Abstract

A nano-scaled coupled-line coupler based on the guidance of surface plasmon-polaritons (SPPs) is proposed, designed and simulated at optical frequencies. The coupler comprises layered dielectric materials and silver, which serve as two stacked nano-transmission lines to achieve broadside coupling. The key property of this coupler is that it operates based on the principle of contra-directional coupling between a forward and a backward wave giving rise to supermodes that are characterized by complex-conjugate eigenvalues (even when the materials are assumed lossless). The resulting exponential attenuation along the coupler leads to dramatically reduced coupling lengths compared to previously reported co-directional SPP couplers (e.g. from millimeters to submicrons). The effect of material losses and finite coupler width are also analyzed.

© 2006 Optical Society of America

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References

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  1. J. Takahara and T. Kobayashi, "From subwavelength optics to nano-optics," Opt. Photonics News 15,54-59 (2004).
    [CrossRef]
  2. G. Shvets, "Photonic approach to making a material with a negative index of refraction," Phys. Rev. B 67, 035109 (2003).
    [CrossRef]
  3. E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182,539-554 (1969).
    [CrossRef]
  4. A. Alu and N. Engheta, "Optical nanotransmission lines: synthesis of planar left-handed metamaterials in the infrared and visible regimes," J. Opt. Soc. Am. B 23,571-583 (2006).
    [CrossRef]
  5. 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]
  6. G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, "Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Trans. Microwave Theory Tech.. 50,2702-2712 (2002).
    [CrossRef]
  7. R. Islam, F. Elek, and G. V. Eleftheriades, "A coupled-line metamaterial coupler having co-directional phase but contra-directional power flow," IEE Electron. Lett. 40,315-317 (2004).
    [CrossRef]
  8. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, "Integrated optical components utilizing long-range surface plasmon polaritons," J. Lightwave Technol. 23,413-422 (2005).
    [CrossRef]
  9. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, "Demonstration of integrated optics elements based on long-range surface plasmon polaritons," Opt. Express 13,977-984 (2005).
    [CrossRef] [PubMed]
  10. R. Islam and G. V. Eleftheriades, "Printed high-directivity metamaterial MS/NRI coupled-line coupler for signal monitoring applications," IEEE Microwave Wirel. Compon. Lett. 16,164-166 (2006).
    [CrossRef]
  11. E. T. Arakawa, M. W. Williams, R. N. Hamm, and R. H. Ritchie. "Effect of damping on surface plasmon dispersion," Phys. Rev. Lett. 31,1127-1129 (1973).
    [CrossRef]
  12. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6,4370-4379 (1972).
    [CrossRef]

2006 (2)

R. Islam and G. V. Eleftheriades, "Printed high-directivity metamaterial MS/NRI coupled-line coupler for signal monitoring applications," IEEE Microwave Wirel. Compon. Lett. 16,164-166 (2006).
[CrossRef]

A. Alu and N. Engheta, "Optical nanotransmission lines: synthesis of planar left-handed metamaterials in the infrared and visible regimes," J. Opt. Soc. Am. B 23,571-583 (2006).
[CrossRef]

2005 (2)

2004 (2)

J. Takahara and T. Kobayashi, "From subwavelength optics to nano-optics," Opt. Photonics News 15,54-59 (2004).
[CrossRef]

R. Islam, F. Elek, and G. V. Eleftheriades, "A coupled-line metamaterial coupler having co-directional phase but contra-directional power flow," IEE Electron. Lett. 40,315-317 (2004).
[CrossRef]

2003 (1)

G. Shvets, "Photonic approach to making a material with a negative index of refraction," Phys. Rev. B 67, 035109 (2003).
[CrossRef]

2002 (1)

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, "Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Trans. Microwave Theory Tech.. 50,2702-2712 (2002).
[CrossRef]

2000 (1)

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]

1973 (1)

E. T. Arakawa, M. W. Williams, R. N. Hamm, and R. H. Ritchie. "Effect of damping on surface plasmon dispersion," Phys. Rev. Lett. 31,1127-1129 (1973).
[CrossRef]

1972 (1)

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

1969 (1)

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182,539-554 (1969).
[CrossRef]

Alu, A.

