Abstract

We propose the inclusion of a structured pattern of nanoscale metal wires in a silica fiber to form a symmetric plasmonic waveguide. The surface plasmon polariton modes within the waveguide are studied by varying the wire diameter and spacing. Simulation results show that hybridization of the single-wire mode and the gap plasmon mode can yield a hybrid mode with optimum propagation lengths comparable to those reported for other structures but with better light confinement. The fiber can be easily doped with a gain material to offset the loss so that the resultant waveguide will be useful for integration with electronic circuits at nanometer dimensions.

© 2010 Optical Society of America

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References

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2010 (2)

2009 (3)

A. Manjavacas and F. J. G. Abajo, Nano Lett. 9, 1285 (2009).
[CrossRef]

A. Manjavacas and F. J. G. Abajo, Opt. Express 17, 19401(2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

2008 (3)

J. Hou, D. Bird, A. George, S. Maier, B. T. Kuhlmey, and J. C. Knight, Opt. Express 16, 5983 (2008).
[CrossRef] [PubMed]

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and P. S. J. Russell, Appl. Phys. Lett. 93, 111102 (2008).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photon. 2, 496 (2008).
[CrossRef]

2005 (1)

2004 (1)

2003 (2)

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

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, Appl. Phys. Lett. 82, 668 (2003).
[CrossRef]

2000 (1)

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, Phys. Rev. B 62, R16356 (2000).
[CrossRef]

1999 (1)

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, Phys. Rev. B 60, 9061 (1999).
[CrossRef]

1997 (1)

1991 (1)

B. Prade, J. Y. Vinet, and A. Mysyrowicz, Phys. Rev. B 44, 13556 (1991).
[CrossRef]

1983 (1)

Abajo, F. J. G.

A. Manjavacas and F. J. G. Abajo, Opt. Express 17, 19401(2009).
[CrossRef] [PubMed]

A. Manjavacas and F. J. G. Abajo, Nano Lett. 9, 1285 (2009).
[CrossRef]

Alexander, R. W.

Atwater, H. A.

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, Phys. Rev. B 62, R16356 (2000).
[CrossRef]

Barnes, W. L.

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

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

Bell, R. J.

Bell, R. R.

Bell, S. E.

Bird, D.

Bozhevolnyi, S. I.

C. Marquart, S. I. Bozhevolnyi, and K. Leosson, Opt. Express 13, 3303 (2005).
[CrossRef] [PubMed]

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, Appl. Phys. Lett. 82, 668 (2003).
[CrossRef]

Brongersma, M. L.

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, Phys. Rev. B 62, R16356 (2000).
[CrossRef]

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

Dereux, A.

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

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, Phys. Rev. B 60, 9061 (1999).
[CrossRef]

Ebbesen, T. W.

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

Eggleton, B. J.

Genov, D. A.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photon. 2, 496 (2008).
[CrossRef]

George, A.

Girard, C.

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, Phys. Rev. B 60, 9061 (1999).
[CrossRef]

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

Goudonnet, J. P.

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, Phys. Rev. B 60, 9061 (1999).
[CrossRef]

Hartman, J. W.

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, Phys. Rev. B 62, R16356 (2000).
[CrossRef]

Hou, J.

Joly, N.

Knight, J. C.

Kobayashi, T.

Krasavin, A. V.

Krenn, J. R.

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, Phys. Rev. B 60, 9061 (1999).
[CrossRef]

Kuhlmey, B. T.

Lee, H. W.

H. K. Tyagi, H. W. Lee, P. Uebel, M. A. Schmidt, N. Joly, M. Scharrer, and P. St.J. Russell, Opt. Lett. 35, 2573 (2010).
[CrossRef] [PubMed]

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and P. S. J. Russell, Appl. Phys. Lett. 93, 111102 (2008).
[CrossRef]

Leosson, K.

C. Marquart, S. I. Bozhevolnyi, and K. Leosson, Opt. Express 13, 3303 (2005).
[CrossRef] [PubMed]

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, Appl. Phys. Lett. 82, 668 (2003).
[CrossRef]

Long, L. L.

Ma, R. M.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

Magi, E. C.

Maier, S.

Maier, S. A.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Manjavacas, A.

A. Manjavacas and F. J. G. Abajo, Opt. Express 17, 19401(2009).
[CrossRef] [PubMed]

A. Manjavacas and F. J. G. Abajo, Nano Lett. 9, 1285 (2009).
[CrossRef]

Marquart, C.

Morimoto, A.

Mysyrowicz, A.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, Phys. Rev. B 44, 13556 (1991).
[CrossRef]

Nikolajsen, T.

