Abstract

We investigate the optical gradient force in 2D hybrid and plasmonic waveguides. By comparing with conventional dielectric waveguides, we show that the optical force can be enhanced by at least 1 order of magnitude in the hybrid and plasmonic waveguides due to strongly enhanced optical fields at the waveguide surfaces. We compare coupled plasmonic waveguides with different geometries, including rectangular, circular, and triangular cross sections and find that the rectangular waveguides provide the strongest force. We also show that the plasmonic enhancement is nonresonant and thus can be used for a broad range of wavelengths.

© 2010 Optical Society of America

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    [CrossRef]
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2010

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

2009

2008

Z. P. Li, M. Kall, and H. Xu, Phys. Rev. B 77, 085412 (2008).
[CrossRef]

V. Yannopapas, Phys. Rev. B 78, 045412 (2008).
[CrossRef]

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[CrossRef]

M. Li, W. H. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[CrossRef] [PubMed]

2007

R. Quidant, S. Zelenina, and M. Nieto-Vesperinas, Appl. Phys. A 89, 233 (2007).
[CrossRef]

2005

2004

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, Appl. Phys. Lett. 85, 1466 (2004).
[CrossRef]

2003

Arias-Gonzalez, J. R.

Baehr-Jones, T.

M. Li, W. H. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[CrossRef] [PubMed]

Barnard, E. S.

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

Bartal, G.

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, Plasmonic Nanoguides and Circuits (Pan Stanford Publishing, 2009).

Brongersma, M. L.

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

Cai, W.

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

Camacho, R.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, Nature 459, 550 (2009).
[CrossRef] [PubMed]

Capasso, F.

Chan, J.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, Nature 459, 550 (2009).
[CrossRef] [PubMed]

Eichenfield, M.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, Nature 459, 550 (2009).
[CrossRef] [PubMed]

Fan, S.

Fong, K. Y.

Hochberg, M.

M. Li, W. H. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[CrossRef] [PubMed]

Ibanescu, M.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Hamilton Printing Co., 1998).

Joannopoulos, J. D.

Johnson, S. G.

Jun, Y. C.

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

Kall, M.

Z. P. Li, M. Kall, and H. Xu, Phys. Rev. B 77, 085412 (2008).
[CrossRef]

Li, M.

M. Li, W. H. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).
[CrossRef]

M. Li, W. H. Pernice, and H. X. Tang, Nat. Nanotechnol. 4, 377 (2009).
[CrossRef] [PubMed]

W. H. Pernice, M. Li, K. Y. Fong, and H. X. Tang, Opt. Express 17, 16032 (2009).
[CrossRef] [PubMed]

M. Li, W. H. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[CrossRef] [PubMed]

Li, Z. P.

Z. P. Li, M. Kall, and H. Xu, Phys. Rev. B 77, 085412 (2008).
[CrossRef]

Liu, V.

Loncar, M.

Nieto-Vesperinas, M.

R. Quidant, S. Zelenina, and M. Nieto-Vesperinas, Appl. Phys. A 89, 233 (2007).
[CrossRef]

J. R. Arias-Gonzalez and M. Nieto-Vesperinas, J. Opt. Soc. Am. A 20, 1201 (2003).
[CrossRef]

Oulton, R. F.

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[CrossRef]

Painter, O.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, Nature 459, 550 (2009).
[CrossRef] [PubMed]

Pernice, W. H.

W. H. Pernice, M. Li, K. Y. Fong, and H. X. Tang, Opt. Express 17, 16032 (2009).
[CrossRef] [PubMed]

M. Li, W. H. Pernice, and H. X. Tang, Nat. Nanotechnol. 4, 377 (2009).
[CrossRef] [PubMed]

M. Li, W. H. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).
[CrossRef]

M. Li, W. H. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[CrossRef] [PubMed]

Pile, D. F. P.

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[CrossRef]

Povinelli, M.

Povinelli, M. L.

Quidant, R.

R. Quidant, S. Zelenina, and M. Nieto-Vesperinas, Appl. Phys. A 89, 233 (2007).
[CrossRef]

Schuller, J. A.

