Abstract

Optical plasmon-polariton modes confined in both transverse dimensions to significantly less than a wavelength are exhibited in open waveguides structured as sharp metal wedges. The analysis reveals two distinctive modes corresponding to a localized mode on the wedge point and surface mode propagation on the abruptly bent interface. These predictions are accompanied by unique field distributions and dispersion characteristics.

© 2006 Optical Society of America

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References

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  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (2003).
    [CrossRef] [PubMed]
  2. P. Berini, "Plasmon-polariton modes guided by a metal film of a finite width bounded by different dielectrics," Opt. Express 7, 329 (2000).
    [CrossRef] [PubMed]
  3. V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Phys. Mater. 11, 65 (2002).
    [CrossRef]
  4. L. Dobrzynski, and A. A. Maradudin, "Electrostatic edge modes in a Dielectric Wedge," Phys. Rev. B 6, 3810 (1972).
    [CrossRef]
  5. A. Eguiluz, and A. A. Maradudin, "Electrostatic edge modes along a parabolic wedge," Phys. Rev. B 14, 5526 (1976).
    [CrossRef]
  6. A. D. Boardman, R. Garcia-Molina, A. Gras-Marti, and E. Louis, "Electrostatic edge modes of a hyperbolic dielectric wedge: Analytical solution," Phys. Rev. B 32, 6045 (1985).
    [CrossRef]
  7. D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87,061106 (2005).
    [CrossRef]
  8. I. V. Novikov, and A. A. Maradudin, "Channel polaritons," Phys. Rev. B 66, 035403 (2002).
    [CrossRef]
  9. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
    [CrossRef] [PubMed]
  10. D. F. P. Pile, and D. K. Gramotnev, "Channel plasmon-polariton in a triangular groove on a metal surface," Opt. Lett. 29, 1069 (2004).
    [CrossRef] [PubMed]
  11. G. Z. Forristall and J. D. Ingram, "Evaluation of distributions useful in Kontorovich-Lebedev transform theory," SIAM J. Math. Anal. 3, 561 (1972).
    [CrossRef]
  12. B. Prade and J. Y. Vinet, "Guided optical waves in fibers with negative dielectric constant," J. Lightwave Technol. 12, 6 (1994).
    [CrossRef]
  13. H. Reather, Surface plasmon (Springer, Berlin, 1988).
  14. M. P. Nezhad, K. Tetz, and Y. Fainman, "Gain assisted propagation of surface plasmon polariton on planar metallic waveguides," Opt. Express 12, 4072 (2004).
    [CrossRef] [PubMed]

2005

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87,061106 (2005).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

2004

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (2003).
[CrossRef] [PubMed]

2002

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Phys. Mater. 11, 65 (2002).
[CrossRef]

I. V. Novikov, and A. A. Maradudin, "Channel polaritons," Phys. Rev. B 66, 035403 (2002).
[CrossRef]

2000

1994

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

1985

A. D. Boardman, R. Garcia-Molina, A. Gras-Marti, and E. Louis, "Electrostatic edge modes of a hyperbolic dielectric wedge: Analytical solution," Phys. Rev. B 32, 6045 (1985).
[CrossRef]

1976

A. Eguiluz, and A. A. Maradudin, "Electrostatic edge modes along a parabolic wedge," Phys. Rev. B 14, 5526 (1976).
[CrossRef]

1972

L. Dobrzynski, and A. A. Maradudin, "Electrostatic edge modes in a Dielectric Wedge," Phys. Rev. B 6, 3810 (1972).
[CrossRef]

G. Z. Forristall and J. D. Ingram, "Evaluation of distributions useful in Kontorovich-Lebedev transform theory," SIAM J. Math. Anal. 3, 561 (1972).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (2003).
[CrossRef] [PubMed]

Berini, P.

Boardman, A. D.

A. D. Boardman, R. Garcia-Molina, A. Gras-Marti, and E. Louis, "Electrostatic edge modes of a hyperbolic dielectric wedge: Analytical solution," Phys. Rev. B 32, 6045 (1985).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (2003).
[CrossRef] [PubMed]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

Dobrzynski, L.

