Abstract

A method for determining the modes that can be guided along infinite chains of metallic nanowires when they are embedded, as in most realistic set-ups, in layered media is presented. The method is based on a rigorous full-wave frequency-domain Source-Model Technique (SMT). The method allows efficient determination of the complex propagation constants and the surface-plasmon type modal fields. Sample results are presented for silver nanowires with circular and triangle-like cross-sections lying in an air-Si-glass layered structure.

© 2011 OSA

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2010 (2)

2009 (1)

2008 (3)

N. Talebi and M. Shahabdi, “Analysis of the propagation of light along an array of nanorods using the Generalized Multipole Techniques,” J. Comput. Theor. Nanosci. 5, 711–716(6) (2008).
[CrossRef]

A. A. Govyadinov and V. A. Markel, “From slow to superluminal propagation: Dispersive properties of surface plasmon polaritons in linear chains of metallic nanospheroids,” Phys. Rev. B 78, 035403 (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] [PubMed]

2007 (7)

X. Ji, W. Cai, and P. Zhang, “High-order DGTD methods for dispersive maxwell’s equations and modelling of silver nanowire coupling,” Int. J. Numer. Meth. Eng. 69, 308–325 (2007).
[CrossRef]

H. S. Chu, W. B. Ewe, E. P. Li, and R. Vahldieck, “Analysis of sub-wavelength light propagation through long double-chain nanowires with funnel feeding,” Opt. Express 15, 4216–4223 (2007).
[CrossRef] [PubMed]

R. Buckley and P. Berini, “Figures of merit for 2d surface plasmon waveguides and application to metal stripes,” Opt. Express 15, 12174–12182 (2007).
[CrossRef] [PubMed]

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] [PubMed]

F. Capolino, D. Wilton, and W. Johnson, “Efficient computation of the 3D Green’s function for the Helmholtz operator for a linear array of point sources using the Ewald method,” J. Comput. Phys. 223, 250 – 261 (2007).
[CrossRef]

G. Valerio, P. Baccarelli, P. Burghignoli, and A. Galli, “Comparative analysis of acceleration techniques for 2-D and 3-D Green’s functions in periodic structures along one and two directions,” IEEE Trans. Antennas Propag. 55, 1630–1643 (2007).
[CrossRef]

A. Hochman and Y. Leviatan, “Efficient and spurious-free integral-equation-based optical waveguide mode solver,” Opt. Express 15, 14431–14453 (2007).
[CrossRef] [PubMed]

2006 (4)

M. Szpulak, W. Urbanczyk, E. Serebryannikov, A. Zheltikov, A. Hochman, Y. Leviatan, R. Kotynski, and K. Panajotov, “Comparison of different methods for rigorous modeling of photonic crystal fibers,” Opt. Express 14, 5699–5714 (2006).
[CrossRef] [PubMed]

P. Berini, “Figures of merit for surface plasmon waveguides,” Opt. Express 14, 13030–13042 (2006).
[CrossRef] [PubMed]

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

2005 (2)

W. Saj, “FDTD simulations of 2D plasmon waveguide on silver nanorods in hexagonal lattice,” Opt. Express 13, 4818–4827 (2005).
[CrossRef] [PubMed]

O. M. Bucci, G. D’Elia, and M. Santojanni, “Non-redundant implementation of Method of Auxiliary Sources for smooth 2D geometries,” Electronics Letters 41, 1203–1205 (2005).
[CrossRef]

2004 (4)

G. Tayeb and S. Enoch, “Combined fictitious-sources-scattering-matrix method,” J. Opt. Soc. Am. A 21, 1417–1423 (2004).
[CrossRef]

R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21, 2442–2446 (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]

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

2003 (4)

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67, 205402 (2003).
[CrossRef]

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

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]

A. Ludwig and Y. Leviatan, “Analysis of bandgap characteristics of two-dimensional periodic structures by using the Source-Model Technique,” J. Opt. Soc. Am. A 20, 1553–1562 (2003).
[CrossRef]

2002 (1)

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]

2000 (1)

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62, R16356–R16359 (2000).
[CrossRef]