Arakawa, E. T.

E. T. Arakawa, M. W. Williams, R. N. Hamm, and R. H. Ritchie. "Effect of damping on surface plasmon dispersion," Phys. Rev. Lett. 31,1127-1129 (1973).
[CrossRef]

Berini, P.

R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, "Demonstration of integrated optics elements based on long-range surface plasmon polaritons," Opt. Express 13,977-984 (2005).
[CrossRef] [PubMed]

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]

Boltasseva, A.

Bozhevolnyi, S. I.

Charbonneau, R.

Christy, R. W.

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

Economou, E. N.

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182,539-554 (1969).
[CrossRef]

Eleftheriades, G. V.

R. Islam and G. V. Eleftheriades, "Printed high-directivity metamaterial MS/NRI coupled-line coupler for signal monitoring applications," IEEE Microwave Wirel. Compon. Lett. 16,164-166 (2006).
[CrossRef]

R. Islam, F. Elek, and G. V. Eleftheriades, "A coupled-line metamaterial coupler having co-directional phase but contra-directional power flow," IEE Electron. Lett. 40,315-317 (2004).
[CrossRef]

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, "Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Trans. Microwave Theory Tech.. 50,2702-2712 (2002).
[CrossRef]

Elek, F.

R. Islam, F. Elek, and G. V. Eleftheriades, "A coupled-line metamaterial coupler having co-directional phase but contra-directional power flow," IEE Electron. Lett. 40,315-317 (2004).
[CrossRef]

Engheta, N.

Hamm, R. N.

E. T. Arakawa, M. W. Williams, R. N. Hamm, and R. H. Ritchie. "Effect of damping on surface plasmon dispersion," Phys. Rev. Lett. 31,1127-1129 (1973).
[CrossRef]

Islam, R.

R. Islam and G. V. Eleftheriades, "Printed high-directivity metamaterial MS/NRI coupled-line coupler for signal monitoring applications," IEEE Microwave Wirel. Compon. Lett. 16,164-166 (2006).
[CrossRef]

R. Islam, F. Elek, and G. V. Eleftheriades, "A coupled-line metamaterial coupler having co-directional phase but contra-directional power flow," IEE Electron. Lett. 40,315-317 (2004).
[CrossRef]

Iyer, A. K.

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, "Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Trans. Microwave Theory Tech.. 50,2702-2712 (2002).
[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]

Kjaer, K.

Kobayashi, T.

J. Takahara and T. Kobayashi, "From subwavelength optics to nano-optics," Opt. Photonics News 15,54-59 (2004).
[CrossRef]

Kremer, P. C.

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, "Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Trans. Microwave Theory Tech.. 50,2702-2712 (2002).
[CrossRef]

Lahoud, N.

Larsen, M. S.

Leosson, K.

Mattiussi, G.

Nikolajsen, T.

Ritchie, R. H.

E. T. Arakawa, M. W. Williams, R. N. Hamm, and R. H. Ritchie. "Effect of damping on surface plasmon dispersion," Phys. Rev. Lett. 31,1127-1129 (1973).
[CrossRef]

Shvets, G.

G. Shvets, "Photonic approach to making a material with a negative index of refraction," Phys. Rev. B 67, 035109 (2003).
[CrossRef]

Takahara, J.

J. Takahara and T. Kobayashi, "From subwavelength optics to nano-optics," Opt. Photonics News 15,54-59 (2004).
[CrossRef]

Williams, M. W.

