Abstract

We describe a mechanism and propose design strategies to selectively tailor repulsive–gradient-optical forces between parallel, nanophotonic waveguides via morphology augmented by slow-light band-edge modes. We show that at small separation lengths, the repulsive force can be made nearly 2 orders of magnitude larger than that of standard dielectric waveguides with a square cross section. The increased coupling interactions should enable a wider dynamic range of optomechanical functionality for potential applications in sensing, switching, and nanoelectromechanical systems.

© 2011 Optical Society of America

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  1. D. V. Thourhout and J. Roels, Nat. Photon. 4, 211 (2010).
    [CrossRef]
  2. M. Li, W. Pernice, and H. Tang, Nat. Photon. 3, 464 (2009).
    [CrossRef]
  3. J. Roels, I. D. Vlaminck, L. Lagae, B. Maes, D. V. Thourhout, and R. Baets, Nat. Nanotechnol. 4, 510 (2009).
    [CrossRef] [PubMed]
  4. M. Povinelli, S. Johnson, M. Loncar, M. Ibanescu, E. Smythe, F. Capasso, and J. Joannopoulos, Opt. Express 13, 8286 (2005).
    [CrossRef] [PubMed]
  5. M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, Phys. Rev. Lett. 97 (2006).
    [CrossRef] [PubMed]
  6. M. Eichenfield, C. Michael, R. Perahia, and O. Painter, Nat. Photon. 1, 416 (2007).
    [CrossRef]
  7. G. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
    [CrossRef] [PubMed]
  8. J. Ma and M. Povinelli, Appl. Phys. Lett. 97 (2010).
    [CrossRef]
  9. M. Povinelli, M. Loncar, M. Ibanescu, E. Smythe, S. Johnson, F. Capasso, and J. Joannopoulos, Opt. Lett. 30, 3042 (2005).
    [CrossRef] [PubMed]
  10. P. Rakich, M. Popovic, and Z. Wang, Opt. Express 17, 18116 (2009).
    [CrossRef] [PubMed]
  11. S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
    [CrossRef] [PubMed]
  12. J. D. Joannopoulos, S. G. Johnson, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ., 2008).

2010 (2)

D. V. Thourhout and J. Roels, Nat. Photon. 4, 211 (2010).
[CrossRef]

J. Ma and M. Povinelli, Appl. Phys. Lett. 97 (2010).
[CrossRef]

2009 (4)

G. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef] [PubMed]

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

J. Roels, I. D. Vlaminck, L. Lagae, B. Maes, D. V. Thourhout, and R. Baets, Nat. Nanotechnol. 4, 510 (2009).
[CrossRef] [PubMed]

P. Rakich, M. Popovic, and Z. Wang, Opt. Express 17, 18116 (2009).
[CrossRef] [PubMed]

2007 (1)

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

2006 (1)

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, Phys. Rev. Lett. 97 (2006).
[CrossRef] [PubMed]

2005 (2)

2001 (1)

Baets, R.

J. Roels, I. D. Vlaminck, L. Lagae, B. Maes, D. V. Thourhout, and R. Baets, Nat. Nanotechnol. 4, 510 (2009).
[CrossRef] [PubMed]

Capasso, F.

Chen, L.

G. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef] [PubMed]

Eichenfield, M.

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

Gondarenko, A.

G. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef] [PubMed]

Ibanescu, M.

Joannopoulos, J.

Joannopoulos, J. D.

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef] [PubMed]

J. D. Joannopoulos, S. G. Johnson, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ., 2008).

Johnson, S.

Johnson, S. G.

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef] [PubMed]

J. D. Joannopoulos, S. G. Johnson, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ., 2008).

Kuramochi, E.

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, Phys. Rev. Lett. 97 (2006).
[CrossRef] [PubMed]

Lagae, L.

J. Roels, I. D. Vlaminck, L. Lagae, B. Maes, D. V. Thourhout, and R. Baets, Nat. Nanotechnol. 4, 510 (2009).
[CrossRef] [PubMed]

Li, M.

