Abstract

The energy transport properties of plasmonic waveguides can be analyzed by solving the dispersion relation for surface plasmon-polaritons (SPPs). We use this approach to derive an approximate analytical expression for SPP propagation length when the waveguide is composed of linearly arranged metallic nanoparticles, while assuming that metal losses are small or partially compensated by gain. Applied to metal–dielectric (composite) nanospheres, the obtained expression allows us to optimize the performance of the waveguide and arrive at a number of practical design rules. Specifically, we show that SPP attenuation can be minimized at a certain interparticle distance for transverse modes, but gradually grows for both longitudinal and transverse modes with the increase of particle separation. We also show that the two basic methods of supplying gain to the system, i.e., embedding the particles into a gain medium or having a metal–gain composition for the particles, do not perform equally well and the former method is more efficient, but the way the two methods affect depends on the polarization of SPPs. To investigate the role of the nanoparticles’ arrangement in determining SPP characteristics, we follow a purely numerical approach and consider a two-segment bent waveguide as an example. Analyzing the waveguide’s transmission shows that it behaves in an oscillatory manner with respect to the angle between the two segments and is therefore higher for certain angles than for the others. This suggests that, in the design of waveguides with bends, careful attention needs to be paid in order to avoid bend angles that yield low transmission and to choose angles that give maximum transmission.

© 2011 OSA

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2011 (6)

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]

A. Pannipitiya, I. D. Rukhlenko, and M. Premaratne, “Analytical modeling of efficient couples for plasmonic-slot-waveguide junctions,” IEEE Photonics J. 3, 220–233 (2011).
[CrossRef]

M. Guasoni and C. de Angelis, “Analytical approximations of the dispersion relation of a linear chain of metal nanoparticles,” Opt. Commun. 284, 1822–1827 (2011).
[CrossRef]

M. I. Stockman, “Nanoplasmonics: The physics behind the applications,” Phys. Today 64, 39–44 (2011).
[CrossRef]

B. Willingham and S. Link, “Energy transport in metal nanoparticle chains via sub-radiant plasmon modes,” Opt. Express 19, 6450–6461 (2011).
[CrossRef] [PubMed]

D. Handapangoda, M. Premaratne, I. D. Rukhlenko, and C. Jagadish, “Optimal design of composite nanowires for extended reach of surface plasmon-polaritons,” Opt. Express 19, 16058–16074 (2011).
[CrossRef] [PubMed]

2010 (7)

2008 (3)

C. Tserkezis, G. Gantzounis, and N. Stefanou, “Collective plasmonic modes in ordered assemblies of metallic nanoshells,” J. Phys. Condens. Matter 20, 075232 (2008).
[CrossRef]

A. Govyadinov and V. 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]

X. Cui and D. Erni, “Enhanced propagation in a plasmonic chain waveguide with nanoshell structures based on low-and high-order mode coupling,” J. Opt. Soc. Am. A 25, 1783–1789 (2008).
[CrossRef]

2007 (8)

V. Markel and A. Sarychev, “Propagation of surface plasmons in ordered and disordered chains of metal nanospheres,” Phys. Rev. B 75, 085426 (2007).
[CrossRef]

J. A. Gordon and R. W. Ziolkowski, “The design and simulated performance of a coated nano-particle laser,” Opt. Express 15, 2622–2653 (2007).
[CrossRef] [PubMed]

J. A. Gordon and R. W. Ziolkowski, “Investigating functionalized active coated nanoparticles for use in nano-sensing applications,” Opt. Express 15, 12562–12582 (2007).
[CrossRef] [PubMed]

K. B. Crozier, E. Togan, E. Simsek, and T. Yang, “Experimental measurement of the dispersion relations of the surface plasmon modes of metal nanoparticle chains,” Opt. Express 15, 17482–17493 (2007).
[CrossRef] [PubMed]

S. Wang, J. Xiao, and K. Yu, “Tunable coupled plasmon modes via nanoshell particle chains,” Opt. Commun. 279, 384–389 (2007).
[CrossRef]

J. Chen, J. Benjamin, and Y. Xia, “One-dimensional nanostructures of metals: Large-scale synthesis and some potential applications,” Langmuir 23, 4120–4129 (2007).
[CrossRef] [PubMed]