1998 (2)

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]

G. Fairweather and A. Karageorghis, “The Method of Fundamental Solutions for elliptic boundary value problems,” Adv. Comput. Math. 9, 69–95 (1998).
[CrossRef]

1994 (2)

W. Schroeder and I. Wolff, “The origin of spurious modes in numerical solutions of electromagnetic field eigenvalue problems,” IEEE Trans. Microw. Theory 42, 644 –653 (1994).
[CrossRef]

B. Prade and J. Y. Vinet, “Guided optical waves in fibers with negative dielectric constant,” J. Lightwave Technol. 12, 6–18 (1994).
[CrossRef]

1990 (1)

1989 (1)

A. Boag and Y. Leviatan, “Analysis of two-dimensional electromagnetic scattering from nonplanar periodic surfaces using a strip current model,” IEEE Trans. Antennas Propag. 37, 1437 –1446 (1989).
[CrossRef]

1988 (3)

Y. Leviatan and A. Boag, “Analysis of TE scattering from dielectric cylinders using a multifilament magnetic current model,” IEEE Trans. Antennas Propag. 36, 1026 –1031 (1988).
[CrossRef]

A. Boag, Y. Leviatan, and A. Boag, “Analysis of two-dimensional electromagnetic scattering from a periodic grating of cylinders using a hybrid current model,” Radio Sci. 23, 612–624 (1988).
[CrossRef]

Y. Leviatan and A. Boag, “Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies-theory and numerical solution,” IEEE Trans. Antennas Propag. 36, 1722 –1734 (1988).
[CrossRef]

1978 (1)

F. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proceedings of the IEEE 66, 51–83 (1978).
[CrossRef]

1972 (1)

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

Alù, A.

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]

Atwater, H. A.

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67, 205402 (2003).
[CrossRef]

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

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]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62, R16356–R16359 (2000).
[CrossRef]

Aussenegg, F. R.

Baccarelli, P.

G. Valerio, P. Baccarelli, P. Burghignoli, and A. Galli, “Comparative analysis of acceleration techniques for 2-D and 3-D Green’s functions in periodic structures along one and two directions,” IEEE Trans. Antennas Propag. 55, 1630–1643 (2007).
[CrossRef]

Berini, P.

Boag, A.

A. Boag, Y. Leviatan, and A. Boag, “Analysis of diffraction from doubly periodic arrays of perfectly conducting bodies by using a patch-current model,” J. Opt. Soc. Am. A 7, 1712–1718 (1990).
[CrossRef]

A. Boag, Y. Leviatan, and A. Boag, “Analysis of diffraction from doubly periodic arrays of perfectly conducting bodies by using a patch-current model,” J. Opt. Soc. Am. A 7, 1712–1718 (1990).
[CrossRef]

A. Boag and Y. Leviatan, “Analysis of two-dimensional electromagnetic scattering from nonplanar periodic surfaces using a strip current model,” IEEE Trans. Antennas Propag. 37, 1437 –1446 (1989).
[CrossRef]

A. Boag, Y. Leviatan, and A. Boag, “Analysis of two-dimensional electromagnetic scattering from a periodic grating of cylinders using a hybrid current model,” Radio Sci. 23, 612–624 (1988).
[CrossRef]

A. Boag, Y. Leviatan, and A. Boag, “Analysis of two-dimensional electromagnetic scattering from a periodic grating of cylinders using a hybrid current model,” Radio Sci. 23, 612–624 (1988).
[CrossRef]

Y. Leviatan and A. Boag, “Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies-theory and numerical solution,” IEEE Trans. Antennas Propag. 36, 1722 –1734 (1988).
[CrossRef]

Y. Leviatan and A. Boag, “Analysis of TE scattering from dielectric cylinders using a multifilament magnetic current model,” IEEE Trans. Antennas Propag. 36, 1026 –1031 (1988).
[CrossRef]

Brongersma, M. L.

R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21, 2442–2446 (2004).
[CrossRef]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62, R16356–R16359 (2000).
[CrossRef]

Bucci, O. M.

