Abstract

We reveal that slow-light enhanced optical forces between side-coupled photonic-crystal nanowire waveguides can be flexibly controlled by introducing a relative longitudinal shift. We predict that close to the photonic band edge, where the group velocity is reduced, the transverse force can be tuned from repulsive to attractive, and the force is suppressed for a particular shift value. Additionally the shift leads to symmetry breaking that can facilitate longitudinal forces acting on the waveguides, in contrast to unshifted structures where such forces vanish.

© 2012 Optical Society of America

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  1. M. Li, W. H. P. Pernice, and H. X. Tang, Nat. Photon. 3, 464 (2009).
    [CrossRef]
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    [CrossRef]
  3. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, Nature 459, 550 (2009).
    [CrossRef]
  4. J. Ma and M. L. Povinelli, Appl. Phys. Lett. 97, 151102 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
    [CrossRef]
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  9. M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, Opt. Express 13, 7145 (2005).
    [CrossRef]
  10. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).
  11. S. Ha, A. A. Sukhorukov, A. V. Lavrinenko, I. V. Shadrivov, D. A. Powell, and Yu. S. Kivshar, Appl. Phys. Lett. 98, 061909 (2010).
    [CrossRef]

2010 (2)

J. Ma and M. L. Povinelli, Appl. Phys. Lett. 97, 151102 (2010).
[CrossRef]

S. Ha, A. A. Sukhorukov, A. V. Lavrinenko, I. V. Shadrivov, D. A. Powell, and Yu. S. Kivshar, Appl. Phys. Lett. 98, 061909 (2010).
[CrossRef]

2009 (4)

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

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

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

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, Opt. Express 17, 3802 (2009).
[CrossRef]

2005 (2)

2001 (1)

Baets, R.

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

Camacho, R.

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

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, Opt. Express 17, 3802 (2009).
[CrossRef]

Capasso, F.

Chan, J.

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

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, Opt. Express 17, 3802 (2009).
[CrossRef]

De Vlaminck, I.

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

Eichenfield, M.

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

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, Opt. Express 17, 3802 (2009).
[CrossRef]

Ha, S.

S. Ha, A. A. Sukhorukov, A. V. Lavrinenko, I. V. Shadrivov, D. A. Powell, and Yu. S. Kivshar, Appl. Phys. Lett. 98, 061909 (2010).
[CrossRef]

Ibanescu, M.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1998).

Joannopoulos, J. D.

Johnson, S. G.

Kivshar, Yu. S.

S. Ha, A. A. Sukhorukov, A. V. Lavrinenko, I. V. Shadrivov, D. A. Powell, and Yu. S. Kivshar, Appl. Phys. Lett. 98, 061909 (2010).
[CrossRef]

Lagae, L.

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

Lavrinenko, A. V.

S. Ha, A. A. Sukhorukov, A. V. Lavrinenko, I. V. Shadrivov, D. A. Powell, and Yu. S. Kivshar, Appl. Phys. Lett. 98, 061909 (2010).
[CrossRef]

Li, M.

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

Loncar, M.

Ma, J.

J. Ma and M. L. Povinelli, Appl. Phys. Lett. 97, 151102 (2010).
[CrossRef]

Maes, B.

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

Meade, R. D.

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

Painter, O.

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, Opt. Express 17, 3802 (2009).
[CrossRef]

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

Pernice, W. H. P.

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

Povinelli, M. L.

Powell, D. A.

S. Ha, A. A. Sukhorukov, A. V. Lavrinenko, I. V. Shadrivov, D. A. Powell, and Yu. S. Kivshar, Appl. Phys. Lett. 98, 061909 (2010).
[CrossRef]

Roels, J.

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

Shadrivov, I. V.

S. Ha, A. A. Sukhorukov, A. V. Lavrinenko, I. V. Shadrivov, D. A. Powell, and Yu. S. Kivshar, Appl. Phys. Lett. 98, 061909 (2010).
[CrossRef]

Smythe, E. J.

Sukhorukov, A. A.

S. Ha, A. A. Sukhorukov, A. V. Lavrinenko, I. V. Shadrivov, D. A. Powell, and Yu. S. Kivshar, Appl. Phys. Lett. 98, 061909 (2010).
[CrossRef]

Tang, H. X.

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

Vahala, K. J.

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

Van Thourhout, D.

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

Winn, J. N.

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

Appl. Phys. Lett. (2)

J. Ma and M. L. Povinelli, Appl. Phys. Lett. 97, 151102 (2010).
[CrossRef]

S. Ha, A. A. Sukhorukov, A. V. Lavrinenko, I. V. Shadrivov, D. A. Powell, and Yu. S. Kivshar, Appl. Phys. Lett. 98, 061909 (2010).
[CrossRef]

Nat. Nanotechnol. (1)

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

Nat. Photon. (1)

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

Nature (1)

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

Opt. Express (3)

Opt. Lett. (1)

Other (2)

J. D. Jackson, Classical Electrodynamics (Wiley, 1998).

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

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Figures (4)

Fig. 1.
Fig. 1.

(a) Three-dimensional sketch of the longitudinally shifted side-coupled photonic-crystal waveguides and (b) top view of the structure.

Fig. 2.
Fig. 2.

TM mode properties in coupled waveguides with different longitudinal shifts: (a), (d), (g) Δx=0; (b), (e), (h) Δx=0.15a; and (c), (f), (i) Δx=0.5a. (a), (b), (c) Dispersion relations shown as normalized frequency versus wavenumber for the first- (dashed line) and second-lowest (solid line) TM bands near the band edge; gray shading marks the band gap. (d), (e), (f) Group velocities for the second-lowest band. (g), (h), (i) Mode profiles at the band edge: intensity |E|2 (top row), magnitude |Hz| (top row), and phase of Hz (bottom row), white contours show an outline of the waveguides.

Fig. 3.
Fig. 3.

The force in the transverse (+y) direction on the right waveguide. (a) The force per unit length per unit energy density versus the longitudinal shift at the band edge. (b)–(g) Forces for different longitudinal shifts: (b), (c) Δx=0; (d), (e) Δx=0.15a; and (f), (g) Δx=0.5a. (b), (d), (f) The distributed force along the waveguide per unit energy density at the band edge. (c), (e), (g) Total force per unit length and unit power versus the wavenumber near the photonic band edge.

Fig. 4.
Fig. 4.

The force in the longitudinal (+x) direction on the right waveguide. (a) The force per unit length per unit energy density versus the longitudinal shift at the band edge. (b)–(g) Forces for different longitudinal shifts: (b), (c) Δx=0; (d), (e) Δx=0.15a; and (f), (g) Δx=0.5a. (b), (d), (f) The distributed force along the waveguide per unit energy density at the band edge. (c), (e), (g) Total force per unit length and unit power versus the wavenumber near the photonic band edge.

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