sweatlock, L.

H. A. Atwater, S. Maier, A. Polman, J. A. Dionne, and L. Sweatlock, "The new "p-n junction": Plasmonics enables photonic access to the nanoworld," MRS Bull. 30, 385-389 (2005).
[CrossRef]

Thompson, L.

M. Stewart, C. Anderton, L. Thompson, J. Maria, S. Gray, J. Rogers, and R. Nuzzo, "Nanostructured plasmonic sensors," Chem. Rev. 108, 494-521 (2008).
[CrossRef] [PubMed]

Wurtz, G.

G. Wurtz, P. Evans, W. Hendren, R. Atkinson, W. Dickson, R. Pollard, W. Harrison, C. Bower, and A. Zayats, "Molecular plasmonics with tunable exciton-plasmon coupling strength in j-aggregate hybridized Au nanorod assemblies," Nano. Lett. 7, 1297-1303 (2007).
[CrossRef] [PubMed]

Wurtz, G. A.

W. Dickson, P. R. Evans, G. A. Wurtz, W. Hendren, R. Atkinson, R. J. Pollard, and A. V. Zayats, "Towards nonlinear plasmonic devices based on metallic nanorods." J. Microsc. 229, 415-420 (2008).
[CrossRef] [PubMed]

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 coupling regime," Opt. Express 16, 7460-7470 (2008).
[CrossRef] [PubMed]

Xu, H.

S. Lee, Z. Guan, H. Xu, and M. Moskovits, "Surface-enhanced raman spectroscopy and nanogeometry: The plasmonic origin of SERS," J. Phys. Chem. C 111, 17985-17988 (2007).
[CrossRef]

Yuan, H.-K.

Zayats, A.

G. Wurtz, P. Evans, W. Hendren, R. Atkinson, W. Dickson, R. Pollard, W. Harrison, C. Bower, and A. Zayats, "Molecular plasmonics with tunable exciton-plasmon coupling strength in j-aggregate hybridized Au nanorod assemblies," Nano. Lett. 7, 1297-1303 (2007).
[CrossRef] [PubMed]

Zayats, A. V.

W. Dickson, P. R. Evans, G. A. Wurtz, W. Hendren, R. Atkinson, R. J. Pollard, and A. V. Zayats, "Towards nonlinear plasmonic devices based on metallic nanorods." J. Microsc. 229, 415-420 (2008).
[CrossRef] [PubMed]

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 coupling regime," Opt. Express 16, 7460-7470 (2008).
[CrossRef] [PubMed]

Zhang, Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nat. Photon. 438, 335-338 (2005).

Zhou, J.

R.-L. Zong, J. Zhou, Q. Li, B. Du, B. Li, M. Fu, X.-W. Qi, L.-T. Li, and S. Buddhudu, "Synthesis and optical properties of silver nanowire arrays embedded in anodic alumina membrane," J. Phys. Chem. B 108, 16713-16716 (2004).
[CrossRef]

Zong, R.-L.

R.-L. Zong, J. Zhou, Q. Li, B. Du, B. Li, M. Fu, X.-W. Qi, L.-T. Li, and S. Buddhudu, "Synthesis and optical properties of silver nanowire arrays embedded in anodic alumina membrane," J. Phys. Chem. B 108, 16713-16716 (2004).
[CrossRef]

Adv. Funct. Mater. (1)

P. Evans, R. Kullock, W. Hendren, R. Atkinson, R. Pollard, and L. M. Eng, "Optical transmission properties and electric field distribution of interacting 2d silver nanorod arrays." Adv. Funct. Mater. 18, 1075-1079 (2008).
[CrossRef]

Adv. Mater. (1)

M.-K. Kwon, J.-Y. Kim, B.-H. Kim, I.-K. Park, C.-Y. Cho, C. C. Byeon, and S.-J. Park, "Surface-plasmonenhanced light-emitting diodes," Adv. Mater. 20, 1253-1257 (2008).
[CrossRef]

