Abstract

The eigenmodes analysis of Bloch modes in a chain of metallic nanowires (MNWs) provides a significant physical understanding about the light propagation phenomena involved in such structures. However, most of these analyses have been done above the light line in the dispersion relation, where the Bloch modes can only be excited with radiative modes. By making use of the Fourier modal method, in this paper we rigorously calculate the eigenmode and mode excitation of a chain of MNWs via the fundamental transverse magnetic (TM) mode of a dielectric waveguide. Quadrupolar and dipolar transversal Bloch modes were obtained in an MNW chain embedded in a dielectric material. These modes can be coupled efficiently with the fundamental TM mode of the waveguide. Since the eigenmodes supported by the integrated plasmonic structure exhibit strong localized surface plasmon (LSP) resonances, they could serve as a nanodevice for sensing applications. Also, the analysis opens a direction for novel nanostructures, potentially helpful for the efficient excitation of LSPs and strong field enhancement.

© 2014 Chinese Laser Press

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References

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2013 (1)

A. Apuzzo, M. Fevrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13, 1000–1006 (2013).
[CrossRef]

2012 (3)

M. Fevrier, P. Gogol, A. Aassime, R. Megy, D. Bouville, J. M. Lourtioz, and B. Dagens, “Localized surface plasmon Bragg grating on SOI waveguide at telecom wavelengths,” Appl. Phys. A 109, 935–942 (2012).
[CrossRef]

F. Beranl Arango, A. Kwadrin, and A. F. Koenderink, “Plasmonic antennas hybridized with dielectric waveguides,” ACS Nano. 6, 10156–10167 (2012).
[CrossRef]

M. Fevrier, P. Gogol, A. Aassime, R. Megy, C. Delacour, A. Chelnokov, A. Apuzzo, S. Blaize, J. M. Lourtioz, and B. Dagens, “Giant coupling effect between metal nanoparticle chain and optical waveguide,” Nano Lett. 12, 1032–1037 (2012).
[CrossRef]

2010 (2)

H. Wei, A. Reyes-Coronado, P. Nordlander, J. Aizpurua, and H. Xu, “Multipolar plasmon resonances in individual Ag nanorice,” ACS Nano. 4, 2649–2654 (2010).
[CrossRef]

E. Simsek, “Full analytical model for obtaining surface plasmon resonance modes of metal nanoparticle structures embedded in layered media,” Opt. Express 18, 1722–1733 (2010).
[CrossRef]

2009 (1)

2008 (1)

2007 (3)

2006 (1)

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

2004 (3)

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

E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmons resonance,” Adv. Mater. 16, 1685–1706 (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 (2)

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91, 183901 (2003).
[CrossRef]

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

2001 (1)

2000 (2)

E. Popov and M. Neviere, “Grating theory: new equations in Fourier space leading to fast converging results for TM polarization,” J. Opt. Soc. Am. A 17, 1773–1784 (2000).
[CrossRef]

P. Lalanne and E. Silberstein, “Fourier-modal methods applied to waveguide computational problems,” Opt. Express 25, 1092–1094 (2000).

1999 (1)

1996 (1)

1995 (1)

1994 (1)

1966 (1)

Aassime, A.

M. Fevrier, P. Gogol, A. Aassime, R. Megy, D. Bouville, J. M. Lourtioz, and B. Dagens, “Localized surface plasmon Bragg grating on SOI waveguide at telecom wavelengths,” Appl. Phys. A 109, 935–942 (2012).
[CrossRef]

M. Fevrier, P. Gogol, A. Aassime, R. Megy, C. Delacour, A. Chelnokov, A. Apuzzo, S. Blaize, J. M. Lourtioz, and B. Dagens, “Giant coupling effect between metal nanoparticle chain and optical waveguide,” Nano Lett. 12, 1032–1037 (2012).
[CrossRef]

Aizpurua, J.