O. M. Bucci, G. D’Elia, and M. Santojanni, “Non-redundant implementation of Method of Auxiliary Sources for smooth 2D geometries,” Electronics Letters 41, 1203–1205 (2005).
[CrossRef]

Buckley, R.

Burghignoli, P.

G. Valerio, P. Baccarelli, P. Burghignoli, and A. Galli, “Comparative analysis of acceleration techniques for 2-D and 3-D Green’s functions in periodic structures along one and two directions,” IEEE Trans. Antennas Propag. 55, 1630–1643 (2007).
[CrossRef]

Cai, W.

X. Ji, W. Cai, and P. Zhang, “High-order DGTD methods for dispersive maxwell’s equations and modelling of silver nanowire coupling,” Int. J. Numer. Meth. Eng. 69, 308–325 (2007).
[CrossRef]

Capolino, F.

F. Capolino, D. Wilton, and W. Johnson, “Efficient computation of the 3D Green’s function for the Helmholtz operator for a linear array of point sources using the Ewald method,” J. Comput. Phys. 223, 250 – 261 (2007).
[CrossRef]

Catrysse, P. B.

Chan, C. T.

Christy, R. W.

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

Chu, H. S.

H. S. Chu, W. B. Ewe, E. P. Li, and R. Vahldieck, “Analysis of sub-wavelength light propagation through long double-chain nanowires with funnel feeding,” Opt. Express 15, 4216–4223 (2007).
[CrossRef] [PubMed]

H. S. Chu, W. B. Ewe, and E. P. Li, “Optical properties of a single-chain of elliptical silver nanowires,” in Proceedings of the 7th IEEE International Conference on Nanotechnology (IEEE2007), pp. 850–853.

Citrin, D. S.

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

Conforti, M.

Crozier, K. B.

D’Elia, G.

O. M. Bucci, G. D’Elia, and M. Santojanni, “Non-redundant implementation of Method of Auxiliary Sources for smooth 2D geometries,” Electronics Letters 41, 1203–1205 (2005).
[CrossRef]

Engheta, N.

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]

Enoch, S.

Ewe, W. B.

H. S. Chu, W. B. Ewe, E. P. Li, and R. Vahldieck, “Analysis of sub-wavelength light propagation through long double-chain nanowires with funnel feeding,” Opt. Express 15, 4216–4223 (2007).
[CrossRef] [PubMed]

H. S. Chu, W. B. Ewe, and E. P. Li, “Optical properties of a single-chain of elliptical silver nanowires,” in Proceedings of the 7th IEEE International Conference on Nanotechnology (IEEE2007), pp. 850–853.

Fairweather, G.

G. Fairweather and A. Karageorghis, “The Method of Fundamental Solutions for elliptic boundary value problems,” Adv. Comput. Math. 9, 69–95 (1998).
[CrossRef]

Ford, G. W.

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]

Fung, K. H.

Galli, A.

G. Valerio, P. Baccarelli, P. Burghignoli, and A. Galli, “Comparative analysis of acceleration techniques for 2-D and 3-D Green’s functions in periodic structures along one and two directions,” IEEE Trans. Antennas Propag. 55, 1630–1643 (2007).
[CrossRef]

Govyadinov, A. A.

A. A. Govyadinov and V. A. Markel, “From slow to superluminal propagation: Dispersive properties of surface plasmon polaritons in linear chains of metallic nanospheroids,” Phys. Rev. B 78, 035403 (2008).
[CrossRef]

Gray, S. K.

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]

Guasoni, M.

Hafner, C.

C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, Norwood, MA, 1990).

Harel, E.

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

Harris, F.

F. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proceedings of the IEEE 66, 51–83 (1978).
[CrossRef]

Hartman, J. W.

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62, R16356–R16359 (2000).
[CrossRef]

Hochman, A.

Ji, X.

X. Ji, W. Cai, and P. Zhang, “High-order DGTD methods for dispersive maxwell’s equations and modelling of silver nanowire coupling,” Int. J. Numer. Meth. Eng. 69, 308–325 (2007).
[CrossRef]

Johnson, P. B.

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

Johnson, W.

