Abstract

Optical phenomena supported by ordered and disordered chains of metal nano-particles on a metal surface are investigated by considering a particular example of gold nano-bumps on a gold surface. The TWs supported by these structures are analyzed by studying the frequency-wavenumber spectra of the fields excited by localized sources placed near the chain. Periodic nano-bump chains support traveling waves (TWs) that propagate without radiation loss along, and are confined to the region near, the chain. These TWs are slow waves with respect to both space fields and surface plasmon polaritons supported by the metal surface. For nearly resonant nano-bumps, the TWs are well confined and can be excited efficiently by a localized source placed near the chain but the TW propagation length is short. For non-resonant nano-bumps, the TWs have large propagation lengths but are not well confined and are excited less efficiently. The TWs supported by nano-bump chains were shown to have larger propagation lengths than free-standing chains of the same dimension/size and cross-sectional confinement. TWs also are supported by disordered chains and chains with sharp bends. Perturbations in nano-bump positions are shown to reduce the TW propagation length much less significantly than perturbations in their sizes. Transmission through sharp chain bends is much stronger for nearly resonant nano-bumps than for nonresonant ones. In addition to their ability to support TWs, nano-bump chains can be used to manipulate (excite/reflect/refract) SPPs on the metal surface.

© 2007 Optical Society of America

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References

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  1. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (J. Wiley New York, 1983).
  2. J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, and A. Leitner, "Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles," Phys. Rev. Lett. 82, 2590-2593 (1999).
    [CrossRef]
  3. M. Quinten, A. Leitner, R. Krenn, and F. R. Aussenegg, "Electromagnetic energy transport via linear chains of silver nanoparticles," Opt. Lett. 23, 1331-1333 (1998).
    [CrossRef]
  4. 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]
  5. S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990-3992 (2004).
    [CrossRef]
  6. S. A. Maier and H. A. Atwater, "Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 11101-11101 (2005).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  24. V. Lomakin, N. W. Chen, S. Q. Li, and E. Michielssen, "Enhanced transmission through two-period arrays of sub-wavelength holes," IEEE Microwave Wirel. Compon. Lett. 14, 355-357 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
  27. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, MA, 1995).
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    [CrossRef]
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2007 (1)

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

2006 (3)

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]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

J. M. Steele, Z. Liu, Y. Wang, and X. Zhang, "Resonant and non-resonant generation and focusing of surface plasmons with circular gratings," Opt. Express 14, 5664-5670 (2006).
[CrossRef] [PubMed]

2005 (5)

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing surface plasmons with a plasmonic lens," Nano Lett. 5, 1726 -1729 (2005).
[CrossRef] [PubMed]

H. L. Offerhaus, B. E. van den Bergen, M., F. B. Segerink, J. P. Korterik, and N. F. van Hulst, "Creating Focused Plasmons by Noncollinear Phasematching on Functional Gratings," Nano Lett. 5, 2144-2148 (2005).
[CrossRef] [PubMed]

S. A. Maier and H. A. Atwater, "Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 11101-11101 (2005).
[CrossRef]

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

R. A. Shore and A. D. Yaghjian, "Travelling electromagnetic waves on linear periodic arrays of lossless spheres," Electron. Lett. 41, 578-580 (2005).
[CrossRef]

2004 (5)

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]

I. A. Larkin, M. I. Stockman, M. Achermann, and V. I. Klimov, "Dipolar emitters at nanoscale proximity of metal surfaces: Giant enhancement of relaxation in microscopic theory," Phys. Rev. B 69, 121403 (2004).
[CrossRef]

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990-3992 (2004).
[CrossRef]

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, "Babinet principle applied in the design of metasurfaces and metamaterials," Phys. Rev. Lett. 93, 197401 (2004).
[CrossRef] [PubMed]

V. Lomakin, N. W. Chen, S. Q. Li, and E. Michielssen, "Enhanced transmission through two-period arrays of sub-wavelength holes," IEEE Microwave Wirel. Compon. Lett. 14, 355-357 (2004).
[CrossRef]

2002 (2)

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762-1764 (2002).
[CrossRef]

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

2001 (2)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K.M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole array," Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008 (2001).
[CrossRef] [PubMed]

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, 16356-16359 (2000).
[CrossRef]

1999 (1)

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

1998 (2)