H. Wei, A. Reyes-Coronado, P. Nordlander, J. Aizpurua, and H. Xu, “Multipolar plasmon resonances in individual Ag nanorice,” ACS Nano. 4, 2649–2654 (2010).
[CrossRef]

Apuzzo, A.

A. Apuzzo, M. Fevrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13, 1000–1006 (2013).
[CrossRef]

M. Fevrier, P. Gogol, A. Aassime, R. Megy, C. Delacour, A. Chelnokov, A. Apuzzo, S. Blaize, J. M. Lourtioz, and B. Dagens, “Giant coupling effect between metal nanoparticle chain and optical waveguide,” Nano Lett. 12, 1032–1037 (2012).
[CrossRef]

Beranl Arango, F.

F. Beranl Arango, A. Kwadrin, and A. F. Koenderink, “Plasmonic antennas hybridized with dielectric waveguides,” ACS Nano. 6, 10156–10167 (2012).
[CrossRef]

Blaize, S.

A. Apuzzo, M. Fevrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13, 1000–1006 (2013).
[CrossRef]

M. Fevrier, P. Gogol, A. Aassime, R. Megy, C. Delacour, A. Chelnokov, A. Apuzzo, S. Blaize, J. M. Lourtioz, and B. Dagens, “Giant coupling effect between metal nanoparticle chain and optical waveguide,” Nano Lett. 12, 1032–1037 (2012).
[CrossRef]

Bohren, C.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Bonod, N.

Bouville, D.

M. Fevrier, P. Gogol, A. Aassime, R. Megy, D. Bouville, J. M. Lourtioz, and B. Dagens, “Localized surface plasmon Bragg grating on SOI waveguide at telecom wavelengths,” Appl. Phys. A 109, 935–942 (2012).
[CrossRef]

Bruyant, A.

A. Apuzzo, M. Fevrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13, 1000–1006 (2013).
[CrossRef]

Burckhardt, C. B.

Chateau, N.

Chelnokov, A.

A. Apuzzo, M. Fevrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13, 1000–1006 (2013).
[CrossRef]

M. Fevrier, P. Gogol, A. Aassime, R. Megy, C. Delacour, A. Chelnokov, A. Apuzzo, S. Blaize, J. M. Lourtioz, and B. Dagens, “Giant coupling effect between metal nanoparticle chain and optical waveguide,” Nano Lett. 12, 1032–1037 (2012).
[CrossRef]

Christ, A.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91, 183901 (2003).
[CrossRef]

Coronado, E.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Crozier, K. B.

Dagens, B.

A. Apuzzo, M. Fevrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13, 1000–1006 (2013).
[CrossRef]

M. Fevrier, P. Gogol, A. Aassime, R. Megy, C. Delacour, A. Chelnokov, A. Apuzzo, S. Blaize, J. M. Lourtioz, and B. Dagens, “Giant coupling effect between metal nanoparticle chain and optical waveguide,” Nano Lett. 12, 1032–1037 (2012).
[CrossRef]

M. Fevrier, P. Gogol, A. Aassime, R. Megy, D. Bouville, J. M. Lourtioz, and B. Dagens, “Localized surface plasmon Bragg grating on SOI waveguide at telecom wavelengths,” Appl. Phys. A 109, 935–942 (2012).
[CrossRef]

de Waele, R.

A. F. Koenderink, R. de Waele, 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 (2007).
[CrossRef]

Delacour, C.

M. Fevrier, P. Gogol, A. Aassime, R. Megy, C. Delacour, A. Chelnokov, A. Apuzzo, S. Blaize, J. M. Lourtioz, and B. Dagens, “Giant coupling effect between metal nanoparticle chain and optical waveguide,” Nano Lett. 12, 1032–1037 (2012).
[CrossRef]

Dereux, A.

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]

Enoch, S.

Fendler, J. H.

E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmons resonance,” Adv. Mater. 16, 1685–1706 (2004).
[CrossRef]

Fevrier, M.

