Abstract

The ability to control light over very small distances is a problem of fundamental importance for a vast range of applications in communications, nanophotonics, and quantum information technologies. For this purpose, several methods have been proposed and demonstrated to confine and guide light, for example in dielectric and surface plasmon polariton (SPP) waveguides. Here, we study the interaction between different kinds of planar waveguides, which produces dramatic changes in the dispersion relation of the waveguide pair and even leads to mode suppression at small separations. This interaction also produces a transfer of power between the waveguides, which depends on the gap and propagation distances, thus providing a mechanism for optical signal transfer. We analytically study the properties of this interaction and the power transfer in different structures of interest including plasmonic and particle-array waveguides, for which we propose an experimental realization of these ideas.

© 2012 OSA

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  1. S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater “Plasmonics—a route to nanoscale optical devices,” Adv. Mater. 13, 1501 (2001).
    [CrossRef]
  2. D. MarcuseTheory of Dielectric Optical Waveguides (Academic, 1974).
  3. H. Raether, Surface Plasmons (Springer-Verlag, 1988).
  4. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61, 10484–10503 (2000).
    [CrossRef]
  5. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of asymmetric structures,” Phys. Rev. B 63, 125417 (2001).
    [CrossRef]
  6. X. M. Bendana and F. J. Garcia de Abajo, “Confined collective excitations of self-standing and supported planar periodic particle arrays,” Opt. Express 17, 18826–18835 (2009).
    [CrossRef]
  7. T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61, 44 (2008).
    [CrossRef]
  8. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics”, Nature (London) 424, 824–830 (2003).
    [CrossRef]
  9. 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]
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    [CrossRef]
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    [CrossRef]
  12. E. Verhagen, M. Spasenovic, A. Polman, and L. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102, 203904 (2009).
    [CrossRef] [PubMed]
  13. J. D. Jackson, Classical Electrodynamics (Wiley, 1999).
  14. E. D. PalikHandbook of Optical Constants and Solids (Academic, 1985).
  15. M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1970).
  16. P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
    [CrossRef]
  17. A. Manjavacas and F. J. Garcia de Abajo, “Robust plasmon waveguides in strongly interacting nanowire arrays,” Nano Lett. 9, 1285–1289 (2009).
    [CrossRef]
  18. Z. Chen, T. Holmgaard, S. I. Bozhevolnyi, A. V. Krasavin, A. V. Zayats, L. Markey, and A. Dereux, “Wavelength-selective directional coupling with dielectric-loaded plasmonic waveguides,” Opt. Lett. 34, 310–312 (2009).
    [CrossRef] [PubMed]
  19. A. V. Krasavin and A. V. Zayats, “Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett. 90, 211101 (2007).
    [CrossRef]

2009 (4)

X. M. Bendana and F. J. Garcia de Abajo, “Confined collective excitations of self-standing and supported planar periodic particle arrays,” Opt. Express 17, 18826–18835 (2009).
[CrossRef]

E. Verhagen, M. Spasenovic, A. Polman, and L. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

A. Manjavacas and F. J. Garcia de Abajo, “Robust plasmon waveguides in strongly interacting nanowire arrays,” Nano Lett. 9, 1285–1289 (2009).
[CrossRef]

Z. Chen, T. Holmgaard, S. I. Bozhevolnyi, A. V. Krasavin, A. V. Zayats, L. Markey, and A. Dereux, “Wavelength-selective directional coupling with dielectric-loaded plasmonic waveguides,” Opt. Lett. 34, 310–312 (2009).
[CrossRef] [PubMed]

2008 (1)

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61, 44 (2008).
[CrossRef]

2007 (1)

A. V. Krasavin and A. V. Zayats, “Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett. 90, 211101 (2007).
[CrossRef]

2004 (1)

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[CrossRef]

2003 (1)

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

2001 (2)

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater “Plasmonics—a route to nanoscale optical devices,” Adv. Mater. 13, 1501 (2001).
[CrossRef]

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of asymmetric structures,” Phys. Rev. B 63, 125417 (2001).
[CrossRef]

2000 (2)

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61, 10484–10503 (2000).
[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]

1999 (1)

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751 (1999).
[CrossRef]

1998 (1)

Atwater, H. A.

