Abstract

We present the theoretical condition and actual numerical design that achieves an optical pulling force in resonator–waveguide systems, where the direction of the force on the resonator is in the opposite direction to the input light in the waveguide. We also show that this pulling force can occur in conjunction with the lateral optical equilibrium effect, such that the resonator is maintained at the fixed distance from the waveguide while experiencing the pulling force.

© 2013 Optical Society of America

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  1. A. Dogariu, S. Sukhov, and J. J. Saenz, Nat. Photonics 7, 24 (2012).
    [CrossRef]
  2. S. M. Block, Nature 360, 493 (1992).
    [CrossRef]
  3. T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, New J. Phys. 8, 43 (2006).
    [CrossRef]
  4. D. B. Ruffner and D. G. Grier, Phys. Rev. Lett. 109, 163903 (2012).
    [CrossRef]
  5. O. Brzobohaty, V. Karasek, M. Siler, L. Chvatal, T. Cizmar, and P. Zemanek, Nat. Photonics 7, 123 (2013).
    [CrossRef]
  6. J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
    [CrossRef]
  7. A. Novitsky, C. Qiu, and H. Wang, Phys. Rev. Lett. 107, 203601 (2011).
    [CrossRef]
  8. S. Sukhov and A. Dogariu, Phys. Rev. Lett. 107, 203602 (2011).
    [CrossRef]
  9. A. Ashkin and J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
    [CrossRef]
  10. Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, Light: Sci. Appl. 2, e64 (2013).
    [CrossRef]
  11. D. Van Thourhout and J. Roels, Nat. Photonics 4, 211 (2010).
    [CrossRef]
  12. A. Einat and U. Levy, Opt. Express 19, 20405 (2011).
    [CrossRef]
  13. V. Intaraprasonk and S. Fan, Phys. Rev. A 86, 063833 (2012).
    [CrossRef]
  14. M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
    [CrossRef]
  15. M. Li, W. H. P. Pernice, and H. X. Tang, Phys. Rev. Lett. 103, 223901 (2009).
    [CrossRef]
  16. V. Intaraprasonk and S. Fan, http://arxiv.org/abs/1306.2417 .
  17. J. J. Xiao, J. Ng, Z. F. Lin, and C. T. Chan, Appl. Phys. Lett. 94, 011102 (2009).
    [CrossRef]
  18. J. J. Xiao, H. H. Zheng, Y. X. Sun, and Y. Yao, Opt. Lett. 35, 962 (2010).
    [CrossRef]
  19. “Comsol Multiphysics,” www.comsol.com .
  20. P. T. Rakich, M. A. Popovic, and Z. Wang, Opt. Express 17, 18116 (2009).
    [CrossRef]
  21. G. S. Wiederhecker, L. Chen, A. Gondarenk, and M. Lipson, Nature 462, 633 (2009).
    [CrossRef]
  22. G. S. Wiederhecker, S. Manipatruni, S. Lee, and M. Lipson, Opt. Express 19, 2782 (2011).
    [CrossRef]
  23. B. S. Schmidt, A. H. J. Yang, D. Erickson, and M. Lipson, Opt. Express 15, 14322 (2007).
    [CrossRef]

2013 (2)

O. Brzobohaty, V. Karasek, M. Siler, L. Chvatal, T. Cizmar, and P. Zemanek, Nat. Photonics 7, 123 (2013).
[CrossRef]

Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, Light: Sci. Appl. 2, e64 (2013).
[CrossRef]

2012 (3)

V. Intaraprasonk and S. Fan, Phys. Rev. A 86, 063833 (2012).
[CrossRef]

A. Dogariu, S. Sukhov, and J. J. Saenz, Nat. Photonics 7, 24 (2012).
[CrossRef]

D. B. Ruffner and D. G. Grier, Phys. Rev. Lett. 109, 163903 (2012).
[CrossRef]

2011 (5)

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

A. Novitsky, C. Qiu, and H. Wang, Phys. Rev. Lett. 107, 203601 (2011).
[CrossRef]

S. Sukhov and A. Dogariu, Phys. Rev. Lett. 107, 203602 (2011).
[CrossRef]

G. S. Wiederhecker, S. Manipatruni, S. Lee, and M. Lipson, Opt. Express 19, 2782 (2011).
[CrossRef]

A. Einat and U. Levy, Opt. Express 19, 20405 (2011).
[CrossRef]

2010 (2)

2009 (4)

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

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

M. Li, W. H. P. Pernice, and H. X. Tang, Phys. Rev. Lett. 103, 223901 (2009).
[CrossRef]

J. J. Xiao, J. Ng, Z. F. Lin, and C. T. Chan, Appl. Phys. Lett. 94, 011102 (2009).
[CrossRef]

2007 (2)

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

B. S. Schmidt, A. H. J. Yang, D. Erickson, and M. Lipson, Opt. Express 15, 14322 (2007).
[CrossRef]

2006 (1)

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, New J. Phys. 8, 43 (2006).
[CrossRef]

1992 (1)

S. M. Block, Nature 360, 493 (1992).
[CrossRef]

1977 (1)

A. Ashkin and J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

Ashkin, A.

