Abstract

A three-dimensional method for obtaining the bending losses and field distributions of bent surface plamon-polariton waveguides is presented. The method is based on a so called ‘method of line’, which discretises potential in the direction of the metal-widths, and leads to Airy-equations in the radial direction. From the results obtained. It is confirmed that thiner metal waveguide enable longer-ranging propagation of surface plasmon-polariton mode, but the weakened confinement requires larger bending radii on order to keep radiation loss.

© 2006 Optical Society of America

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References

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  1. P. Berini, "Plasmon-polariton wave guided by thin lossy metal films of finite width:bounded modes of symmetric structures," Phys. Rev. B 61, 484-503 (2000).
    [CrossRef]
  2. T. Nikolajsen, etc., "Polymer-based surface plasmon-polariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668-670 (2003).
    [CrossRef]
  3. R. Charbonneau, etc., "Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons," Opt. Express 13, 977-984 (2005).
    [CrossRef] [PubMed]
  4. R. Charbonneau, etc., "Experimental observation of plasmon-polariton waves supported by a thin metal film of finite width," Opt. Lett. 25, 844-846 (2000).
    [CrossRef]
  5. P. Berini, "Curved long-range surface plasmon-polariton waveguides," Opt. Express 14, 2365-2371 (2006).
    [CrossRef] [PubMed]
  6. H. Diestel, "A method for calculating the guided modes of strip-loaded optical waveguides with arbitrary index profile," IEEE J. Quantum Electron. 20, 1288-1292 (1984).
    [CrossRef]
  7. I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: A new method of anaysis," IEEE J. Lightwave Technol. 8, 768-774 (1990).
    [CrossRef]

2006 (1)

2005 (1)

2003 (1)

T. Nikolajsen, etc., "Polymer-based surface plasmon-polariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668-670 (2003).
[CrossRef]

2000 (2)

P. Berini, "Plasmon-polariton wave guided by thin lossy metal films of finite width:bounded modes of symmetric structures," Phys. Rev. B 61, 484-503 (2000).
[CrossRef]

R. Charbonneau, etc., "Experimental observation of plasmon-polariton waves supported by a thin metal film of finite width," Opt. Lett. 25, 844-846 (2000).
[CrossRef]

1990 (1)

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: A new method of anaysis," IEEE J. Lightwave Technol. 8, 768-774 (1990).
[CrossRef]

1984 (1)

H. Diestel, "A method for calculating the guided modes of strip-loaded optical waveguides with arbitrary index profile," IEEE J. Quantum Electron. 20, 1288-1292 (1984).
[CrossRef]

Berini, P.

P. Berini, "Curved long-range surface plasmon-polariton waveguides," Opt. Express 14, 2365-2371 (2006).
[CrossRef] [PubMed]

P. Berini, "Plasmon-polariton wave guided by thin lossy metal films of finite width:bounded modes of symmetric structures," Phys. Rev. B 61, 484-503 (2000).
[CrossRef]

Charbonneau, R.

Diestel, H.

H. Diestel, "A method for calculating the guided modes of strip-loaded optical waveguides with arbitrary index profile," IEEE J. Quantum Electron. 20, 1288-1292 (1984).
[CrossRef]

Gallawa, R. L.

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: A new method of anaysis," IEEE J. Lightwave Technol. 8, 768-774 (1990).
[CrossRef]

Ghatak, A. K.

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: A new method of anaysis," IEEE J. Lightwave Technol. 8, 768-774 (1990).
[CrossRef]

Goyal, I. C.

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: A new method of anaysis," IEEE J. Lightwave Technol. 8, 768-774 (1990).
[CrossRef]

Nikolajsen, T.

T. Nikolajsen, etc., "Polymer-based surface plasmon-polariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668-670 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

T. Nikolajsen, etc., "Polymer-based surface plasmon-polariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668-670 (2003).
[CrossRef]

IEEE J. Lightwave Technol. (1)

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: A new method of anaysis," IEEE J. Lightwave Technol. 8, 768-774 (1990).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. Diestel, "A method for calculating the guided modes of strip-loaded optical waveguides with arbitrary index profile," IEEE J. Quantum Electron. 20, 1288-1292 (1984).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

P. Berini, "Plasmon-polariton wave guided by thin lossy metal films of finite width:bounded modes of symmetric structures," Phys. Rev. B 61, 484-503 (2000).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Cross-section view of curved surface plasmon-polariton waveguides

Fig. 2.
Fig. 2.

Relative field distribution of ssb 0 mode(t=20nm, w=4µm, λ=1.3µm, n 1=1.535, n 2=0.3859-i7.965); (a) Contours of the |Er | for straight waveguide, (b) Contours of the |Er | for bent waveguide with r 0=5mm, (c) Field distribution along a vertical cut immediately above the metal film for r 0=5mm.

Fig. 3.
Fig. 3.

curvature radius r 0 versus propagation loss.

Fig. 4.
Fig. 4.

Excess loss versus curvature radius r 0.

Equations (13)

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E r ( r , ϕ , y ) = E r ( r , y ) exp ( j β R ϕ )
[ 2 r 2 + 1 r r + 2 y 2 + k 0 2 n 2 ( y ) R 2 β 2 r 2 ] E r ( r , y ) = 0
[ 2 r 2 + 2 y 2 + k 0 2 n 2 ( y ) R 2 r 2 ( β 2 + 1 4 R 2 ) ] ψ ( r , y ) = 0
R 2 ( R + x ) 2 1 2 x R
[ 2 r 2 + 2 y 2 + k 0 2 n 2 ( y ) ( 1 2 x R ) ( β 2 + 1 4 R 2 ) ] ψ ( x , y ) = 0
( 2 r 2 + [ D yy ] + k 0 2 [ n i 2 ] ( 1 2 x R ) ( β 2 + 1 4 R 2 ) ) { ψ i } = 0 , i = I , II , and III
[ D yy ] + k 0 2 [ n i 2 ] = [ T i ] [ Λ i ] [ T i ] 1
2 { U i } r 2 + ( [ Λ i ] ( 1 2 x R ) ( β 2 + 1 4 R 2 ) ) { U i } = 0
2 U i ( k ) Z i ( k ) 2 Z i ( k ) U i ( k ) = 0 ,
where Z i ( k ) = Λ i ( k ) + β 2 1 4 R 2 a x a 2 3 , a = 2 R ( β 2 1 4 R 2 )
U i ( k ) = { c 1 ( k ) Ai ( Z I ( k ) ) x 0 : inner cladding c 2 ( k ) A i ( Z II ( k ) ) + c 3 ( k ) B i ( Z II ( k ) ) 0 x t : core c 4 ( k ) A i ( Z III ( k ) e j 2 3 π ) x t : outer cladding
[ F ( β ) ] { U } = 0
det ( [ F ( β ) ] ) = [ 0 ]

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