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

Lipson, M.

G. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef] [PubMed]

Loncar, M.

Ma, J.

J. Ma and M. Povinelli, Appl. Phys. Lett. 97 (2010).
[CrossRef]

Maes, B.

J. Roels, I. D. Vlaminck, L. Lagae, B. Maes, D. V. Thourhout, and R. Baets, Nat. Nanotechnol. 4, 510 (2009).
[CrossRef] [PubMed]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ., 2008).

Michael, C.

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

Mitsugi, S.

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, Phys. Rev. Lett. 97 (2006).
[CrossRef] [PubMed]

Notomi, M.

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, Phys. Rev. Lett. 97 (2006).
[CrossRef] [PubMed]

Painter, O.

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

Perahia, R.

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

Pernice, W.

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

Popovic, M.

Povinelli, M.

Rakich, P.

Roels, J.

D. V. Thourhout and J. Roels, Nat. Photon. 4, 211 (2010).
[CrossRef]

J. Roels, I. D. Vlaminck, L. Lagae, B. Maes, D. V. Thourhout, and R. Baets, Nat. Nanotechnol. 4, 510 (2009).
[CrossRef] [PubMed]

Smythe, E.

Tang, H.

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

Taniyama, H.

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, Phys. Rev. Lett. 97 (2006).
[CrossRef] [PubMed]

Thourhout, D. V.

D. V. Thourhout and J. Roels, Nat. Photon. 4, 211 (2010).
[CrossRef]

J. Roels, I. D. Vlaminck, L. Lagae, B. Maes, D. V. Thourhout, and R. Baets, Nat. Nanotechnol. 4, 510 (2009).
[CrossRef] [PubMed]

Vlaminck, I. D.

J. Roels, I. D. Vlaminck, L. Lagae, B. Maes, D. V. Thourhout, and R. Baets, Nat. Nanotechnol. 4, 510 (2009).
[CrossRef] [PubMed]

Wang, Z.

Wiederhecker, G.

G. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef] [PubMed]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ., 2008).

Appl. Phys. Lett. (1)

J. Ma and M. Povinelli, Appl. Phys. Lett. 97 (2010).
[CrossRef]

Nat. Nanotechnol. (1)

J. Roels, I. D. Vlaminck, L. Lagae, B. Maes, D. V. Thourhout, and R. Baets, Nat. Nanotechnol. 4, 510 (2009).
[CrossRef] [PubMed]

Nat. Photon. (3)

D. V. Thourhout and J. Roels, Nat. Photon. 4, 211 (2010).
[CrossRef]

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

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

Nature (1)

G. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, Phys. Rev. Lett. 97 (2006).
[CrossRef] [PubMed]

Other (1)

J. D. Joannopoulos, S. G. Johnson, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ., 2008).

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Figures (3)

Fig. 1
Fig. 1

Normalized force per unit length and input power versus waveguide separation for the symmetric (z-even, red, lower curve) and antisymmetric (z-odd, blue, upper curve) y-odd modes of parallel waveguides with a square profile (width a) at a fixed-axial wave vector of π / a . Insets show the in-plane E-field vector distribution (foreground) with the total E-field intensity in the background (darker is more intense).

Fig. 2
Fig. 2

Normalized force versus waveguide separation for the symmetric (z-even, red) and antisymmetric (z-odd, blue) y-odd modes of parallel waveguides with circular and hemicircular profile (diameter a) at a fixed-axial wave vector of π / a . Insets show the in-plane E-field vector (foreground) with the total E-field intensity in background (darker is more intense).

Fig. 3
Fig. 3

Normalized force versus waveguide separation of four antisymmetric slow-light modes for two parallel waveguide systems, one with hemicircular (solid circles) and the other with square (solid squares) cross sections, both with air holes (periodicity a, radius 0.2 a ) along the waveguide axis.

Equations (2)

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F = 1 ω d ω d s | k U ,
ω 2 c 2 = min E d 3 r | × E ( r ) | 2 d 3 r ε ( r ) | E ( r ) | 2 .

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