S. Lal, S. Link, and N. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

M. I. Stockman, “Criterion for negative refraction with low optical losses from a fundamental principle of causality,” Phys. Rev. Lett. 98, 177404 (2007).
[CrossRef]

2006 (5)

A. 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]

S. Maier, “Plasmonics: Metal nanostructures for subwavelength photonic devices,” IEEE J. Sel. Top. Quantum Electron. 12, 1214–1220 (2006).
[CrossRef]

R. Zia, J. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: The next chip-scale technology,” Mater. Today 9, 20–27 (2006).
[CrossRef]

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

2005 (4)

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long-range surface-plasmon-polariton waveguides,” J. Appl. Phys. 98, 043109 (2005).
[CrossRef]

G. Gantzounis, N. Stefanou, and V. Yannopapas, “Optical properties of a periodic monolayer of metallic nanospheres on a dielectric waveguide,” J. Phys. Condens. Matter 17, 1791 (2005).
[CrossRef]

D. Citrin, “Plasmon polaritons in finite-length metal-nanoparticle chains: The role of chain length unravelled,” Nano Lett. 5, 985–989 (2005).
[CrossRef] [PubMed]

2004 (5)

N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. 85, 5040–5042 (2004).
[CrossRef]

J. Krenn and J. Weeber, “Surface plasmon polaritons in metal stripes and wires,” Philos. Trans. R. Soc. London, Ser. A 362, 739–756 (2004).
[CrossRef]

S. 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. 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]

2003 (3)

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

L. Zhao, K. Kelly, and G. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. 107, 7343–7350 (2003).
[CrossRef]

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

2002 (1)

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

2001 (1)

S. Maier, M. Brongersma, P. Kik, S. Meltzer, A. Requicha, and H. Atwater, “Plasmonics: A route to nanoscale optical devices,” Adv. Mater. 13, 2 (2001).
[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, 16356 (2000).
[CrossRef]

1999 (1)

1998 (1)

1994 (1)

B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. B 11, 1491–1499 (1994).
[CrossRef]

1982 (2)

J. Gérardy and M. Ausloos, “Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations. II. Optical properties of aggregated metal spheres,” Phys. Rev. B 25, 4204–4229 (1982).
[CrossRef]

A. Wokaun, J. Gordon, and P. Liao, “Radiation damping in surface-enhanced Raman scattering,” Phys. Rev. Lett. 48, 957–960 (1982).
[CrossRef]

1969 (1)

E. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539 (1969).
[CrossRef]

Agrawal, G. P.

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.

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

S. Maier, M. Brongersma, P. Kik, S. Meltzer, A. Requicha, and H. Atwater, “Plasmonics: A route to nanoscale optical devices,” Adv. Mater. 13, 2 (2001).
[CrossRef]

Atwater, H. A.

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[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, 16356 (2000).
[CrossRef]

Ausloos, M.

J. Gérardy and M. Ausloos, “Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations. II. Optical properties of aggregated metal spheres,” Phys. Rev. B 25, 4204–4229 (1982).
[CrossRef]

Aussenegg, F. R.

Averitt, R. D.

Baranov, A. V.

A. V. Fedorov, A. V. Baranov, I. D. Rukhlenko, and S. V. Gaponenko, “Enhanced intraband carrier relaxation in quantum dots due to the effect of plasmon–LO-phonon density of states in doped heterostructures,” Phys. Rev. B 71, 195310 (2005).

Barnes, W.

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

Benjamin, J.

J. Chen, J. Benjamin, and Y. Xia, “One-dimensional nanostructures of metals: Large-scale synthesis and some potential applications,” Langmuir 23, 4120–4129 (2007).
[CrossRef] [PubMed]

Berini, P.

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long-range surface-plasmon-polariton waveguides,” J. Appl. Phys. 98, 043109 (2005).
[CrossRef]

Bienstman, P.

K. Huang, E. Lidorikis, X. Jiang, J. Joannopoulos, K. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).

Bohren, C. F.

C. F. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Bozhevolnyi, S.

D. Gramotnev and S. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[CrossRef]

Bratkovsky, A.

P. Holmström, L. Thylén, and A. Bratkovsky, “Composite metal/quantum-dot nanoparticle-array waveguides with compensated loss,” Appl. Phys. Lett. 97, 073110 (2010).
[CrossRef]

Brongersma, M.

