Abstract

The dispersion relations of surface plasmon wave (SPW) propagating along a convex or concave metal-dielectric interface with a radius of curvature are studied by solving the root of a characteristic equation in terms of Bessel and Hankel functions of complex order numerically. For the convex geometry, a metallic circular cylinder embedded in a dielectric host is modeled, whereas for the concave one, a dielectric cylinder in a metallic host is modeled. We found that the phase velocity of SPW along a convex interface is always less than that of SPW along a planar one. On the contrary, the phase velocity of a concave case is faster than that of a planar one. For both cases, the attenuation constants are larger than a planar one, due to the radial radiation of the energy into the surrounding medium, except the dissipation in the metal.

© 2008 Optical Society of America

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References

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  1. B. E. Sernelius, Surface Modes in Physics (Wiley-Vch, 2001).
    [CrossRef]
  2. R. H. Ritchie, "Plasma losses by fast electrons in thin films," Phys. Rev. 106, 874-881 (1957).
    [CrossRef]
  3. K. Hasegawa, J. U. Nockel, and M. Deutsch, "Surface plasmon polariton propagation around bends at a metal-dielectric interface," Appl. Phys. Lett. 84, 1835-1837 (2004).
    [CrossRef]
  4. K. Hasegawa, J. U. Nockel, and M. Deutsch, "Curvature-induced radiation of surface plasmon polaritons propagating around bends," Phys. Rev. A 75, 063816 (2007).
    [CrossRef]
  5. Z. Sun, "Vertical dielectric-sandwiched thin metal layer for compact, low-loss long range surface plasmon waveguiding," Appl. Phys. Lett. 91, 111112 (2007).
    [CrossRef]
  6. P. Berini and J. Lu, "Curved long-range surface plasmon-polariton waveguides," Opt. Express 14, 2365-2371 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. J.-W. Liaw, "Simulation of surface plasmon resonance of metallic nanoparticles by boundary-element method," J. Opt. Soc. Am. A 23, 108-116 (2006).
    [CrossRef]
  9. A. Viktorov, Rayleigh and Lamb Waves (Plenum, New York, 1967).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2007 (2)

K. Hasegawa, J. U. Nockel, and M. Deutsch, "Curvature-induced radiation of surface plasmon polaritons propagating around bends," Phys. Rev. A 75, 063816 (2007).
[CrossRef]

Z. Sun, "Vertical dielectric-sandwiched thin metal layer for compact, low-loss long range surface plasmon waveguiding," Appl. Phys. Lett. 91, 111112 (2007).
[CrossRef]

2006 (5)

2004 (1)

K. Hasegawa, J. U. Nockel, and M. Deutsch, "Surface plasmon polariton propagation around bends at a metal-dielectric interface," Appl. Phys. Lett. 84, 1835-1837 (2004).
[CrossRef]

1972 (1)

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

1957 (1)

R. H. Ritchie, "Plasma losses by fast electrons in thin films," Phys. Rev. 106, 874-881 (1957).
[CrossRef]

Berini, P.

Christy, R. W.

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

Deutsch, M.

K. Hasegawa, J. U. Nockel, and M. Deutsch, "Curvature-induced radiation of surface plasmon polaritons propagating around bends," Phys. Rev. A 75, 063816 (2007).
[CrossRef]

K. Hasegawa, J. U. Nockel, and M. Deutsch, "Surface plasmon polariton propagation around bends at a metal-dielectric interface," Appl. Phys. Lett. 84, 1835-1837 (2004).
[CrossRef]

Hasegawa, K.

K. Hasegawa, J. U. Nockel, and M. Deutsch, "Curvature-induced radiation of surface plasmon polaritons propagating around bends," Phys. Rev. A 75, 063816 (2007).
[CrossRef]

K. Hasegawa, J. U. Nockel, and M. Deutsch, "Surface plasmon polariton propagation around bends at a metal-dielectric interface," Appl. Phys. Lett. 84, 1835-1837 (2004).
[CrossRef]

Johnson, B.

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

Jung, W.-J.

Kim, W.-K.

Lee, H.-M.

Lee, H.-Y.

Lee, M.-H.

Levesque, L.

Liaw, J.-W.

Lu, J.

Nockel, J. U.