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater “Plasmonics—a route to nanoscale optical devices,” Adv. Mater. 13, 1501 (2001).
[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]

Aussenegg, F. R.

Barnes, W. L.

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

Bendana, X. M.

Berini, P.

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of asymmetric structures,” Phys. Rev. B 63, 125417 (2001).
[CrossRef]

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61, 10484–10503 (2000).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1970).

Bozhevolnyi, S. I.

Brongersma, M. L.

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater “Plasmonics—a route to nanoscale optical devices,” Adv. Mater. 13, 1501 (2001).
[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]

Chen, Z.

Dereux, A.

Ebbesen, T. W.

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61, 44 (2008).
[CrossRef]

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

Fan, S.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Garcia de Abajo, F. J.

X. M. Bendana and F. J. Garcia de Abajo, “Confined collective excitations of self-standing and supported planar periodic particle arrays,” Opt. Express 17, 18826–18835 (2009).
[CrossRef]

A. Manjavacas and F. J. Garcia de Abajo, “Robust plasmon waveguides in strongly interacting nanowire arrays,” Nano Lett. 9, 1285–1289 (2009).
[CrossRef]

Genet, C.

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61, 44 (2008).
[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, 16356–16359 (2000).
[CrossRef]

Holmgaard, T.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

Joannopoulos, J. D.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Johnson, S. G.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Kik, P. G.

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater “Plasmonics—a route to nanoscale optical devices,” Adv. Mater. 13, 1501 (2001).
[CrossRef]

Kolodziejski, L. A.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Krasavin, A. V.

Z. Chen, T. Holmgaard, S. I. Bozhevolnyi, A. V. Krasavin, A. V. Zayats, L. Markey, and A. Dereux, “Wavelength-selective directional coupling with dielectric-loaded plasmonic waveguides,” Opt. Lett. 34, 310–312 (2009).
[CrossRef] [PubMed]

A. V. Krasavin and A. V. Zayats, “Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett. 90, 211101 (2007).
[CrossRef]

Krenn, J. R.

Kuipers, L.

E. Verhagen, M. Spasenovic, A. Polman, and L. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

Leitner, A.

Li, K.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[CrossRef]

Maier, S. A.

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater “Plasmonics—a route to nanoscale optical devices,” Adv. Mater. 13, 1501 (2001).
[CrossRef]

Manjavacas, A.

A. Manjavacas and F. J. Garcia de Abajo, “Robust plasmon waveguides in strongly interacting nanowire arrays,” Nano Lett. 9, 1285–1289 (2009).
[CrossRef]

Marcuse, D.

D. MarcuseTheory of Dielectric Optical Waveguides (Academic, 1974).

Markey, L.

Meltzer, S.

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater “Plasmonics—a route to nanoscale optical devices,” Adv. Mater. 13, 1501 (2001).
[CrossRef]

Nordlander, P.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[CrossRef]

Oubre, C.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[CrossRef]

Palik, E. D.

E. D. PalikHandbook of Optical Constants and Solids (Academic, 1985).

Polman, A.

E. Verhagen, M. Spasenovic, A. Polman, and L. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

Prodan, E.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[CrossRef]

Quinten, M.

Raether, H.

H. Raether, Surface Plasmons (Springer-Verlag, 1988).

Requicha, A. A. G.

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater “Plasmonics—a route to nanoscale optical devices,” Adv. Mater. 13, 1501 (2001).
[CrossRef]

Spasenovic, M.

E. Verhagen, M. Spasenovic, A. Polman, and L. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

Stockman, M. I.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[CrossRef]

Verhagen, E.

E. Verhagen, M. Spasenovic, A. Polman, and L. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

Villeneuve, P. R.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1970).

Zayats, A. V.