Ann. Phys. (1)

G. Mie, "Beitrage zur Optik truber Medien, speziell kolloidaler Metallosungen," Ann. Phys. 25, 377-445 (1908).
[CrossRef]

Chem. Rev. (1)

M. Stewart, C. Anderton, L. Thompson, J. Maria, S. Gray, J. Rogers, and R. Nuzzo, "Nanostructured plasmonic sensors," Chem. Rev. 108, 494-521 (2008).
[CrossRef] [PubMed]

Curr. Opin. Chem. Biol. (1)

K. Aslan, J. R. Lakowicz, and C. D. Geddes, "Plasmon light scattering in biology and medicine: new sensing approaches, visions and perspectives," Curr. Opin. Chem. Biol. 9, 538-544 (2005).
[CrossRef] [PubMed]

J. Electroanal. Chem. (1)

B. McMillan, L. Berlouis, F. Cruickshank, and P. Brevet, "Reflectance and electrolyte electroreflectance from gold nanorod arrays embedded in a porous alumina matrix," J. Electroanal. Chem. 599, 177-182 (2007).
[CrossRef]

J. Microsc. (1)

W. Dickson, P. R. Evans, G. A. Wurtz, W. Hendren, R. Atkinson, R. J. Pollard, and A. V. Zayats, "Towards nonlinear plasmonic devices based on metallic nanorods." J. Microsc. 229, 415-420 (2008).
[CrossRef] [PubMed]

J. Phys. Chem. B (2)

S. Link, M. B. Mohamed, and M. A. El-Sayed, "Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant," J. Phys. Chem. B 103, 3073-3077 (1999).
[CrossRef]

R.-L. Zong, J. Zhou, Q. Li, B. Du, B. Li, M. Fu, X.-W. Qi, L.-T. Li, and S. Buddhudu, "Synthesis and optical properties of silver nanowire arrays embedded in anodic alumina membrane," J. Phys. Chem. B 108, 16713-16716 (2004).
[CrossRef]

J. Phys. Chem. C (1)

S. Lee, Z. Guan, H. Xu, and M. Moskovits, "Surface-enhanced raman spectroscopy and nanogeometry: The plasmonic origin of SERS," J. Phys. Chem. C 111, 17985-17988 (2007).
[CrossRef]

J. Phys. D (1)

H. Haick, "Chemical sensors based on molecularly modified metallic nanoparticles," J. Phys. D 40, 7173-7186 (2007).
[CrossRef]

MRS Bull. (1)

H. A. Atwater, S. Maier, A. Polman, J. A. Dionne, and L. Sweatlock, "The new "p-n junction": Plasmonics enables photonic access to the nanoworld," MRS Bull. 30, 385-389 (2005).
[CrossRef]

Nano. Lett. (2)

G. Wurtz, P. Evans, W. Hendren, R. Atkinson, W. Dickson, R. Pollard, W. Harrison, C. Bower, and A. Zayats, "Molecular plasmonics with tunable exciton-plasmon coupling strength in j-aggregate hybridized Au nanorod assemblies," Nano. Lett. 7, 1297-1303 (2007).
[CrossRef] [PubMed]

G. W. Bryant, F. J. G. de Abajo, and J. Aizpurua, "Mapping the plasmon resonances of metallic nanoantennas." Nano. Lett. 8, 631-636 (2008).
[CrossRef] [PubMed]

Nat. Photon. (1)

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nat. Photon. 438, 335-338 (2005).