R. Zia, J. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: The next chip-scale technology,” Mater. Today 9, 20–27 (2006).
[CrossRef]

S. Maier, M. Brongersma, P. Kik, S. Meltzer, A. Requicha, and H. Atwater, “Plasmonics: A route to nanoscale optical devices,” Adv. Mater. 13, 2 (2001).
[CrossRef]

Brongersma, M. L.

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, 16356 (2000).
[CrossRef]

Chandran, A.

R. Zia, J. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: The next chip-scale technology,” Mater. Today 9, 20–27 (2006).
[CrossRef]

Charbonneau, R.

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long-range surface-plasmon-polariton waveguides,” J. Appl. Phys. 98, 043109 (2005).
[CrossRef]

Chen, J.

J. Chen, J. Benjamin, and Y. Xia, “One-dimensional nanostructures of metals: Large-scale synthesis and some potential applications,” Langmuir 23, 4120–4129 (2007).
[CrossRef] [PubMed]

Citrin, D.

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

D. Citrin, “Plasmon polaritons in finite-length metal-nanoparticle chains: The role of chain length unravelled,” Nano Lett. 5, 985–989 (2005).
[CrossRef] [PubMed]

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

Conforti, M.

Coronado, E.

K. Kelly, E. Coronado, L. Zhao, and G. 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.

Cui, X.

de Angelis, C.

M. Guasoni and C. de Angelis, “Analytical approximations of the dispersion relation of a linear chain of metal nanoparticles,” Opt. Commun. 284, 1822–1827 (2011).
[CrossRef]

Dereux, A.

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

Draine, B. T.

B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. B 11, 1491–1499 (1994).
[CrossRef]

Ebbesen, T.

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

Economou, E.

E. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539 (1969).
[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]

Erni, D.

Fan, S.

K. Huang, E. Lidorikis, X. Jiang, J. Joannopoulos, K. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).

Fedorov, A. V.

A. V. Fedorov, A. V. Baranov, I. D. Rukhlenko, and S. V. Gaponenko, “Enhanced intraband carrier relaxation in quantum dots due to the effect of plasmon–LO-phonon density of states in doped heterostructures,” Phys. Rev. B 71, 195310 (2005).

Flatau, P. J.

B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. B 11, 1491–1499 (1994).
[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]

Gantzounis, G.

C. Tserkezis, G. Gantzounis, and N. Stefanou, “Collective plasmonic modes in ordered assemblies of metallic nanoshells,” J. Phys. Condens. Matter 20, 075232 (2008).
[CrossRef]

G. Gantzounis, N. Stefanou, and V. Yannopapas, “Optical properties of a periodic monolayer of metallic nanospheres on a dielectric waveguide,” J. Phys. Condens. Matter 17, 1791 (2005).
[CrossRef]

Gaponenko, S. V.

A. V. Fedorov, A. V. Baranov, I. D. Rukhlenko, and S. V. Gaponenko, “Enhanced intraband carrier relaxation in quantum dots due to the effect of plasmon–LO-phonon density of states in doped heterostructures,” Phys. Rev. B 71, 195310 (2005).

Gérardy, J.

J. Gérardy and M. Ausloos, “Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations. II. Optical properties of aggregated metal spheres,” Phys. Rev. B 25, 4204–4229 (1982).
[CrossRef]

Gordon, J.

A. Wokaun, J. Gordon, and P. Liao, “Radiation damping in surface-enhanced Raman scattering,” Phys. Rev. Lett. 48, 957–960 (1982).
[CrossRef]

Gordon, J. A.

Govyadinov, A.

A. Govyadinov and V. 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]

Gramotnev, D.

D. Gramotnev and S. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[CrossRef]

Guasoni, M.

M. Guasoni and C. de Angelis, “Analytical approximations of the dispersion relation of a linear chain of metal nanoparticles,” Opt. Commun. 284, 1822–1827 (2011).
[CrossRef]

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

Halas, N.

S. Lal, S. Link, and N. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

Halas, N. J.

Handapangoda, D.

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, 16356 (2000).
[CrossRef]

Hattori, H. T.

Ho, H.-P.

Holmström, P.

P. Holmström, L. Thylén, and A. Bratkovsky, “Composite metal/quantum-dot nanoparticle-array waveguides with compensated loss,” Appl. Phys. Lett. 97, 073110 (2010).
[CrossRef]

Huang, K.

