Abstract

We report a numerical study of plasmonic waveguides that localize light in two dimensions at a cross section of 4.2nm×2.1nm with the propagation length of 38 μm. By varying the geometrical parameters, strong mode confinements (range from λ2/3352 to λ2/2557525) are achieved with controllable propagation distance (44.68–40.988 μm), and mode size below 1nm2 has been demonstrated for the first time. Furthermore, a cross-index-modulation mechanism is proposed to explain the strong field localization behavior, providing guidelines for future waveguide designs.

© 2012 Optical Society of America

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2011

2010

M. Chamanzar, M. Soltani, B. Mi, S. Yegnanarayanan, and A. Adibi, Appl. Phys. B 101, 263 (2010).
[CrossRef]

Z. Han, A. Y. Elezzabi, and V. Van, Opt. Lett. 35, 502 (2010).
[CrossRef]

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Jun, J. S. White, and M. S. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

H. Benisty and M. Besbes, J. Appl. Phys. 108, 063108 (2010).
[CrossRef]

2009

2008

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

2006

2005

G. Veromis and S. H. Fan, Opt. Lett. 30, 3359 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

Adibi, A.

M. Chamanzar, M. Soltani, B. Mi, S. Yegnanarayanan, and A. Adibi, Appl. Phys. B 101, 263 (2010).
[CrossRef]

Bajestani, S. M. R. Z.

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Jun, J. S. White, and M. S. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Bartal, G.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

Benisty, H.

H. Benisty and M. Besbes, J. Appl. Phys. 108, 063108 (2010).
[CrossRef]

Besbes, M.

H. Benisty and M. Besbes, J. Appl. Phys. 108, 063108 (2010).
[CrossRef]

Bozhevolnyi, S. I.

Brongersma, M. S.

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Jun, J. S. White, and M. S. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Cai, W. S.

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Jun, J. S. White, and M. S. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Chamanzar, M.

M. Chamanzar, M. Soltani, B. Mi, S. Yegnanarayanan, and A. Adibi, Appl. Phys. B 101, 263 (2010).
[CrossRef]

Citrin, D. S.

Dai, D.

Elezzabi, A. Y.

Fan, S. H.

Fukui, M.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

Garcia-Vidal, F. 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]

Gramotnev, D. K.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

Han, Z.

Haraguchi, M.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

He, S.

Jun, Y. C.

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Jun, J. S. White, and M. S. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Maier, S. A.

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

Martin-Moreno, L.

Matsuo, S.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

Mi, B.

M. Chamanzar, M. Soltani, B. Mi, S. Yegnanarayanan, and A. Adibi, Appl. Phys. B 101, 263 (2010).
[CrossRef]

Moreno, E.

Nerkararyan, K. V.

Ogawa, T.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, 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, Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

Oulton, R. F.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

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]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

Rodrigo, S. G.

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Jun, J. S. White, and M. S. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Shahabadi, M.

Shi, Y.

Soltani, M.

M. Chamanzar, M. Soltani, B. Mi, S. Yegnanarayanan, and A. Adibi, Appl. Phys. B 101, 263 (2010).
[CrossRef]

Sorger, V. J.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

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

Talebi, N.

Thylen, L.

Van, V.

Veromis, G.

Wang, Y.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

White, J. S.

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Jun, J. S. White, and M. S. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Wosinski, L.

Ye, Z.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

Yegnanarayanan, S.

M. Chamanzar, M. Soltani, B. Mi, S. Yegnanarayanan, and A. Adibi, Appl. Phys. B 101, 263 (2010).
[CrossRef]

Yin, X.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

Zhang, X.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

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

Appl. Phys. B

M. Chamanzar, M. Soltani, B. Mi, S. Yegnanarayanan, and A. Adibi, Appl. Phys. B 101, 263 (2010).
[CrossRef]

Appl. Phys. Lett.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

J. Appl. Phys.

H. Benisty and M. Besbes, J. Appl. Phys. 108, 063108 (2010).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Commun.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

Nat. Mater.

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Jun, J. S. White, and M. S. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Nat. Photon.

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

Opt. Express

Opt. Lett.

Other

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

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Figures (4)

Fig. 1.
Fig. 1.

(a) The silicon cylindrical nanowire with radius R=100nm and permittivity 12.25 is parallel to a silver substrate over a nanometer scale distance d=2nm. The silver substrate consists of a convex rib waveguide located on the metallic surface but below the waveguide core, in the center of the gap. The convex metallic rib and the metallic substrate have the permittivity 129+3.3i at the wavelength λ=1550nm. The waveguide is in the air background. (b)–(e) Normalized electrical field distribution in the xy cross section plane for (b) ax=0nm, ay=0nm; (c) ax=30nm, ay=2nm; (d) ax=2nm, ay=2nm. (e) Normalized electrical field distribution for ax=2nm, ay=2nm in a three-dimensional form whose height expresses the intensity of the field.

Fig. 2.
Fig. 2.

(a) Comparison of normalized energy density distribution along the cutting line at Y=d/2 (dashed curve in inset picture) under different ax values, assuming ay is fixed at 2 nm and d is constant at 2 nm. (b) Red square line, propagation length; green circle line, effective mode index; blue triangular line, effective mode area for diverse ax values.

Fig. 3.
Fig. 3.

(a) Comparison of normalized energy density distributions along the cutting line at X=0 (dashed line in inset picture) under different ay values, assuming gap size d is constant at 2 nm and ax is fixed at 2 nm. (b) Red square line, propagation length; green circle line, effective mode index; blue triangular line, effective mode area for diverse ax values.

Fig. 4.
Fig. 4.

Electric field distribution and directions. (a) Electric field polarized in the X direction; we artificially add points A, B, C, D, E, F to identify metallic–dielectric surfaces. (b) Electric field polarized in the Y direction. The white arrows indicate the directions of electric fields.

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