A. Apuzzo, M. Fevrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13, 1000–1006 (2013).
[CrossRef]

M. Fevrier, P. Gogol, A. Aassime, R. Megy, C. Delacour, A. Chelnokov, A. Apuzzo, S. Blaize, J. M. Lourtioz, and B. Dagens, “Giant coupling effect between metal nanoparticle chain and optical waveguide,” Nano Lett. 12, 1032–1037 (2012).
[CrossRef]

M. Fevrier, P. Gogol, A. Aassime, R. Megy, D. Bouville, J. M. Lourtioz, and B. Dagens, “Localized surface plasmon Bragg grating on SOI waveguide at telecom wavelengths,” Appl. Phys. A 109, 935–942 (2012).
[CrossRef]

Ford, G. W.

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

Giessen, H.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91, 183901 (2003).
[CrossRef]

Gippius, N. A.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91, 183901 (2003).
[CrossRef]

Girard, 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]

Gogol, P.

M. Fevrier, P. Gogol, A. Aassime, R. Megy, D. Bouville, J. M. Lourtioz, and B. Dagens, “Localized surface plasmon Bragg grating on SOI waveguide at telecom wavelengths,” Appl. Phys. A 109, 935–942 (2012).
[CrossRef]

M. Fevrier, P. Gogol, A. Aassime, R. Megy, C. Delacour, A. Chelnokov, A. Apuzzo, S. Blaize, J. M. Lourtioz, and B. Dagens, “Giant coupling effect between metal nanoparticle chain and optical waveguide,” Nano Lett. 12, 1032–1037 (2012).
[CrossRef]

Granet, G.

Grann, E. B.

Hochman, A.

Huffman, D.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Hugonin, J. P.

Hutter, E.

E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmons resonance,” Adv. Mater. 16, 1685–1706 (2004).
[CrossRef]

Kelly, K. L.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Koenderink, A. F.

F. Beranl Arango, A. Kwadrin, and A. F. Koenderink, “Plasmonic antennas hybridized with dielectric waveguides,” ACS Nano. 6, 10156–10167 (2012).
[CrossRef]

A. F. Koenderink, R. de Waele, 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 (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).
[CrossRef]

Kuhl, J.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91, 183901 (2003).
[CrossRef]

Kwadrin, A.

F. Beranl Arango, A. Kwadrin, and A. F. Koenderink, “Plasmonic antennas hybridized with dielectric waveguides,” ACS Nano. 6, 10156–10167 (2012).
[CrossRef]

Lalanne, P.

P. Lalanne and E. Silberstein, “Fourier-modal methods applied to waveguide computational problems,” Opt. Express 25, 1092–1094 (2000).

Lerondel, G.

A. Apuzzo, M. Fevrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13, 1000–1006 (2013).
[CrossRef]

Leviatan, Y.

Li, L.

Lourtioz, J. M.

M. Fevrier, P. Gogol, A. Aassime, R. Megy, C. Delacour, A. Chelnokov, A. Apuzzo, S. Blaize, J. M. Lourtioz, and B. Dagens, “Giant coupling effect between metal nanoparticle chain and optical waveguide,” Nano Lett. 12, 1032–1037 (2012).
[CrossRef]

M. Fevrier, P. Gogol, A. Aassime, R. Megy, D. Bouville, J. M. Lourtioz, and B. Dagens, “Localized surface plasmon Bragg grating on SOI waveguide at telecom wavelengths,” Appl. Phys. A 109, 935–942 (2012).
[CrossRef]

Megy, R.