K. Hasegawa, J. U. Nockel, and M. Deutsch, "Curvature-induced radiation of surface plasmon polaritons propagating around bends," Phys. Rev. A 75, 063816 (2007).
[CrossRef]

K. Hasegawa, J. U. Nockel, and M. Deutsch, "Surface plasmon polariton propagation around bends at a metal-dielectric interface," Appl. Phys. Lett. 84, 1835-1837 (2004).
[CrossRef]

Ritchie, R. H.

R. H. Ritchie, "Plasma losses by fast electrons in thin films," Phys. Rev. 106, 874-881 (1957).
[CrossRef]

Rochon, P. L.

Sun, Z.

Z. Sun, "Vertical dielectric-sandwiched thin metal layer for compact, low-loss long range surface plasmon waveguiding," Appl. Phys. Lett. 91, 111112 (2007).
[CrossRef]

Wang, B.

B. Wang and G. P. Wang, "Plasmonic waveguide ring resonator at terahertz frequencies," Appl. Phys. Lett. 89, 133106 (2006).
[CrossRef]

Wang, G. P.

B. Wang and G. P. Wang, "Plasmonic waveguide ring resonator at terahertz frequencies," Appl. Phys. Lett. 89, 133106 (2006).
[CrossRef]

Yang, W.-S.

Appl. Phys. Lett. (3)

K. Hasegawa, J. U. Nockel, and M. Deutsch, "Surface plasmon polariton propagation around bends at a metal-dielectric interface," Appl. Phys. Lett. 84, 1835-1837 (2004).
[CrossRef]

Z. Sun, "Vertical dielectric-sandwiched thin metal layer for compact, low-loss long range surface plasmon waveguiding," Appl. Phys. Lett. 91, 111112 (2007).
[CrossRef]

B. Wang and G. P. Wang, "Plasmonic waveguide ring resonator at terahertz frequencies," Appl. Phys. Lett. 89, 133106 (2006).
[CrossRef]

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

Opt. Express (3)

Phys. Rev. (1)

R. H. Ritchie, "Plasma losses by fast electrons in thin films," Phys. Rev. 106, 874-881 (1957).
[CrossRef]

Phys. Rev. A (1)

K. Hasegawa, J. U. Nockel, and M. Deutsch, "Curvature-induced radiation of surface plasmon polaritons propagating around bends," Phys. Rev. A 75, 063816 (2007).
[CrossRef]

Phys. Rev. B (1)

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

Other (2)

B. E. Sernelius, Surface Modes in Physics (Wiley-Vch, 2001).
[CrossRef]

A. Viktorov, Rayleigh and Lamb Waves (Plenum, New York, 1967).

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Figures (6)

Fig. 1.
Fig. 1.

The configurations of SPW propagating along (a) a convex and (b) a concave metal-dielectric interfaces with radius of curvature a.

Fig. 2.
Fig. 2.

The distribution of the absolute value of the residue in the first quadrant of the order p.

Fig. 3.
Fig. 3.

The curves of (a) the relative wavenumber α vs. frequency, and (b) the relative attenuation constant β vs. frequency of SPW at Ag-air interface of different radii a (200, 400, 1000 nm), where the solid points: convex, and the void points: concave.

Fig. 4.
Fig. 4.

The curves of (a) the relative wavenumber α vs. radius a, and (b) the relative attenuation constant β vs. radius a of SPW at Ag-air interface for different frequencies (2.13, 2.63, 3 eV), where the solid points: convex, and the void points: concave.

Fig. 5.
Fig. 5.

The curves of (a) the relative wavenumber α, and (b) the relative attenuation constant β vs. the relative permittivity of the dielectric medium for different radii a (200, 400, and 1000 nm) at 2.63 eV, where the solid points: convex, and the void points: concave.

Fig. 6.
Fig. 6.

(a). The distribution of the magnetic field at t=5T/64. (b) The distribution of the absolute of the electric field at t=13T/64 of Ag cylinder of a=400nm irradiated by a plane wave at 2.88eV. All the values are normalized with the amplitudes of the incident fields.

Equations (5)

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k sp = ω c ε 1 ε 2 ε 1 + ε 2
z 2 J p ( z 2 ) H p ( 1 ) ( z 1 ) [ z 1 J p ( z 2 ) H p ( 1 ) ( z 1 ) ] 1 = 0
α = Re ( p / a ) / Re ( k s p ) ,
β = Im ( p / a ) / Im ( k s p ) ,
g ( x , t ) = Re ( G ( x ) · e i ω t ) , 0 t < T

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