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (1)

P. Johnson and R. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Phys. Status Solidi B (1)

A.-G. Kussow, A. Akyurtlu, and N. Angkawisittpan, "Optically isotropic negative index of refraction metamaterial," Phys. Status Solidi B 245, 992-997 (2008).
[CrossRef]

Other (7)

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, 235402-1-8 (2006).
[CrossRef]

P. R. Evans, G. A. Wurtz, W. R. Hendren, R. Atkinson, W. Dickson, A. V. Zayats, and R. J. Pollard, "Electrically switchable nonreciprocal transmission of plasmonic nanorods with liquid crystal," Appl. Phys. Lett. 91, 043101-1-3 (2007).
[CrossRef]

S. H. Lim, W. Mar, P. Matheu, D. Derkacs, and E. T. Yu, "Photocurrent spectroscopy of optical absorption enhancement in silicon photodiodes via scattering from surface plasmon polaritons in gold nanoparticles," J. Appl. Phys. 101, 104309-1-7 (2007).
[CrossRef]

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, "Silver nanowires as surface plasmon resonators," Phys. Rev. Lett. 95, 257403-1-7 (2005).
[CrossRef]

C. Hafner, MaX-1 A Visual Electromagnetics Platform for PCs. (John Wiley & Sons, Chichester, 1998).

C. Hafner, Post-modern Electromagnetics: Using Intelligent MaXwell Solvers. (John Wiley & Sons, Chichester, 1999).

L. Novotny, "Effective wavelength scaling for optical antennas," Phys. Rev. Lett. 98, 266802-1-4 (2007).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

(a) Micrograph of a gold nanorod structure, and (b) model of the nanorod array combined with a depiction of the lateral field distribution of a collective surface plasmon (CSP).

Fig. 2.
Fig. 2.

Dispersion relation of a SPP/CSP on infinitely long Au nanowires (diameter 25 nm, embedded in nAAO =1.6, single nanowire or array of nanowires).

Fig. 3.
Fig. 3.

Three electric-field plots showing the phase-averaged electric field (a) in a nanorod array (3D MMP calculations, α=25 and λ=690 nm), (b) on an isolated nanorod and (c) of two SPPs forming a standing wave on an isolated cylinder with θ=0.

Fig. 4.
Fig. 4.

Calculated electric-field distribution for a p-polarized plane wave hitting the array, which is embedded in AAO, at an angle α=28.6° (external angle 50°). The free-space wavelength is λ=760 nm and the plot is phase-resolved. Δφ (here ~90° - see Fig. 5) is the phase delay of the p component due to the array.

Fig. 5.
Fig. 5.

Calculated extinction and phase behavior of a gold nanorod array for various angles of incidence (=300 nm, r=12.5 nm, d=60 nm, nAAO =1.6, square symmetry). (a) Extinction for p-polarized light, and (b) phase between the s and p components. Note, in MMP phases of plane waves are in the range (-180°,180°] which leads to unphysical jumps in the phase behavior. Hence, multiples of 2π were added to obtain continuous curves. The peak around 520 nm corresponds to the short-axis resonance of the structure, which is not discussed in this paper.

Fig. 6.
Fig. 6.

Measured extinction and phase behavior of a gold nanorod array structure for various angles of incidence (=300 nm, r=12.5 nm, d=60 nm, in AAO, quasi-hexagonal symmetry). (a) Extinction for p-polarized light and (b) phase between the s and p components. For determining the phase, arcsin(sin(D)) was used up to 30°, while for larger angles arccos(+cos(Δ)) (solid line) and 360°-arccos(-cos(Δ)) (dashed line) were used, respectively. Note, the peak around 520 nm corresponds to the short-axis resonance of the structure, which is not discussed in this paper.

Fig. 7.
Fig. 7.

Extinction of a gold nanorod array structure for the normal (p-polarized) and X-pol (cross-polarized) case for various incident angles. The two different setups are sketched as insets. Note that the two polarization filters work reliably only between 450 and 780 nm.

Tables (1)

Tables Icon

Table 1. The first three plasmon modes calculated for CSPs in a nanorod array using the analytic approach. Settings are: ℓ=300 nm, r=12.5 nm, and d=60 nm.

Equations (1)

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k z = m · π + θ

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