L. Dobrzynski, and A. A. Maradudin, "Electrostatic edge modes in a Dielectric Wedge," Phys. Rev. B 6, 3810 (1972).
[CrossRef]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (2003).
[CrossRef] [PubMed]

Eguiluz, A.

A. Eguiluz, and A. A. Maradudin, "Electrostatic edge modes along a parabolic wedge," Phys. Rev. B 14, 5526 (1976).
[CrossRef]

Fainman, Y.

Forristall, G. Z.

G. Z. Forristall and J. D. Ingram, "Evaluation of distributions useful in Kontorovich-Lebedev transform theory," SIAM J. Math. Anal. 3, 561 (1972).
[CrossRef]

Fukui, M.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87,061106 (2005).
[CrossRef]

Garcia-Molina, R.

A. D. Boardman, R. Garcia-Molina, A. Gras-Marti, and E. Louis, "Electrostatic edge modes of a hyperbolic dielectric wedge: Analytical solution," Phys. Rev. B 32, 6045 (1985).
[CrossRef]

Gramotnev, D. K.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87,061106 (2005).
[CrossRef]

D. F. P. Pile, and D. K. Gramotnev, "Channel plasmon-polariton in a triangular groove on a metal surface," Opt. Lett. 29, 1069 (2004).
[CrossRef] [PubMed]

Gras-Marti, A.

A. D. Boardman, R. Garcia-Molina, A. Gras-Marti, and E. Louis, "Electrostatic edge modes of a hyperbolic dielectric wedge: Analytical solution," Phys. Rev. B 32, 6045 (1985).
[CrossRef]

Haraguchi, M.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87,061106 (2005).
[CrossRef]

Ingram, J. D.

G. Z. Forristall and J. D. Ingram, "Evaluation of distributions useful in Kontorovich-Lebedev transform theory," SIAM J. Math. Anal. 3, 561 (1972).
[CrossRef]

Louis, E.

A. D. Boardman, R. Garcia-Molina, A. Gras-Marti, and E. Louis, "Electrostatic edge modes of a hyperbolic dielectric wedge: Analytical solution," Phys. Rev. B 32, 6045 (1985).
[CrossRef]

Maradudin, A. A.

I. V. Novikov, and A. A. Maradudin, "Channel polaritons," Phys. Rev. B 66, 035403 (2002).
[CrossRef]

A. Eguiluz, and A. A. Maradudin, "Electrostatic edge modes along a parabolic wedge," Phys. Rev. B 14, 5526 (1976).
[CrossRef]

L. Dobrzynski, and A. A. Maradudin, "Electrostatic edge modes in a Dielectric Wedge," Phys. Rev. B 6, 3810 (1972).
[CrossRef]

Matsuo, S.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87,061106 (2005).
[CrossRef]

Nezhad, M. P.

Novikov, I. V.

I. V. Novikov, and A. A. Maradudin, "Channel polaritons," Phys. Rev. B 66, 035403 (2002).
[CrossRef]

Ogawa, T.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87,061106 (2005).
[CrossRef]

Okamoto, T.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87,061106 (2005).
[CrossRef]

Pile, D. F. P.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87,061106 (2005).
[CrossRef]

D. F. P. Pile, and D. K. Gramotnev, "Channel plasmon-polariton in a triangular groove on a metal surface," Opt. Lett. 29, 1069 (2004).
[CrossRef] [PubMed]

Podolskiy, V. A.

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Phys. Mater. 11, 65 (2002).
[CrossRef]

Prade, B.

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

Sarychev, A. K.

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Phys. Mater. 11, 65 (2002).
[CrossRef]

Shalaev, V. M.

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Phys. Mater. 11, 65 (2002).
[CrossRef]

Tetz, K.

Vinet, J. Y.