M. Fevrier, P. Gogol, A. Aassime, R. Megy, D. Bouville, J. M. Lourtioz, and B. Dagens, “Localized surface plasmon Bragg grating on SOI waveguide at telecom wavelengths,” Appl. Phys. A 109, 935–942 (2012).
[CrossRef]

M. Fevrier, P. Gogol, A. Aassime, R. Megy, C. Delacour, A. Chelnokov, A. Apuzzo, S. Blaize, J. M. Lourtioz, and B. Dagens, “Giant coupling effect between metal nanoparticle chain and optical waveguide,” Nano Lett. 12, 1032–1037 (2012).
[CrossRef]

Merle Elson, J.

Moharam, M. G.

Neviere, M.

Nordlander, P.

H. Wei, A. Reyes-Coronado, P. Nordlander, J. Aizpurua, and H. Xu, “Multipolar plasmon resonances in individual Ag nanorice,” ACS Nano. 4, 2649–2654 (2010).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids, 4th ed. (Academic, 1985).

Polman, A.

A. F. Koenderink, R. de Waele, 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 (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).
[CrossRef]

Pommet, D. A.

Popov, E.

Prangsma, J. C.

A. F. Koenderink, R. de Waele, 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 (2007).
[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]

Reyes-Coronado, A.

H. Wei, A. Reyes-Coronado, P. Nordlander, J. Aizpurua, and H. Xu, “Multipolar plasmon resonances in individual Ag nanorice,” ACS Nano. 4, 2649–2654 (2010).
[CrossRef]

Salas-Montiel, R.

A. Apuzzo, M. Fevrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13, 1000–1006 (2013).
[CrossRef]

Schatz, G. C.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Silberstein, E.

P. Lalanne and E. Silberstein, “Fourier-modal methods applied to waveguide computational problems,” Opt. Express 25, 1092–1094 (2000).

Simsek, E.

Tikhodeev, S. G.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91, 183901 (2003).
[CrossRef]

Togan, E.

Weber, W. H.

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

H. Wei, A. Reyes-Coronado, P. Nordlander, J. Aizpurua, and H. Xu, “Multipolar plasmon resonances in individual Ag nanorice,” ACS Nano. 4, 2649–2654 (2010).
[CrossRef]

Xu, H.

H. Wei, A. Reyes-Coronado, P. Nordlander, J. Aizpurua, and H. Xu, “Multipolar plasmon resonances in individual Ag nanorice,” ACS Nano. 4, 2649–2654 (2010).
[CrossRef]

Yang, T.

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 2003), Chap. 11.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 2003), Chap. 11.

Zhao, L. L.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

ACS Nano. (2)

H. Wei, A. Reyes-Coronado, P. Nordlander, J. Aizpurua, and H. Xu, “Multipolar plasmon resonances in individual Ag nanorice,” ACS Nano. 4, 2649–2654 (2010).
[CrossRef]

F. Beranl Arango, A. Kwadrin, and A. F. Koenderink, “Plasmonic antennas hybridized with dielectric waveguides,” ACS Nano. 6, 10156–10167 (2012).
[CrossRef]

Adv. Mater. (1)

E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmons resonance,” Adv. Mater. 16, 1685–1706 (2004).
[CrossRef]

Appl. Phys. A (1)

M. Fevrier, P. Gogol, A. Aassime, R. Megy, D. Bouville, J. M. Lourtioz, and B. Dagens, “Localized surface plasmon Bragg grating on SOI waveguide at telecom wavelengths,” Appl. Phys. A 109, 935–942 (2012).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (5)

J. Phys. Chem. B (1)

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Nano Lett. (2)

M. Fevrier, P. Gogol, A. Aassime, R. Megy, C. Delacour, A. Chelnokov, A. Apuzzo, S. Blaize, J. M. Lourtioz, and B. Dagens, “Giant coupling effect between metal nanoparticle chain and optical waveguide,” Nano Lett. 12, 1032–1037 (2012).
[CrossRef]

A. Apuzzo, M. Fevrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13, 1000–1006 (2013).
[CrossRef]

Opt. Express (7)

Phys. Rev. B (4)

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

A. F. Koenderink, R. de Waele, 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 (2007).
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W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticles 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]

Phys. Rev. Lett. (1)

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91, 183901 (2003).
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Other (3)

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 2003), Chap. 11.