K. Huang, E. Lidorikis, X. Jiang, J. Joannopoulos, K. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).

Huffman, D.

C. F. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Jagadish, C.

Jiang, X.

K. Huang, E. Lidorikis, X. Jiang, J. Joannopoulos, K. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).

Joannopoulos, J.

K. Huang, E. Lidorikis, X. Jiang, J. Joannopoulos, K. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).

Kelly, K.

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

L. Zhao, K. Kelly, and G. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. 107, 7343–7350 (2003).
[CrossRef]

Khurgin, J.

J. Khurgin and G. Sun, “In search of the elusive lossless metal,” Appl. Phys. Lett. 96, 181102 (2010).
[CrossRef]

Kik, P.

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

S. Maier, M. Brongersma, P. Kik, S. Meltzer, A. Requicha, and H. Atwater, “Plasmonics: A route to nanoscale optical devices,” Adv. Mater. 13, 2 (2001).
[CrossRef]

Koenderink, A.

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

Krenn, J.

J. Krenn and J. Weeber, “Surface plasmon polaritons in metal stripes and wires,” Philos. Trans. R. Soc. London, Ser. A 362, 739–756 (2004).
[CrossRef]

Krenn, R.

Lahoud, N.

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long-range surface-plasmon-polariton waveguides,” J. Appl. Phys. 98, 043109 (2005).
[CrossRef]

Lal, S.

S. Lal, S. Link, and N. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

Lawandy, N. M.

N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. 85, 5040–5042 (2004).
[CrossRef]

Leitner, A. J.

Lewin, L.

L. Lewin, Dilogarithms and Associated Functions (McDonald, 1958).

Liao, P.

A. Wokaun, J. Gordon, and P. Liao, “Radiation damping in surface-enhanced Raman scattering,” Phys. Rev. Lett. 48, 957–960 (1982).
[CrossRef]

Lidorikis, E.

K. Huang, E. Lidorikis, X. Jiang, J. Joannopoulos, K. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).

Link, S.

Maier, S.

S. Maier, “Plasmonics: Metal nanostructures for subwavelength photonic devices,” IEEE J. Sel. Top. Quantum Electron. 12, 1214–1220 (2006).
[CrossRef]

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

S. Maier, M. Brongersma, P. Kik, S. Meltzer, A. Requicha, and H. Atwater, “Plasmonics: A route to nanoscale optical devices,” Adv. Mater. 13, 2 (2001).
[CrossRef]

Maier, S. A.

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Markel, V.

A. Govyadinov and V. 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]

V. Markel and A. Sarychev, “Propagation of surface plasmons in ordered and disordered chains of metal nanospheres,” Phys. Rev. B 75, 085426 (2007).
[CrossRef]

Mattiussi, G.

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long-range surface-plasmon-polariton waveguides,” J. Appl. Phys. 98, 043109 (2005).
[CrossRef]

Meltzer, S.

S. Maier, M. Brongersma, P. Kik, S. Meltzer, A. Requicha, and H. Atwater, “Plasmonics: A route to nanoscale optical devices,” Adv. Mater. 13, 2 (2001).
[CrossRef]

Nelson, K.

K. Huang, E. Lidorikis, X. Jiang, J. Joannopoulos, K. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).

Pannipitiya, A.

A. Pannipitiya, I. D. Rukhlenko, and M. Premaratne, “Analytical modeling of efficient couples for plasmonic-slot-waveguide junctions,” IEEE Photonics J. 3, 220–233 (2011).
[CrossRef]

A. Pannipitiya, I. D. Rukhlenko, M. Premaratne, H. T. Hattori, and G. P. Agrawal, “Improved transmission model for metal-dielectric-metal plasmonic waveguides with stub structure,” Opt. Express 18, 6191–6204 (2010).
[CrossRef] [PubMed]

Park, S.

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

Polman, A.

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

Premaratne, M.

Quinten, M.

Requicha, A.

S. Maier, M. Brongersma, P. Kik, S. Meltzer, A. Requicha, and H. Atwater, “Plasmonics: A route to nanoscale optical devices,” Adv. Mater. 13, 2 (2001).
[CrossRef]

Rukhlenko, I. D.