E. T. Arakawa, M. W. Williams, R. N. Hamm, and R. H. Ritchie. "Effect of damping on surface plasmon dispersion," Phys. Rev. Lett. 31,1127-1129 (1973).
[CrossRef]

IEE Electron. Lett. (1)

R. Islam, F. Elek, and G. V. Eleftheriades, "A coupled-line metamaterial coupler having co-directional phase but contra-directional power flow," IEE Electron. Lett. 40,315-317 (2004).
[CrossRef]

IEEE Microwave Wirel. Compon. Lett. (1)

R. Islam and G. V. Eleftheriades, "Printed high-directivity metamaterial MS/NRI coupled-line coupler for signal monitoring applications," IEEE Microwave Wirel. Compon. Lett. 16,164-166 (2006).
[CrossRef]

IEEE Trans. Microwave Theory Tech.. (1)

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, "Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Trans. Microwave Theory Tech.. 50,2702-2712 (2002).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Express (1)

Opt. Photonics News (1)

J. Takahara and T. Kobayashi, "From subwavelength optics to nano-optics," Opt. Photonics News 15,54-59 (2004).
[CrossRef]

Phys. Rev. (1)

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182,539-554 (1969).
[CrossRef]

Phys. Rev. B (3)

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]

G. Shvets, "Photonic approach to making a material with a negative index of refraction," Phys. Rev. B 67, 035109 (2003).
[CrossRef]

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

Phys. Rev. Lett. (1)

E. T. Arakawa, M. W. Williams, R. N. Hamm, and R. H. Ritchie. "Effect of damping on surface plasmon dispersion," Phys. Rev. Lett. 31,1127-1129 (1973).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Geometry and possible materials for the contra-directional SPP coupler featuring the stacked ND-film and ND-gap topology. (The arrows represent the power flow.)

Fig. 2.
Fig. 2.

Dispersion diagrams (The relative electric permittivity of the dielectric media are: εair = 1,εsilica-glass = 2.09,εglass = 4.2,εsilicon = 12.1. The ND-film guides BW even modes and the ND-gap guides FW even modes.)

Fig. 3.
Fig. 3.

Dispersion diagram using the lossless Drude model of silver

Fig. 4.
Fig. 4.

Coupled eigenmodes at the center frequency of the stopband (ω/ωp = 0.487)

Fig. 5.
Fig. 5.

Power flow along the 1μm coupler assuming the metal is lossless (Note: the power scale shown in the figure is normalized with respect to the incident power)

Fig. 6.
Fig. 6.

S-parameter analysis for 1μm coupler assuming the metal is lossless

Fig. 7.
Fig. 7.

Dispersion diagram using the lossy Drude model of silver

Fig. 8.
Fig. 8.

Power flow along 1 μm coupler assuming the metal loss in Eq. (8) (Note: the power scale shown in the figure is normalized with respect to the incident power)

Fig. 9.
Fig. 9.

S-parameter analysis for 1μm coupler assuming the metal loss in Eq. (8)

Fig. 10.
Fig. 10.

Dispersion diagram of the coupled modes near the stopband with finite width

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

ε m ( ω ) = 1 ω p 2 ω 2
H x 1 = A e k y , d y e j β z
H x 2 = ( B e k y , m y + C e k y , m y ) e j β z
H x 3 = D e k y , d y e j β z
E z = 1 j ω ε H x y
k y , d h ε d = k y , m h ε m tanh ( k y , m h 2 )
k y , d h ε d = k y , m h ε m coth ( k y , m h 2 )
β 2 k y , d 2 = ε 0 ε d k 0 2
β 2 k y , m 2 = ε 0 ε m k 0 2
H x 1 = A e k y 1 y e j β z
H x 2 = ( B e k y 2 y + C e k y 2 y ) e j β z
H x 3 = ( D e k y 3 y + F e k y 3 y ) e j β z
H x 4 = ( G e k y 4 y + H e k y 4 y ) e j β z
H x 5 = ( K e k y 5 y + L e k y 5 y ) e j β z
H x 6 = M e k y 6 y e j β z
ε m ( ω ) = 1 ω p 2 ω 2 j ω τ

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