Z. Chen, T. Holmgaard, S. I. Bozhevolnyi, A. V. Krasavin, A. V. Zayats, L. Markey, and A. Dereux, “Wavelength-selective directional coupling with dielectric-loaded plasmonic waveguides,” Opt. Lett. 34, 310–312 (2009).
[CrossRef] [PubMed]

A. V. Krasavin and A. V. Zayats, “Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett. 90, 211101 (2007).
[CrossRef]

Adv. Mater. (1)

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater “Plasmonics—a route to nanoscale optical devices,” Adv. Mater. 13, 1501 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

A. V. Krasavin and A. V. Zayats, “Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett. 90, 211101 (2007).
[CrossRef]

Nano Lett. (2)

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[CrossRef]

A. Manjavacas and F. J. Garcia de Abajo, “Robust plasmon waveguides in strongly interacting nanowire arrays,” Nano Lett. 9, 1285–1289 (2009).
[CrossRef]

Nature (London) (1)

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

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (4)

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751 (1999).
[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]

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61, 10484–10503 (2000).
[CrossRef]

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of asymmetric structures,” Phys. Rev. B 63, 125417 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

E. Verhagen, M. Spasenovic, A. Polman, and L. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

Phys. Today (1)

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61, 44 (2008).
[CrossRef]

Other (5)

D. MarcuseTheory of Dielectric Optical Waveguides (Academic, 1974).

H. Raether, Surface Plasmons (Springer-Verlag, 1988).

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

E. D. PalikHandbook of Optical Constants and Solids (Academic, 1985).

M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1970).

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Figures (3)

Fig. 1
Fig. 1

(a–c) Schematic view and dispersion relations for different planar waveguide structures. The guided mode dispersion relations are shown in red in these frequency-momentum plots. (a) Planar array of dielectric particles. The light cone and the diffracted light line are shown as black lines. (b) Dielectric slab. Straight lines show the light cones in vacuum (black) and in the dielectric medium (green). (c) SPP supporting metal-dielectric interface. Straight lines indicate the light cone (solid line) and the electrostatic surface-plasmon frequency (dashed line). (d–f) Interaction between different combinations of confining structures placed at varying distance d. A similar behavior is observed in all cases, with a strong repulsion between modes at small distances. (d) Two planar arrays of silicon (εSi = 12) spheres of radii 200nm and R2 175nm, respectively, embedded in silica (εSiO2 = 2) and arranged in square lattices of period 1μm. The light wavelength is λ = 4μm. (e) Planar array of silicon spheres of radius 200nm arrange in a square lattice of period 1μm placed near a dielectric slab of thickness 70nm and permittivity ε = 6. (f) Slot waveguide consisting of a silver-air-silver structure [14] illuminated with λ = 1550nm light.

Fig. 2
Fig. 2

(a) SPP energy transfer between neighboring silver cylinders. A SPP is assumed to be excited at line A (e.g., by external illumination over a grating parallel to the left cylinder), so that it propagates along the surface polar direction, as shown by arrows. As the SPP reaches the gap between both wires, their interaction produces power transfer to the right cylinder. (b) Left: Power transfer under the configuration of (a) as a function of cylinder radius R for a gap distance d = 3μm. Right: power transfer as a function of gap distance d for cylinder radius R = 200μm. Black dots display the line A where the modes are excited.

Fig. 3
Fig. 3

(a) Transferred power at the exit of the system described in Fig. 2(a) as a function of cylinder gap distance d and radius R for a wavelength of 1550nm. (b) Same as (a) for particle arrays (square lattice of period 1μm, particle radius 200nm, and wavelength 4μm) arranged in a cylindrical geometry, as shown in the inset. (c) Normalized power in each guide i, Pi, along the interaction length for a configuration of two silver cylinders with radius R = 400μm and separation d = 2μm (see yellow point in (a)).

Equations (3)

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1 r 1 σ r 2 σ exp ( 2 κ z d ) = 0 ,
c 1 ( x ) = c s ( x ) + c a ( x ) 2 , c 2 ( x ) = c s ( x ) c a ( x ) 2 ,
P 1 ( x ) cos 2 ( x 0 x d x Δ k || ( d ( x ) ) / 2 ) , P 2 ( x ) sin 2 ( x 0 x d x Δ k || ( d ( x ) ) / 2 ) ,

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