A. Pannipitiya, I. D. Rukhlenko, and M. Premaratne, “Analytical modeling of efficient couples for plasmonic-slot-waveguide junctions,” IEEE Photonics J. 3, 220–233 (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]

D. Handapangoda, M. Premaratne, I. D. Rukhlenko, and C. Jagadish, “Optimal design of composite nanowires for extended reach of surface plasmon-polaritons,” Opt. Express 19, 16058–16074 (2011).
[CrossRef] [PubMed]

D. Handapangoda, I. D. Rukhlenko, M. Premaratne, and C. Jagadish, “Optimization of gain-assisted waveguiding in metal-dielectric nanowires,” Opt. Lett. 35, 4190–4192 (2010).
[CrossRef] [PubMed]

A. Pannipitiya, I. D. Rukhlenko, M. Premaratne, H. T. Hattori, and G. P. Agrawal, “Improved transmission model for metal-dielectric-metal plasmonic waveguides with stub structure,” Opt. Express 18, 6191–6204 (2010).
[CrossRef] [PubMed]

A. V. Fedorov, A. V. Baranov, I. D. Rukhlenko, and S. V. Gaponenko, “Enhanced intraband carrier relaxation in quantum dots due to the effect of plasmon–LO-phonon density of states in doped heterostructures,” Phys. Rev. B 71, 195310 (2005).

Sarychev, A.

V. Markel and A. Sarychev, “Propagation of surface plasmons in ordered and disordered chains of metal nanospheres,” Phys. Rev. B 75, 085426 (2007).
[CrossRef]

Schatz, G.

L. Zhao, K. Kelly, and G. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. 107, 7343–7350 (2003).
[CrossRef]

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

Schuller, J.

R. Zia, J. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: The next chip-scale technology,” Mater. Today 9, 20–27 (2006).
[CrossRef]

Simsek, E.

Stefanou, N.

C. Tserkezis, G. Gantzounis, and N. Stefanou, “Collective plasmonic modes in ordered assemblies of metallic nanoshells,” J. Phys. Condens. Matter 20, 075232 (2008).
[CrossRef]

G. Gantzounis, N. Stefanou, and V. Yannopapas, “Optical properties of a periodic monolayer of metallic nanospheres on a dielectric waveguide,” J. Phys. Condens. Matter 17, 1791 (2005).
[CrossRef]

Stockman, M. I.

M. I. Stockman, “Nanoplasmonics: The physics behind the applications,” Phys. Today 64, 39–44 (2011).
[CrossRef]

M. I. Stockman, “Criterion for negative refraction with low optical losses from a fundamental principle of causality,” Phys. Rev. Lett. 98, 177404 (2007).
[CrossRef]

Stroud, D.

S. 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, G.

J. Khurgin and G. Sun, “In search of the elusive lossless metal,” Appl. Phys. Lett. 96, 181102 (2010).
[CrossRef]

Thylén, L.

P. Holmström, L. Thylén, and A. Bratkovsky, “Composite metal/quantum-dot nanoparticle-array waveguides with compensated loss,” Appl. Phys. Lett. 97, 073110 (2010).
[CrossRef]

Togan, E.

Tserkezis, C.

C. Tserkezis, G. Gantzounis, and N. Stefanou, “Collective plasmonic modes in ordered assemblies of metallic nanoshells,” J. Phys. Condens. Matter 20, 075232 (2008).
[CrossRef]

Udagedara, I. B.

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]

Wang, S.

S. Wang, J. Xiao, and K. Yu, “Tunable coupled plasmon modes via nanoshell particle chains,” Opt. Commun. 279, 384–389 (2007).
[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.

J. Krenn and J. Weeber, “Surface plasmon polaritons in metal stripes and wires,” Philos. Trans. R. Soc. London, Ser. A 362, 739–756 (2004).
[CrossRef]

Westcott, S. L.

Willingham, B.

Wokaun, A.

A. Wokaun, J. Gordon, and P. Liao, “Radiation damping in surface-enhanced Raman scattering,” Phys. Rev. Lett. 48, 957–960 (1982).
[CrossRef]

Xia, Y.

J. Chen, J. Benjamin, and Y. Xia, “One-dimensional nanostructures of metals: Large-scale synthesis and some potential applications,” Langmuir 23, 4120–4129 (2007).
[CrossRef] [PubMed]

Xiao, J.