F. Capolino, D. Wilton, and W. Johnson, “Efficient computation of the 3D Green’s function for the Helmholtz operator for a linear array of point sources using the Ewald method,” J. Comput. Phys. 223, 250 – 261 (2007).
[CrossRef]

Karageorghis, A.

G. Fairweather and A. Karageorghis, “The Method of Fundamental Solutions for elliptic boundary value problems,” Adv. Comput. Math. 9, 69–95 (1998).
[CrossRef]

Kik, P. G.

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67, 205402 (2003).
[CrossRef]

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

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]

Koel, B. E.

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

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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]

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Krenn, J. 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]

Leitner, A.

Leviatan, Y.

A. Hochman and Y. Leviatan, “Rigorous modal analysis of metallic nanowire chains,” Opt. Express 17, 13561–13575 (2009).
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A. Hochman and Y. Leviatan, “Efficient and spurious-free integral-equation-based optical waveguide mode solver,” Opt. Express 15, 14431–14453 (2007).
[CrossRef] [PubMed]

M. Szpulak, W. Urbanczyk, E. Serebryannikov, A. Zheltikov, A. Hochman, Y. Leviatan, R. Kotynski, and K. Panajotov, “Comparison of different methods for rigorous modeling of photonic crystal fibers,” Opt. Express 14, 5699–5714 (2006).
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A. Ludwig and Y. Leviatan, “Analysis of bandgap characteristics of two-dimensional periodic structures by using the Source-Model Technique,” J. Opt. Soc. Am. A 20, 1553–1562 (2003).
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Y. Leviatan and A. Boag, “Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies-theory and numerical solution,” IEEE Trans. Antennas Propag. 36, 1722 –1734 (1988).
[CrossRef]

A. Boag, Y. Leviatan, and A. Boag, “Analysis of two-dimensional electromagnetic scattering from a periodic grating of cylinders using a hybrid current model,” Radio Sci. 23, 612–624 (1988).
[CrossRef]

Y. Leviatan and A. Boag, “Analysis of TE scattering from dielectric cylinders using a multifilament magnetic current model,” IEEE Trans. Antennas Propag. 36, 1026 –1031 (1988).
[CrossRef]

Li, E. P.

H. S. Chu, W. B. Ewe, E. P. Li, and R. Vahldieck, “Analysis of sub-wavelength light propagation through long double-chain nanowires with funnel feeding,” Opt. Express 15, 4216–4223 (2007).
[CrossRef] [PubMed]

H. S. Chu, W. B. Ewe, and E. P. Li, “Optical properties of a single-chain of elliptical silver nanowires,” in Proceedings of the 7th IEEE International Conference on Nanotechnology (IEEE2007), pp. 850–853.

Ludwig, A.

Maier, S. A.

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67, 205402 (2003).
[CrossRef]

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

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]

Markel, V. A.

A. A. Govyadinov and V. A. Markel, “From slow to superluminal propagation: Dispersive properties of surface plasmon polaritons in linear chains of metallic nanospheroids,” Phys. Rev. B 78, 035403 (2008).
[CrossRef]

Maystre, D.

D. Maystre, M. Saillard, and G. Tayeb, “Special methods of wave diffraction,” in Scattering,, P. Sabatier and E. Pike, eds. (Academic Press, 2001), chap. 1.5.6.

Meltzer, S.

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

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).
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B. Prade and J. Y. Vinet, “Guided optical waves in fibers with negative dielectric constant,” J. Lightwave Technol. 12, 6–18 (1994).
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Requicha, A. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nature Materials 2, 229–232 (2003).
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D. Maystre, M. Saillard, and G. Tayeb, “Special methods of wave diffraction,” in Scattering,, P. Sabatier and E. Pike, eds. (Academic Press, 2001), chap. 1.5.6.

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W. Schroeder and I. Wolff, “The origin of spurious modes in numerical solutions of electromagnetic field eigenvalue problems,” IEEE Trans. Microw. Theory 42, 644 –653 (1994).
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Serebryannikov, E.

Shahabdi, M.