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

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, "Surface plasmons enhance optical transmission through subwavelength holes," Phys. Rev. B 58, 6779-6782 (1998).
[CrossRef]

Appl. Phys. Lett. (3)

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

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990-3992 (2004).
[CrossRef]

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762-1764 (2002).
[CrossRef]

Electron. Lett. (1)

R. A. Shore and A. D. Yaghjian, "Travelling electromagnetic waves on linear periodic arrays of lossless spheres," Electron. Lett. 41, 578-580 (2005).
[CrossRef]

IEEE Microwave Wirel. Compon. Lett. (1)

V. Lomakin, N. W. Chen, S. Q. Li, and E. Michielssen, "Enhanced transmission through two-period arrays of sub-wavelength holes," IEEE Microwave Wirel. Compon. Lett. 14, 355-357 (2004).
[CrossRef]

J. Appl. Phys. (1)

S. A. Maier and H. A. Atwater, "Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 11101-11101 (2005).
[CrossRef]

Nano Lett. (2)

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing surface plasmons with a plasmonic lens," Nano Lett. 5, 1726 -1729 (2005).
[CrossRef] [PubMed]

H. L. Offerhaus, B. E. van den Bergen, M., F. B. Segerink, J. P. Korterik, and N. F. van Hulst, "Creating Focused Plasmons by Noncollinear Phasematching on Functional Gratings," Nano Lett. 5, 2144-2148 (2005).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Phys Rev. E (1)

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

Phys. Rev. B (6)

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]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, "Surface plasmons enhance optical transmission through subwavelength holes," Phys. Rev. B 58, 6779-6782 (1998).
[CrossRef]

I. A. Larkin, M. I. Stockman, M. Achermann, and V. I. Klimov, "Dipolar emitters at nanoscale proximity of metal surfaces: Giant enhancement of relaxation in microscopic theory," Phys. Rev. B 69, 121403 (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, 16356-16359 (2000).
[CrossRef]

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

Phys. Rev. Lett. (4)

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, "Babinet principle applied in the design of metasurfaces and metamaterials," Phys. Rev. Lett. 93, 197401 (2004).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K.M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole array," Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008 (2001).
[CrossRef] [PubMed]

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

Science (1)

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Other (6)

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, MA, 1995).

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (IEEE Press, Piscataway NJ, 1994).
[CrossRef]

A. Alù and N. Engheta, "On Role of Random Disorders and Imperfections on Performance of Metamaterials," presented at the 2007 IEEE Antennas and Propagation Society International Symposium, Honolulu, Hawaii, 2007.

V. Lomakin, "Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched in between dielectric slabs," Phys. Rev. B 71, 235117 (235111-235110) (2005).
[CrossRef]

R. E. Collin and F. J. Zucker, Antenna theory, Part Two (McGraw-Hill, New York, 1969).

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

Supplementary Material (5)

» Media 1: AVI (1483 KB)     
» Media 2: AVI (959 KB)     
» Media 3: AVI (955 KB)     
» Media 4: AVI (929 KB)     
» Media 5: AVI (2253 KB)     

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Figures (12)

Fig. 1.
Fig. 1.

Nano-chains on a metal surface. The line l 1 represents the field along the chain, and the line c 1 represent the field in the chain’s cross-section.

Fig. 2.
Fig. 2.

Electric field normalized frequency response of isolated metal nano-bumps as shown in the insert. The vertical axis is defined as normalized to the maximum magnitude of the time Fourier transforms of the electric field at (100 nm,50 nm,r=100 nm) and exciting current at r 0=(-8µm,50 nm,50 nm). The nano-bumps have a square cross-section of size w×w with w=100nm in the x-y plane and three heights h. The normalized frequency response is defined as the normalized to the maximal value magnitude of the ratio between the time Fourier transforms of the electric field and exciting current.

Fig. 3.
Fig. 3.

Time evolution of the electric field supported by a straight chain of nano-bumps in Fig. 1(b). The chain comprises N=160 of gold nano-bumps of width and height w=h=100 nm with periodicity Λ=200 nm. The excitation dipole resides at (16µm,10µm,150nm), i.e. it is far from the chain. The field is computed at the plane z=150nm. [Media 1]

Fig. 4.
Fig. 4.