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

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett. 87,061106 (2005).
[CrossRef]

J. Lightwave Technol.

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

J. Nonlinear Phys. Mater.

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Phys. Mater. 11, 65 (2002).
[CrossRef]

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. B

I. V. Novikov, and A. A. Maradudin, "Channel polaritons," Phys. Rev. B 66, 035403 (2002).
[CrossRef]

L. Dobrzynski, and A. A. Maradudin, "Electrostatic edge modes in a Dielectric Wedge," Phys. Rev. B 6, 3810 (1972).
[CrossRef]

A. Eguiluz, and A. A. Maradudin, "Electrostatic edge modes along a parabolic wedge," Phys. Rev. B 14, 5526 (1976).
[CrossRef]

A. D. Boardman, R. Garcia-Molina, A. Gras-Marti, and E. Louis, "Electrostatic edge modes of a hyperbolic dielectric wedge: Analytical solution," Phys. Rev. B 32, 6045 (1985).
[CrossRef]

Phys. Rev. Lett.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

SIAM J. Math. Anal.

G. Z. Forristall and J. D. Ingram, "Evaluation of distributions useful in Kontorovich-Lebedev transform theory," SIAM J. Math. Anal. 3, 561 (1972).
[CrossRef]

Other

H. Reather, Surface plasmon (Springer, Berlin, 1988).

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Figures (5)

Fig. 1.
Fig. 1.

Metal wedge waveguide surrounded by air. (a) schematics (b) EeHo mode dispersion relations for 360 gold wedge.

Fig. 2.
Fig. 2.

Electric field components (absolute value, A.U.) at pt. I (β=6k0;ω=0.74ωp).

Fig. 3.
Fig. 3.

Electric field components (absolute value, A.U.) at pt. II (β=6k0;ω=0.69ωp).

Fig. 4.
Fig. 4.

Tangential Pointing vector (Sz) (absolute value, A.U.) at: (a) pt. II, (b) pt. I

Fig. 5.
Fig. 5.

Electric field components (absolute value, A.U.) at pt. III (β=8k0;ω=0.7ωp).

Equations (10)

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{ ( i ) E ˜ M = E ˜ D ( iii ) θ E ˜ M = f 1 θ E ˜ D f 2 r r H ˜ D ( ii ) H ˜ M = H ˜ D ( iv ) θ E ˜ M = f 3 r r E ˜ D f 4 θ H ˜ D
E z e = exp ( i β z ) { dv { a v K iv ( q M r ) cosh ( v ( θ α ) ) } θ [ 0 , 2 α ] dv { b v K iv ( q D r ) cosh ( v ( θ α π ) ) } θ [ 2 α , 2 π ]
v a v cosh ( v α ) G ( v , s ; q M q D ) = b s cosh ( s ( α + π ) ) π 2 2 s sinh ( π s )
v c v sinh ( v α ) G ( v , s ; q M q D ) = b s sinh ( s ( α + π ) ) π 2 2 s sinh ( π s )
v a v v sinh ( v α ) G ( v , s ; q M q D ) = f 1 b s sinh ( s ( α + π ) ) π 2 2 sinh ( π s ) f 2 v d v sinh ( v ( α + π ) H ( v , s )
v c v v cosh ( v α ) G ( v , s ; q M q D ) = f 3 v b v cosh ( v ( α + π ) ) H ( v , s ) + f 4 d s cosh ( s ( α + π ) ) π 2 2 sinh ( π s )
f 1 = ε D ε M q M 2 q D 2 ; f 2 = ω μ β ( ε M + ε D ) q D 2 ε M ; f 3 = ω ε 0 β ( ε M + ε D ) q D 2 ; f 4 = q M 2 q D 2 ;
G ( ξ 1 , ξ 2 ; τ ) = π 2 cos ( ξ 1 ln ( τ ) ) 2 ξ 1 sinh ( π ξ 1 ) δ ( ξ 1 ξ 2 ) + π 2 16 [ cosh ( π ξ 1 ) cosh ( π ξ 2 ) ] 1 g ( ξ 1 , ξ 2 ; τ )
g ( ξ 1 , ξ 2 ; τ ) = [ τ 2 1 ] τ i ξ 1 2 𝔽 1 ( 1 i ξ 1 + ξ 2 2 , 1 i ξ 1 ξ 2 2 ; 2 ; 1 τ 2 )
H ( ξ 1 , ξ 2 ) = π 2 2 [ cosh ( π ξ 1 ) cosh ( π ξ 2 ) ] 1 ; G ( ξ , ξ ; τ ) = 0 ; H ( ξ , ξ ) = 0 ;

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