S. Wang, J. Xiao, and K. Yu, “Tunable coupled plasmon modes via nanoshell particle chains,” Opt. Commun. 279, 384–389 (2007).
[CrossRef]

Yang, T.

Yannopapas, V.

G. Gantzounis, N. Stefanou, and V. Yannopapas, “Optical properties of a periodic monolayer of metallic nanospheres on a dielectric waveguide,” J. Phys. Condens. Matter 17, 1791 (2005).
[CrossRef]

Yu, K.

S. Wang, J. Xiao, and K. Yu, “Tunable coupled plasmon modes via nanoshell particle chains,” Opt. Commun. 279, 384–389 (2007).
[CrossRef]

Zhang, H.

Zhao, L.

L. Zhao, K. Kelly, and G. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. 107, 7343–7350 (2003).
[CrossRef]

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

Zia, R.

R. Zia, J. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: The next chip-scale technology,” Mater. Today 9, 20–27 (2006).
[CrossRef]

Ziolkowski, R. W.

Adv. Mater. (1)

S. Maier, M. Brongersma, P. Kik, S. Meltzer, A. Requicha, and H. Atwater, “Plasmonics: A route to nanoscale optical devices,” Adv. Mater. 13, 2 (2001).
[CrossRef]

Appl. Phys. Lett. (4)

J. Khurgin and G. Sun, “In search of the elusive lossless metal,” Appl. Phys. Lett. 96, 181102 (2010).
[CrossRef]

P. Holmström, L. Thylén, and A. Bratkovsky, “Composite metal/quantum-dot nanoparticle-array waveguides with compensated loss,” Appl. Phys. Lett. 97, 073110 (2010).
[CrossRef]

N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. 85, 5040–5042 (2004).
[CrossRef]

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

IEEE J. Sel. Top. Quantum Electron. (1)

S. Maier, “Plasmonics: Metal nanostructures for subwavelength photonic devices,” IEEE J. Sel. Top. Quantum Electron. 12, 1214–1220 (2006).
[CrossRef]

IEEE Photonics J. (1)

A. Pannipitiya, I. D. Rukhlenko, and M. Premaratne, “Analytical modeling of efficient couples for plasmonic-slot-waveguide junctions,” IEEE Photonics J. 3, 220–233 (2011).
[CrossRef]

J. Appl. Phys. (2)

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long-range surface-plasmon-polariton waveguides,” J. Appl. Phys. 98, 043109 (2005).
[CrossRef]

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

J. Opt. Soc. Am. B (3)

J. Phys. Chem. (1)

L. Zhao, K. Kelly, and G. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. 107, 7343–7350 (2003).
[CrossRef]

J. Phys. Chem. B (1)

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

J. Phys. Condens. Matter (2)

C. Tserkezis, G. Gantzounis, and N. Stefanou, “Collective plasmonic modes in ordered assemblies of metallic nanoshells,” J. Phys. Condens. Matter 20, 075232 (2008).
[CrossRef]

G. Gantzounis, N. Stefanou, and V. Yannopapas, “Optical properties of a periodic monolayer of metallic nanospheres on a dielectric waveguide,” J. Phys. Condens. Matter 17, 1791 (2005).
[CrossRef]

Langmuir (1)

J. Chen, J. Benjamin, and Y. Xia, “One-dimensional nanostructures of metals: Large-scale synthesis and some potential applications,” Langmuir 23, 4120–4129 (2007).
[CrossRef] [PubMed]

Mater. Today (1)

R. Zia, J. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: The next chip-scale technology,” Mater. Today 9, 20–27 (2006).
[CrossRef]

Nano Lett. (2)

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

D. Citrin, “Plasmon polaritons in finite-length metal-nanoparticle chains: The role of chain length unravelled,” Nano Lett. 5, 985–989 (2005).
[CrossRef] [PubMed]

Nat. Photonics (2)

S. Lal, S. Link, and N. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

D. Gramotnev and S. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[CrossRef]

Nature (1)

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

Opt. Commun. (2)

S. Wang, J. Xiao, and K. Yu, “Tunable coupled plasmon modes via nanoshell particle chains,” Opt. Commun. 279, 384–389 (2007).
[CrossRef]

M. Guasoni and C. de Angelis, “Analytical approximations of the dispersion relation of a linear chain of metal nanoparticles,” Opt. Commun. 284, 1822–1827 (2011).
[CrossRef]

