Abstract

We investigate the frequency dependence of the optical force between two coupled waveguides using the supermode theory. We show that the frequency dependence of the optical force in a coupled waveguide system is determined by the dispersion relations of uncoupled individual waveguides. We further numerically calculate the optical force of three representative coupled systems at different frequencies and show that these results agree well with the supermode analysis.

© 2009 Optical Society of America

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References

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  1. A. Yariv, in Optical Electronics in Modern Communications (Oxford U. Press, 1997), pp. 526-531.
  2. E. Kapon, J. Katz, and A. Yariv, Opt. Lett. 9, 125 (1984).
    [CrossRef] [PubMed]
  3. A. Yariv and X. Sun, Opt. Express 15, 9147 (2007).
    [CrossRef] [PubMed]
  4. M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, Opt. Lett. 30, 3042 (2005).
    [CrossRef] [PubMed]
  5. M. Povinelli, S. Johnson, M. Lonèar, M. Ibanescu, E. Smythe, F. Capasso, and J. Joannopoulos, Opt. Express 13, 8286 (2005).
    [CrossRef] [PubMed]
  6. W. H. P. Pernice, Mo Li, and H. X. Tang, Opt. Express 17, 1806 (2009).
    [CrossRef] [PubMed]
  7. A. Mizrahi and L. Schächter, Opt. Lett. 32, 692 (2007).
    [CrossRef] [PubMed]
  8. F. Riboli, A. Recati, M. Antezza, and I. Carusotto, Eur. Phys. J. D 46, 157 (2007).
    [CrossRef]
  9. M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
    [CrossRef] [PubMed]
  10. M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
    [CrossRef]
  11. P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).
    [CrossRef]

2009 (1)

2008 (1)

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

2007 (5)

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).
[CrossRef]

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, Eur. Phys. J. D 46, 157 (2007).
[CrossRef]

A. Mizrahi and L. Schächter, Opt. Lett. 32, 692 (2007).
[CrossRef] [PubMed]

A. Yariv and X. Sun, Opt. Express 15, 9147 (2007).
[CrossRef] [PubMed]

2005 (2)

1997 (1)

A. Yariv, in Optical Electronics in Modern Communications (Oxford U. Press, 1997), pp. 526-531.

1984 (1)

Antezza, M.

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, Eur. Phys. J. D 46, 157 (2007).
[CrossRef]

Baehr-Jones, T.

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

Capasso, F.

Carusotto, I.

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, Eur. Phys. J. D 46, 157 (2007).
[CrossRef]

Eichenfield, M.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

Hochberg, M.

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

Ibanescu, M.

Ippen, E. P.

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).
[CrossRef]

Joannopoulos, J.

Joannopoulos, J. D.

Johnson, S.

Johnson, S. G.

Kapon, E.

Katz, J.

Li, M.

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

Li, Mo

Loncar, M.

Lonèar, M.

Michael, C. P.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

Mizrahi, A.

Painter, O.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

Perahia, R.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

Pernice, W. H. P.

W. H. P. Pernice, Mo Li, and H. X. Tang, Opt. Express 17, 1806 (2009).
[CrossRef] [PubMed]

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

Popovic, M. A.

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).
[CrossRef]

Povinelli, M.

Povinelli, M. L.

Rakich, P. T.

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).
[CrossRef]

Recati, A.

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, Eur. Phys. J. D 46, 157 (2007).
[CrossRef]

Riboli, F.

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, Eur. Phys. J. D 46, 157 (2007).
[CrossRef]

Schächter, L.

Smythe, E.

Smythe, E. J.

Soljacic, M.

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).
[CrossRef]

Sun, X.

Tang, H. X.

W. H. P. Pernice, Mo Li, and H. X. Tang, Opt. Express 17, 1806 (2009).
[CrossRef] [PubMed]

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

Xiong, C.

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

Yariv, A.

A. Yariv and X. Sun, Opt. Express 15, 9147 (2007).
[CrossRef] [PubMed]

A. Yariv, in Optical Electronics in Modern Communications (Oxford U. Press, 1997), pp. 526-531.

E. Kapon, J. Katz, and A. Yariv, Opt. Lett. 9, 125 (1984).
[CrossRef] [PubMed]

Eur. Phys. J. D (1)

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, Eur. Phys. J. D 46, 157 (2007).
[CrossRef]

Nat. Photonics (2)

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).
[CrossRef]

Nature (1)

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

Opt. Express (3)

Opt. Lett. (3)

Other (1)

A. Yariv, in Optical Electronics in Modern Communications (Oxford U. Press, 1997), pp. 526-531.

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Figures (3)

Fig. 1
Fig. 1

(a) Evanescently coupled waveguide system consisting of two different waveguides. (b) Dispersion relations of the two waveguides.

Fig. 2
Fig. 2

(a) Dispersion relations of Type I and Type II waveguides in the simulation. The Type I waveguide is weakly dispersive, and the Type II waveguides are strongly dispersive. (b)–(e) Normalized optical mode (electric field) profiles of the Type I waveguide at 1.3 μm (b) and 1.7 μm (c) as well as normalized optical mode (electric field) profiles of the Type II waveguide at (d) 1.3 μm and (e) 1.7 μm.

Fig. 3
Fig. 3

Optical force of three representative coupled waveguide systems: Type I–Type I (curves with squares), Type II–Type II [curves with circles (red online)], and Type I–Type II [curves with diamonds (green online)]. The solid curves represent the repulsive force, and the dashed curves represent the attractive force.

Equations (5)

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F = 1 ω ω g U = 1 n g n eff g U = n eff g P L c ,
d A 1 d z = κ A 2 e i 2 δ z , d A 2 d z = κ * A 1 e i 2 δ z , 2 δ = β 2 β 1 ,
E s 1 = ( i κ * δ + s 1 ) ( ξ 1 ( x , y ) , ξ 2 ( x , y ) ) e i ( β ¯ s ) z , E s 2 = ( i κ * δ s 1 ) ( ξ 1 ( x , y ) , ξ 2 ( x , y ) ) e i ( β ¯ + s ) z ,
β ¯ = ( β 1 + β 2 ) 2 , s = δ 2 + κ 2 .
n eff g = ( ( β ¯ ± s ) k 0 ) g = ± 1 k 0 s g = ± 1 k 0 δ 2 κ 2 + 1 κ g ,

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