N. Talebi and M. Shahabdi, “Analysis of the propagation of light along an array of nanorods using the Generalized Multipole Techniques,” J. Comput. Theor. Nanosci. 5, 711–716(6) (2008).
[CrossRef]

Simsek, E.

Szpulak, M.

Talebi, N.

N. Talebi and M. Shahabdi, “Analysis of the propagation of light along an array of nanorods using the Generalized Multipole Techniques,” J. Comput. Theor. Nanosci. 5, 711–716(6) (2008).
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G. Tayeb and S. Enoch, “Combined fictitious-sources-scattering-matrix method,” J. Opt. Soc. Am. A 21, 1417–1423 (2004).
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D. Maystre, M. Saillard, and G. Tayeb, “Special methods of wave diffraction,” in Scattering,, P. Sabatier and E. Pike, eds. (Academic Press, 2001), chap. 1.5.6.

Urbanczyk, W.

Vahldieck, R.

Valerio, G.

G. Valerio, P. Baccarelli, P. Burghignoli, and A. Galli, “Comparative analysis of acceleration techniques for 2-D and 3-D Green’s functions in periodic structures along one and two directions,” IEEE Trans. Antennas Propag. 55, 1630–1643 (2007).
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B. Prade and J. Y. Vinet, “Guided optical waves in fibers with negative dielectric constant,” J. Lightwave Technol. 12, 6–18 (1994).
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W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70, 125429 (2004).
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F. Capolino, D. Wilton, and W. Johnson, “Efficient computation of the 3D Green’s function for the Helmholtz operator for a linear array of point sources using the Ewald method,” J. Comput. Phys. 223, 250 – 261 (2007).
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W. Schroeder and I. Wolff, “The origin of spurious modes in numerical solutions of electromagnetic field eigenvalue problems,” IEEE Trans. Microw. Theory 42, 644 –653 (1994).
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X. Ji, W. Cai, and P. Zhang, “High-order DGTD methods for dispersive maxwell’s equations and modelling of silver nanowire coupling,” Int. J. Numer. Meth. Eng. 69, 308–325 (2007).
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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]

Electronics Letters (1)

O. M. Bucci, G. D’Elia, and M. Santojanni, “Non-redundant implementation of Method of Auxiliary Sources for smooth 2D geometries,” Electronics Letters 41, 1203–1205 (2005).
[CrossRef]

IEEE Trans. Antennas Propag. (4)

A. Boag and Y. Leviatan, “Analysis of two-dimensional electromagnetic scattering from nonplanar periodic surfaces using a strip current model,” IEEE Trans. Antennas Propag. 37, 1437 –1446 (1989).
[CrossRef]

Y. Leviatan and A. Boag, “Analysis of TE scattering from dielectric cylinders using a multifilament magnetic current model,” IEEE Trans. Antennas Propag. 36, 1026 –1031 (1988).
[CrossRef]

Y. Leviatan and A. Boag, “Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies-theory and numerical solution,” IEEE Trans. Antennas Propag. 36, 1722 –1734 (1988).
[CrossRef]

G. Valerio, P. Baccarelli, P. Burghignoli, and A. Galli, “Comparative analysis of acceleration techniques for 2-D and 3-D Green’s functions in periodic structures along one and two directions,” IEEE Trans. Antennas Propag. 55, 1630–1643 (2007).
[CrossRef]

IEEE Trans. Microw. Theory (1)

W. Schroeder and I. Wolff, “The origin of spurious modes in numerical solutions of electromagnetic field eigenvalue problems,” IEEE Trans. Microw. Theory 42, 644 –653 (1994).
[CrossRef]

Int. J. Numer. Meth. Eng. (1)

X. Ji, W. Cai, and P. Zhang, “High-order DGTD methods for dispersive maxwell’s equations and modelling of silver nanowire coupling,” Int. J. Numer. Meth. Eng. 69, 308–325 (2007).
[CrossRef]

J. Comput. Phys. (1)

F. Capolino, D. Wilton, and W. Johnson, “Efficient computation of the 3D Green’s function for the Helmholtz operator for a linear array of point sources using the Ewald method,” J. Comput. Phys. 223, 250 – 261 (2007).
[CrossRef]