Opt. Express (7)

Opt. Lett. (3)

Philos. Trans. R. Soc. London, Ser. A (1)

J. Krenn and J. Weeber, “Surface plasmon polaritons in metal stripes and wires,” Philos. Trans. R. Soc. London, Ser. A 362, 739–756 (2004).
[CrossRef]

Phys. Rev. (1)

E. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539 (1969).
[CrossRef]

Phys. Rev. B (11)

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]

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]

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

J. Gérardy and M. Ausloos, “Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations. II. Optical properties of aggregated metal spheres,” Phys. Rev. B 25, 4204–4229 (1982).
[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, 16356 (2000).
[CrossRef]

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

A. Govyadinov and V. 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. V. Fedorov, A. V. Baranov, I. D. Rukhlenko, and S. V. Gaponenko, “Enhanced intraband carrier relaxation in quantum dots due to the effect of plasmon–LO-phonon density of states in doped heterostructures,” Phys. Rev. B 71, 195310 (2005).

V. Markel and A. Sarychev, “Propagation of surface plasmons in ordered and disordered chains of metal nanospheres,” Phys. Rev. B 75, 085426 (2007).
[CrossRef]

K. Huang, E. Lidorikis, X. Jiang, J. Joannopoulos, K. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Phys. Rev. B 69, 195111 (2004).

Phys. Rev. Lett. (2)

A. Wokaun, J. Gordon, and P. Liao, “Radiation damping in surface-enhanced Raman scattering,” Phys. Rev. Lett. 48, 957–960 (1982).
[CrossRef]

M. I. Stockman, “Criterion for negative refraction with low optical losses from a fundamental principle of causality,” Phys. Rev. Lett. 98, 177404 (2007).
[CrossRef]

Phys. Today (1)

M. I. Stockman, “Nanoplasmonics: The physics behind the applications,” Phys. Today 64, 39–44 (2011).
[CrossRef]

Other (3)

C. F. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

L. Lewin, Dilogarithms and Associated Functions (McDonald, 1958).

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Figures (6)

Fig. 1
Fig. 1

Schematic of a composite spherically symmetric metallic nanoparticle (left) made of a dielectric core coated with metal. Composite particle can be effectively represented by a nanosphere with a permittivity ɛnp (right).

Fig. 2
Fig. 2

Dispersion relations for (a) L-polarized and (b) T-polarized SPPs for three chains of lossless nanospheres (x = 0) with different intersphere separations d. Frequency and wave number are shown in normalized units of 2πc/σ and 2π/σ for σ = 3R. Permittivity of metal is given by the Drude function ɛ m = ɛ ( 1 ω p 2 / ω 2 + i γ ω p 2 / ω 3 ), ɛ = 5, ωp = 0.26, and γ = 0; ɛ h = n h 2 and nh = 1.5. Modified dispersion curve when metal has a small loss (γ = 0.01ωp) is shown by open circles for d = 4σ/3. Brillouin zone edges for different systems are shown by vertical dashed lines; bandwidths of SPP modes are marked by shaded regions. Dashed in black is the light line in host medium.

Fig. 3
Fig. 3

(a) Exact solution (solid lines) and approximate solution (open circles) of SPP propagation length for a chain of nanospheres with x = 0 and d = σ. (b) Propagation length as a function of d for excitation frequency ω0; validity of the coupled-dipole approximation breaks for dσ, which is shown as the shaded region. Small Ohmic losses are assumed (γ = 0.01ωp) and the other material parameters are same as in Fig. 2.

Fig. 4
Fig. 4

(a) Dispersion of L-polarized SPP modes for different ratios of core and shell radii and (b) gain required to compensate for damping in the relevant transmission bands (shaded). Solid curves correspond to gain residing in the host medium (κc = 0, κh > 0), while dashed curves illustrate the case in which gain is supplied by the core dielectric (κc > 0, κh = 0). Other material parameters are same as in Fig. 2.

Fig. 5
Fig. 5

Same as Fig. 4 but for T-polarized SPPs. Inset shows the magnified profile of the low-frequency mode for x = 0.8.