E. D. Palik, Handbook of Optical Constants of Solids, 4th ed. (Academic, 1985).

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Figures (8)

Fig. 1.
Fig. 1.

(a) Schematic representation of a unitary cell used for the calculation of the dispersion relations as an eigenvalue problem. The periodicity Λ is along the z axis. (b) Scheme for the calculation of the beam propagation. A unitary cell contains a finite number of nanowires along the propagation direction ( z axis), and the periodicity Δ is now along the x axis including PMLs.

Fig. 2.
Fig. 2.

Schemes of (a) the periodical array of gold nanowires immersed in a homogeneous dielectric medium with refractive index n d = 1.5 . The height of the nanowires is e = 150 nm , the width is w = 80 nm , and the period is Λ = 130 nm . (b) The same MNW chain on a substrate of refractive index n sub = 2.0 , and (c) an integrated structure of MNW on a dielectric waveguide with core index n w = 2.0 .

Fig. 3.
Fig. 3.

(a) Dispersion relations for the quadrupolar (upper branch) and dipolar transversal (lower branch) Bloch modes. The propagation distance of the (b) quadrupolar branch is shorter than that of the (c) dipolar transversal mode.

Fig. 4.
Fig. 4.

Energy density maps and electric field distribution at the Bragg condition for (a) the quadrupolar Bloch mode at λ = 540 nm and (b) the dipolar transversal Bloch mode at λ = 916 nm . The corresponding squares show the phase distributions and orientation of the charges.

Fig. 5.
Fig. 5.

(a) Dispersion relation of the MNW chain on a dielectric substrate ( n sup = 1.5 , n sub = 2.0 ). The top and bottom branches belong to the quadrupolar and transversal Bloch modes, respectively. The middle branch corresponds to the excitation of the SPP at the interface between the metallic nanowires and the substrate. Energy density maps and electric field distributions at the Bragg condition for (b) the quadrupolar mode at λ = 562 nm , (c) the SPP-like mode at λ = 655 nm , and (d) the dipolar transversal mode at λ = 997 nm . The charge distribution in (c) exhibits a dipolar longitudinal interaction between the MNW only at the metal–substrate interface.

Fig. 6.
Fig. 6.

Dispersion curves of the integrated structure (red lines), the isolated dielectric waveguide (blue), and the isolated MNW chain (green lines). The quadrupolar Bloch mode (inset) is coupled to the dielectric waveguide at λ = 546 nm , generating antisymmetric and symmetric supermodes. The dipolar transversal mode does not cross the fundamental TM0 mode of the dielectric waveguide.

Fig. 7.
Fig. 7.

Transmission, reflection, and absorption spectra for the integrated structure. In the transmission curve, the quadrupolar mode is excited at λ = 559 nm , and the constructive interference of the dipolar transversal mode is positioned at λ = 990 nm . The minimum at λ = 1055 nm is a cavity resonance effect. In the reflection curve, Bragg reflections are located at λ = 465 nm , λ = 557 nm , and at λ = 960 nm .

Fig. 8.
Fig. 8.

Amplitude maps of the H y component of the electromagnetic field corresponding to (a) the excitation of the quadrupolar mode ( λ = 559 nm ) and (b) the interference of the dipolar transversal mode with the fundamental TM0 mode of the dielectric waveguide at λ = 990 nm .

Equations (6)

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[ F q + F 0 ] = S ( q ) [ F 0 + F q ] ,
P abs = 1 2 k 0 ε 0 c ε r E · E * d S ,
E x = i c k 0 ε 0 ε r H y z ,
E z = i c k 0 ε 0 ε r H y x .
P 0 = 1 2 ε 0 c n eff | E | 2 d S ,
P 0 = 1 2 n eff ε 0 c | H | 2 ε r d S ,

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