J. Comput. Theor. Nanosci. (1)

N. Talebi and M. Shahabdi, “Analysis of the propagation of light along an array of nanorods using the Generalized Multipole Techniques,” J. Comput. Theor. Nanosci. 5, 711–716(6) (2008).
[CrossRef]

J. Lightwave Technol. (1)

B. Prade and J. Y. Vinet, “Guided optical waves in fibers with negative dielectric constant,” J. Lightwave Technol. 12, 6–18 (1994).
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J. Opt. Soc. Am. A (4)

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

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D. S. Citrin, “Coherent excitation transport in metalnanoparticle chains,” Nano Lett. 4, 1561–1565 (2004).
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Nature Materials (1)

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

Opt. Express (9)

P. Berini, “Figures of merit for surface plasmon waveguides,” Opt. Express 14, 13030–13042 (2006).
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R. Buckley and P. Berini, “Figures of merit for 2d surface plasmon waveguides and application to metal stripes,” Opt. Express 15, 12174–12182 (2007).
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H. S. Chu, W. B. Ewe, E. P. Li, and R. Vahldieck, “Analysis of sub-wavelength light propagation through long double-chain nanowires with funnel feeding,” Opt. Express 15, 4216–4223 (2007).
[CrossRef] [PubMed]

W. Saj, “FDTD simulations of 2D plasmon waveguide on silver nanorods in hexagonal lattice,” Opt. Express 13, 4818–4827 (2005).
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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).
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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] [PubMed]

A. Hochman and Y. Leviatan, “Rigorous modal analysis of metallic nanowire chains,” Opt. Express 17, 13561–13575 (2009).
[CrossRef] [PubMed]

M. Szpulak, W. Urbanczyk, E. Serebryannikov, A. Zheltikov, A. Hochman, Y. Leviatan, R. Kotynski, and K. Panajotov, “Comparison of different methods for rigorous modeling of photonic crystal fibers,” Opt. Express 14, 5699–5714 (2006).
[CrossRef] [PubMed]

A. Hochman and Y. Leviatan, “Efficient and spurious-free integral-equation-based optical waveguide mode solver,” Opt. Express 15, 14431–14453 (2007).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. B (8)

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, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67, 205402 (2003).
[CrossRef]

A. A. Govyadinov and V. A. Markel, “From slow to superluminal propagation: Dispersive properties of surface plasmon polaritons in linear chains of metallic nanospheroids,” Phys. Rev. B 78, 035403 (2008).
[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).
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H. S. Chu, W. B. Ewe, and E. P. Li, “Optical properties of a single-chain of elliptical silver nanowires,” in Proceedings of the 7th IEEE International Conference on Nanotechnology (IEEE2007), pp. 850–853.

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Figures (7)

Fig. 1
Fig. 1

Linear chain of nanowires with arbitrary smooth cross-section and relative permittivity ɛc, embedded in a material slab with relative permittivity ɛmid. Bellow ysub rests a semi-infinite substrate with relative permittivity ɛsub, and above ytop lies a semi-infinite covering layer with relative permittivity ɛtop.

Fig. 2
Fig. 2

Magnetic Current filaments used to approximate the fields inside of the cylinder.

Fig. 3
Fig. 3

Locations of fictitious current for approximating the fields within the unit cell and outside the cylinder.

Fig. 4
Fig. 4

Normalized frequency (ordinate on the left) and wavelength (ordinate on the right) plotted against Re{kx}/ (π/L) in (a), and against Im{kx}/ (π/L) in (b). The analyzed triple layered structure is shown in the inset of (a), with the choice of R = 20nm and L = 50nm. ysub was fixed at −5R and ytop was a parameter.

Fig. 5
Fig. 5

Normalized Re{Hz} of the first TE to z mode for the structure shown in the inset of Fig. 4(a), with the aforementioned parameters. Here, ωL/(2πc) = 0.05355 is fixed and the height of the Si-air interface, ytop, equals 2R, 3R, and 5R in subfigures (a), (b), and (c), respectively. These mode profiles correspond to the boxed points in the dispersion curves in Fig. 4.