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, Appl. Phys. Lett. 82, 668 (2003).
[CrossRef]

Ordal, M. A.

Oulton, R. F.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photon. 2, 496 (2008).
[CrossRef]

Pile, D. F. P.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photon. 2, 496 (2008).
[CrossRef]

Prade, B.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, Phys. Rev. B 44, 13556 (1991).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1986).

H. Raether, Tracts in Modern Physics (Springer-Verlag, 1965), Vol. 38.

Russell, P. S. J.

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and P. S. J. Russell, Appl. Phys. Lett. 93, 111102 (2008).
[CrossRef]

Russell, P. St.J.

Salakhutdinov, I.

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, Appl. Phys. Lett. 82, 668 (2003).
[CrossRef]

Scharrer, M.

Schmidt, M. A.

H. K. Tyagi, H. W. Lee, P. Uebel, M. A. Schmidt, N. Joly, M. Scharrer, and P. St.J. Russell, Opt. Lett. 35, 2573 (2010).
[CrossRef] [PubMed]

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and P. S. J. Russell, Appl. Phys. Lett. 93, 111102 (2008).
[CrossRef]

Sempere, L. P.

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and P. S. J. Russell, Appl. Phys. Lett. 93, 111102 (2008).
[CrossRef]

Sorger, V. J.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photon. 2, 496 (2008).
[CrossRef]

Steinvurzel, P.

Takahara, J.

Taki, H.

Tyagi, H. K.

H. K. Tyagi, H. W. Lee, P. Uebel, M. A. Schmidt, N. Joly, M. Scharrer, and P. St.J. Russell, Opt. Lett. 35, 2573 (2010).
[CrossRef] [PubMed]

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and P. S. J. Russell, Appl. Phys. Lett. 93, 111102 (2008).
[CrossRef]

Uebel, P.

Vinet, J. Y.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, Phys. Rev. B 44, 13556 (1991).
[CrossRef]

Ward, C. A.

Weeber, J. C.

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, Phys. Rev. B 60, 9061 (1999).
[CrossRef]

Yamagishi, S.

Zayats, A. V.

Zentgraf, T.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

Zhang, X.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photon. 2, 496 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and P. S. J. Russell, Appl. Phys. Lett. 93, 111102 (2008).
[CrossRef]

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, Appl. Phys. Lett. 82, 668 (2003).
[CrossRef]

Nano Lett. (1)

A. Manjavacas and F. J. G. Abajo, Nano Lett. 9, 1285 (2009).
[CrossRef]

Nat. Photon. (1)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photon. 2, 496 (2008).
[CrossRef]

Nature (2)

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

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

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. B (3)

B. Prade, J. Y. Vinet, and A. Mysyrowicz, Phys. Rev. B 44, 13556 (1991).
[CrossRef]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, Phys. Rev. B 62, R16356 (2000).
[CrossRef]

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, Phys. Rev. B 60, 9061 (1999).
[CrossRef]

Other (3)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1986).

H. Raether, Tracts in Modern Physics (Springer-Verlag, 1965), Vol. 38.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

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Figures (3)

Fig. 1
Fig. 1

(a) 2D schematic of the waveguide cross section. The parameter s represents the separation between adjacent metal wires, and d represents the diameter of the metal wires. Calculated modal profiles are shown for (b) d = 40 , (c) 110, and (d) 160 nm . s = 200 nm . The white arrows in (b)–(d) represent the orientation of the electric field.

Fig. 2
Fig. 2

(a) Real and imaginary parts of the effective mode index versus the diameter of the metallic wire. Inset, FOM versus the diameter d. (b) Calculated propagation length versus the diameter of the metal wire for the separation s = 200 , 300, and 400 nm and the single wire.

Fig. 3
Fig. 3

Dispersion relations of the waveguide modes for d = 20 (wire modes, solid symbols), 130 (hybrid modes, half-filled symbols), and 195 nm (gap modes, open symbols). The gray region is the silica light cone.

Equations (6)

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Re [ n eff ] = β / k 0 ,
Im ( n eff ) = λ / [ 4 π L ] .
tanh [ k 2 ( 200 nm d ) / 2 ] = k 1 ε 2 k 2 ε 1 ,
tanh [ k 2 ( 200 nm d ) / 2 ] = k 2 ε 1 k 1 ε 2 ,
k i 2 = β 2 k 0 2 ε i , ( i = 1 , 2 ) ,
k 2 I 1 ( k 1 d / 2 ) K 0 ( k 2 d / 2 ) k 1 I 0 ( k 1 d / 2 ) K 1 ( k 2 d / 2 ) = ε 2 ε 1 ,

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