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

Smythe, E. J.

Tang, H. X.

M. Li, W. H. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).
[CrossRef]

M. Li, W. H. Pernice, and H. X. Tang, Nat. Nanotechnol. 4, 377 (2009).
[CrossRef] [PubMed]

W. H. Pernice, M. Li, K. Y. Fong, and H. X. Tang, Opt. Express 17, 16032 (2009).
[CrossRef] [PubMed]

M. Li, W. H. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[CrossRef] [PubMed]

Vahala, K. J.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, Nature 459, 550 (2009).
[CrossRef] [PubMed]

White, J. S.

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

Woolf, D.

Xiong, C.

M. Li, W. H. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[CrossRef] [PubMed]

Xu, H.

Z. P. Li, M. Kall, and H. Xu, Phys. Rev. B 77, 085412 (2008).
[CrossRef]

Yannopapas, V.

V. Yannopapas, Phys. Rev. B 78, 045412 (2008).
[CrossRef]

Zelenina, S.

R. Quidant, S. Zelenina, and M. Nieto-Vesperinas, Appl. Phys. A 89, 233 (2007).
[CrossRef]

Zhang, X.

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[CrossRef]

Zhu, L.

Appl. Phys. A

R. Quidant, S. Zelenina, and M. Nieto-Vesperinas, Appl. Phys. A 89, 233 (2007).
[CrossRef]

Appl. Phys. Lett.

M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, Appl. Phys. Lett. 85, 1466 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Nanotechnol.

M. Li, W. H. Pernice, and H. X. Tang, Nat. Nanotechnol. 4, 377 (2009).
[CrossRef] [PubMed]

Nat. Photonics

M. Li, W. H. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).
[CrossRef]

Nature

M. Li, W. H. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[CrossRef] [PubMed]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, Nature 459, 550 (2009).
[CrossRef] [PubMed]

Nature Mater.

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

New J. Phys.

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

Z. P. Li, M. Kall, and H. Xu, Phys. Rev. B 77, 085412 (2008).
[CrossRef]

V. Yannopapas, Phys. Rev. B 78, 045412 (2008).
[CrossRef]

Other

J. D. Jackson, Classical Electrodynamics (Hamilton Printing Co., 1998).

S. I. Bozhevolnyi, Plasmonic Nanoguides and Circuits (Pan Stanford Publishing, 2009).

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Figures (4)

Fig. 1
Fig. 1

(a) Silicon core/silica substrate-coupled dielectric waveguide. The width and depth of the silicon waveguides are 600 nm and 200 nm , respectively. (b) Silicon core/silver substrate coupled hybrid waveguide. (c) Coupled silicon waveguides. (d) Coupled rectangular silver waveguides. (e) Coupled circular silver waveguides. (f) Coupled triangular silver waveguides.

Fig. 2
Fig. 2

(a) Normalized electric field of the fundamental quasi-TE mode of a silicon core/silica substrate dielectric waveguide. (b) Force exerted on the silicon core as a function of the gap distance between the core and the substrate. (c) Normalized electric field of the hybrid quasi-TE mode. (d) Normalized electric field of the hybrid quasi-TM mode. (e) Forces in the hybrid plasmonic waveguide.

Fig. 3
Fig. 3

(a) E x component of the fundamental even mode. (b) E x component of the fundamental odd mode. (c) The forces generated by the modes in (a) and (b). (d)–(f) E z component of the odd supermode in (d) the coupled rectangular, (e) circular, and (f) triangular silver waveguides. (g) The forces generated by the modes in (d) to (f).

Fig. 4
Fig. 4

(a) Enhancement of optical forces in rectangular plasmonic waveguides with the gap of 10 nm at different wavelengths. (b) Enhancement of optical forces and loss in rectangular plasmonic waveguides at different gap sizes.

Equations (1)

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F = ( T n ̂ ) d A = L { ϵ 2 Re [ ( E n ̂ ) E * ] ϵ 4 ( E E * ) n ̂ + μ 2 Re [ ( H n ̂ ) H * ] μ 4 ( H H * ) n ̂ } d l ,

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