Fig. 6
Fig. 6

Transmission of a two-segment waveguide constructed of 80 nanospheres (x = 0, d = σ, nh = 1.5, and κh = 0.01) as a function of angle θ between the segments. Waveguide is excited by continuous-wave sources polarized in the (a) x, (b) y, and (c) z directions. Frequencies of the x- and y-polarized sources are ω = 0.168 and ω = 0.158, respectively; they correspond to the frequencies of L- and T-polarized SPPs considered in Section 3. The frequencies of z-polarized sources are 0.152 and 0.158.

Equations (17)

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α 1 = α 0 1 2 i q 3 / 3 q 2 / R ,
F S d 3 α 1 = 0 ,
F | k 0 + Δ k , ɛ c , ɛ m , ɛ h ( F + Δ k k F + i ɛ c ɛ c F + i ɛ m ɛ m F + i ɛ h ɛ h F ) | k 0 , ɛ c , ɛ m , ɛ h ,
Δ k i d 3 ɛ c ɛ c α + ɛ m ɛ m α + ɛ h [ ɛ h α + ( α 2 / d 3 ) ɛ h S ] α 2 k S | k 0 , ɛ c , ɛ m , ɛ h ,
ɛ c α α 2 = 27 ɛ m 2 ɛ h ( 1 v ) ( ɛ m ɛ a ɛ h ɛ b ) 2 R 3 , ɛ m α α 2 = 3 ɛ h v ( ɛ c ɛ a + 2 ɛ m ɛ b ) ( ɛ m ɛ a ɛ h ɛ b ) 2 R 3 ,
ɛ h α α 2 = ɛ m ɛ h ɛ m α α 2 ɛ c ɛ h ɛ c α α 2 + q 2 ɛ h R + i q 3 ɛ h .
ɛ h S d 3 = q 2 ɛ h d Φ 1 , k S = 2 i d ( Ψ 2 iqd Ψ 1 ) ,
ɛ h S d 3 = q 2 2 ɛ h d ( Φ 1 + iqd Φ 0 ) , k S = id [ ( qd ) 2 Ψ 0 + iqd Ψ 1 Ψ 2 ] ,
κ c = ɛ m 2 n c ɛ m α ɛ c α | k 0 , ɛ c , ɛ m , ɛ h .
κ h = ɛ m 2 n h ɛ m α ɛ h α + ( α 2 / d 3 ) [ Re ɛ h S + Im ɛ h S ( Im k S / Re k S ) ] | k 0 , ɛ c , ɛ m , ɛ h .
p ( np ) = Inv [ NN ( np ) ] Ns ( ext ) p ( ext ) ,
E n = E ns ( ext ) + m n N E nm ,
α 1 p n = f ( r ns ) r ^ ns ( p s r ^ ns ) + g ( r ns ) p s + m n N f ( r nm ) r ^ nm ( p m r ^ nm ) + g ( r nm ) p m ,
p ( np ) = Inv [ NN ( np ) ] Ns ( ext ) p ( ext ) ,
A 11 δ nm α 1 Δ nm S nm ( 1 ) , A 22 = δ nm α 1 Δ nm S nm ( 2 ) , A 33 = δ nm α 1 Δ nm S nm ( 3 ) , A 12 = A 21 = Δ nm S nm ( 4 ) , A 13 = A 31 = Δ nm S nm ( 5 ) , A 23 = A 32 = Δ nm S nm ( 6 ) ,
S nm ( 1 ) = f ( r nm ) ( r ^ nm x ^ ) 2 + g ( r nm ) , S nm ( 2 ) = f ( r nm ) ( r ^ nm y ^ ) 2 + g ( r nm ) , S nm ( 3 ) = f ( r nm ) ( r ^ nm z ^ ) 2 + g ( r nm ) , S nm ( 4 ) = f ( r nm ) ( r ^ nm x ^ ) 2 ( r ^ nm y ^ ) , S nm ( 5 ) = f ( r nm ) ( r ^ nm x ^ ) 2 ( r ^ nm z ^ ) , S nm ( 6 ) = f ( r nm ) ( r ^ nm y ^ ) 2 ( r ^ nm z ^ ) ,
B 11 = S m s ( 1 ) , B 22 = S ms ( 2 ) , B 33 = S ms ( 3 ) , B 12 = B 21 = S ms ( 4 ) , B 13 = B 31 = S ms ( 5 ) , B 23 = B 32 = S ms ( 6 ) .

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