Time evolution of the electric field supported by a straight nano-bump chain. The chain’s parameters are as in Fig. 3 (i.e. N=160, w=h=100 nm, and Λ=200 nm). The excitation dipole resides at (-200nm, 0,150 nm), i.e. near the left edge of the chain. The field is computed at the plane z=150nm. [Media 2]

Fig. 5.
Fig. 5.

Wave guiding characteristics of a straight nano-nano-bump chain with parameters in Fig. 3 (i.e., N=160, w=h=100 nm, and Λ=200 nm) excited by a dipole at (-200nm, 0,150 nm). (a) Electric field frequency response in the transversal chain cross-section along the line c 1 in Fig. 1 that resides at x=16 µm, z=150 nm ; (b) Electric field frequency response along the line l1 in Fig. 1 that resides at y=0,z=150nm ; (c) Electric field frequency response at the points (10 µm,0, 2h), (18 µm,0,2h), and (26 µm,0,2h) on the line l 1. The frequency response is defined as the magnitude of the ratio between the time Fourier transforms of the electric field and exciting current.

Fig. 6.
Fig. 6.

Space-time Fourier transform |E D | along the chain in Fig. 1(b) excited by a transient dipole with parameters in Fig. 2 residing at (-200nm, 0,150 nm). The chain parameters are as in Fig. 3 (i.e. N=160, w=h=100 nm, and Λ=200 nm). The blue line is the dispersion curve of the SPP supported by the metal surface.

Fig. 7.
Fig. 7.

Comparison between nano-bump chains and free-standing chains of nano-cubes. The two chain types have identical size, excited by an identical source, and the field is calculated along the same line as in Fig. 5. (a). Normalized frequency response in the transversal chain cross-section; (b). Frequency response along the chain. The wavelengths are chosen to render nearly identical cross-sectional decay rate [Fig. 7(a)]. The normalized frequency response is defined as normalized to the maximal value magnitude of the ratio between the time Fourier transforms of the electric field and exciting current.

Fig. 8.
Fig. 8.

Time evolution of the electric field supported by periodic chains of nano-bumps when the excitation dipole with parameters in Fig. 2 resides at (-200nm, 0,150 nm). The parameters of the nano-bumps are as in Fig. 3 and the scale is identical to that in Fig. 4. The field is computed at the plane z=150nm. (a) Disorder in displacement with χL =0.25 [Media 3] and (b) disorder in height with χh =0.25 [Media 4].

Fig. 9.
Fig. 9.

Electric field normalized frequency response along the line l 1 in Figs. 1(b) and 5 for chains excited by a dipole with parameters in Fig. 2 residing at (-200nm, 0,150 nm) with disorder in (a) displacement, (b) height, and (c) width for different randomness parameters and wavelengths. The frequency response is defined as the magnitude of the ratio between the time Fourier transforms of the electric field and exciting current.

Fig. 10.
Fig. 10.

Spectral field|E D | along the chain in Fig. 1(b) excited by the dipole with parameters in Fig. 2 residing at (-200nm, 0,150 nm). (a) disorder in displacement with χL =0.25 and (b) height χL =0.25.

Fig. 11.
Fig. 11.

Chain of nano-bumps with a 90° bend. The chain consists of two identical sections, each having N=75 nano-bumps arranged periodically. The chain parameters are identical to those chosen in Figs. 57.

Fig. 12.
Fig. 12.

(a). Time evolution of the electric field supported by the chain in Fig. 11 for the field computed on the plane 150z=nm (the scale is identical to that in Fig. 4.) [Media 5]; (b) Electric field frequency response along the line l2 in Fig. 11. The normalized frequency response is defined as normalized to the maximal value magnitude of the ratio between the time Fourier transforms of the electric field and exciting current.

Equations (4)

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E TW ( ω , r ) = Ψ ( ρ yz , φ yz ) exp ( ( k TW 2 ( ω c ) 2 ) 1 2 ρ yz ) exp ( ± i k TW x ) ,
E ̂ ( ω , k x ) = dt dx E ( t , x ) e i ( ω t k x x ) .
E ̂ ( ω , k x ) E ̂ cs ( a 1 k x k TW ( ω ) + a 2 k x + k TW ( ω ) )
E ̂ D ( ω , k x ) = w ( x ) E ( t , x ) e i ( ω t k x x ) dtdx ,

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