Fig. 6
Fig. 6

Normalized frequency (ordinate on the left) and wavelength (ordinate on the right) plotted against Re{kx}/ (π/L) in (a), and against Im{kx}/ (π/L) in (b). The curves in purple and brown display the dispersion of a chain of triangle-like NWs in a layered structure, as shown in the inset of Fig. 6(a), with L = 50nm, ytop = 3R and ysub = −5R. The red curve is taken from Fig. 4 for an identical structure yet with circular NWs. The purple curve corresponds to triangle-like NWs with the same perimeter as the circular NWs, and the brown curve corresponds to triangle-like NWs with the same area as the circular NWs.

Fig. 7
Fig. 7

Normalized |H| (in color) and Re{S} (black arrows) of the first three propagating plasmonic modes in the structure shown in the inset of Fig. 6(a), with the aforementioned parameters. The modes (a),(b),(c) correspond to the points marked by circles in Fig. 6, for NWs with circular perimeter. The modes (d),(e),(f) correspond to the points marked by triangles there, for NWs with identical perimeter yet triangle-like shape.

Tables (1)

Tables Icon

Table 1 Convergence of kx with N for circular and triangle-like NWs

Equations (17)

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F ( L / 2 ) = F ( L / 2 ) e j k x L
k x n = k x + 2 π n L .
G c = 1 4 j H 0 ( 2 ) [ k c ( x x 0 ) 2 + ( y y 0 ) 2 ] ,
H z = ɛ mid k 0 2 L η 0 n = f ^ n k y n , mid exp { j [ k x n ( x x 0 ) + k y n , mid | y y 0 | ] } ,
E x = j 2 η 0 L ɛ mid k 0 H z y
E y = j 2 η 0 L ɛ mid k 0 H z x .
k y n , mid = ɛ mid k 0 2 k x n 2 ,
f ^ n = 1 L L / 2 L / 2 f ( x ) exp { j 2 π n x L } d x .
Γ mid sub H n = ɛ sub k y n , mid ɛ mid k y n , sub ɛ sub k y n , mid + ɛ mid k y n , sub exp { j 2 k y n , mid | y 0 y sub | }
T mid sub H n = 2 k y n , mid ɛ mid ɛ sub k y n , mid + ɛ mid k y n , sub exp { j ( k y n , mid k y n , sub ) | y 0 y sub | } .
1 + Γ mid sub H n Γ mid top H n + ( Γ mid sub H n Γ mid top H n ) 2 + ( Γ mid sub H n Γ mid top H n ) 3 + = 1 1 Γ mid sub H n Γ mid top H n .
H z = k 0 2 η 0 n = f ^ n k y n , mid exp { j k x n ( x x 0 ) } . { ɛ top T mid top H n ( 1 + Γ mid sub H n ) 1 Γ mid top H n Γ mid sub H n exp { j k y n , top | y y 0 | } for y > y top ɛ mid 1 Γ mid top H n Γ mid sub H n [ exp { j k y n , mid | y y 0 | } + + Γ mid sub H n Γ mid top H n exp { + j k y n , mid | y y 0 | } + + Γ mid top H n exp { + j k y n , mid ( y y 0 ) } + + Γ mid sub H n exp { j k y n , mid ( y y 0 ) } ] for y sub y y top ɛ sub T mid sub H n ( 1 + Γ mid top H n ) 1 Γ mid top H n Γ mid sub H n exp { j k y n , sub | y y 0 | } for y < y sub .
[ Z ( k x , ω ) ] K = 0 ,
[ Z ] = [ [ Z H in ] [ Z H out ] [ Z E in ] [ Z E out ] ] ,
[ Z ] [ Z ] = ( Δ E ( K ) ) 2 1 2 [ [ Z H in ] [ Z H out ] ] 1 2 [ [ Z H in ] [ Z H out ] ] ,
x ( ϕ ) = R b 4 ν + 1 [ 4 ν cos ( ϕ ) cos ( 2 ϕ ) ]
y ( ϕ ) = R b 4 ν + 1 [ 4 ν sin ( ϕ ) + sin ( 2 ϕ ) ] .

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