A. Ashkin and J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

Astratov, V. N.

Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, Light: Sci. Appl. 2, e64 (2013).
[CrossRef]

Block, S. M.

S. M. Block, Nature 360, 493 (1992).
[CrossRef]

Bouchal, Z.

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, New J. Phys. 8, 43 (2006).
[CrossRef]

Brzobohaty, O.

O. Brzobohaty, V. Karasek, M. Siler, L. Chvatal, T. Cizmar, and P. Zemanek, Nat. Photonics 7, 123 (2013).
[CrossRef]

Carnegie, D.

Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, Light: Sci. Appl. 2, e64 (2013).
[CrossRef]

Chan, C. T.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

J. J. Xiao, J. Ng, Z. F. Lin, and C. T. Chan, Appl. Phys. Lett. 94, 011102 (2009).
[CrossRef]

Chen, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

Chen, L.

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

Chvatal, L.

O. Brzobohaty, V. Karasek, M. Siler, L. Chvatal, T. Cizmar, and P. Zemanek, Nat. Photonics 7, 123 (2013).
[CrossRef]

Cizmar, T.

O. Brzobohaty, V. Karasek, M. Siler, L. Chvatal, T. Cizmar, and P. Zemanek, Nat. Photonics 7, 123 (2013).
[CrossRef]

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, New J. Phys. 8, 43 (2006).
[CrossRef]

Dogariu, A.

A. Dogariu, S. Sukhov, and J. J. Saenz, Nat. Photonics 7, 24 (2012).
[CrossRef]

S. Sukhov and A. Dogariu, Phys. Rev. Lett. 107, 203602 (2011).
[CrossRef]

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

Eichenfield, M.

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

Einat, A.

Erickson, D.

Fan, S.

V. Intaraprasonk and S. Fan, Phys. Rev. A 86, 063833 (2012).
[CrossRef]

V. Intaraprasonk and S. Fan, http://arxiv.org/abs/1306.2417 .

Gondarenk, A.

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

Grier, D. G.

D. B. Ruffner and D. G. Grier, Phys. Rev. Lett. 109, 163903 (2012).
[CrossRef]

Intaraprasonk, V.

V. Intaraprasonk and S. Fan, Phys. Rev. A 86, 063833 (2012).
[CrossRef]

V. Intaraprasonk and S. Fan, http://arxiv.org/abs/1306.2417 .

Karasek, V.

O. Brzobohaty, V. Karasek, M. Siler, L. Chvatal, T. Cizmar, and P. Zemanek, Nat. Photonics 7, 123 (2013).
[CrossRef]

Kollarova, V.

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, New J. Phys. 8, 43 (2006).
[CrossRef]

Lee, S.

Levy, U.

Li, M.

M. Li, W. H. P. Pernice, and H. X. Tang, Phys. Rev. Lett. 103, 223901 (2009).
[CrossRef]

Li, Y.

Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, Light: Sci. Appl. 2, e64 (2013).
[CrossRef]

Lin, Z.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

Lin, Z. F.

J. J. Xiao, J. Ng, Z. F. Lin, and C. T. Chan, Appl. Phys. Lett. 94, 011102 (2009).
[CrossRef]

Lipson, M.

Manipatruni, S.

Maslov, A. V.

Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, Light: Sci. Appl. 2, e64 (2013).
[CrossRef]

Michael, C. P.

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

Ng, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

J. J. Xiao, J. Ng, Z. F. Lin, and C. T. Chan, Appl. Phys. Lett. 94, 011102 (2009).
[CrossRef]

Novitsky, A.

A. Novitsky, C. Qiu, and H. Wang, Phys. Rev. Lett. 107, 203601 (2011).
[CrossRef]

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.

M. Li, W. H. P. Pernice, and H. X. Tang, Phys. Rev. Lett. 103, 223901 (2009).
[CrossRef]

Popovic, M. A.

Qiu, C.

A. Novitsky, C. Qiu, and H. Wang, Phys. Rev. Lett. 107, 203601 (2011).
[CrossRef]

Rafailov, E.

Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, Light: Sci. Appl. 2, e64 (2013).
[CrossRef]

Rakich, P. T.

Roels, J.

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

Ruffner, D. B.

D. B. Ruffner and D. G. Grier, Phys. Rev. Lett. 109, 163903 (2012).
[CrossRef]

Saenz, J. J.

A. Dogariu, S. Sukhov, and J. J. Saenz, Nat. Photonics 7, 24 (2012).
[CrossRef]

Schmidt, B. S.

Siler, M.

O. Brzobohaty, V. Karasek, M. Siler, L. Chvatal, T. Cizmar, and P. Zemanek, Nat. Photonics 7, 123 (2013).
[CrossRef]

Sukhov, S.

A. Dogariu, S. Sukhov, and J. J. Saenz, Nat. Photonics 7, 24 (2012).
[CrossRef]

S. Sukhov and A. Dogariu, Phys. Rev. Lett. 107, 203602 (2011).
[CrossRef]

Sun, Y. X.

Svitelskiy, O. V.

Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, Light: Sci. Appl. 2, e64 (2013).
[CrossRef]

Tang, H. X.

M. Li, W. H. P. Pernice, and H. X. Tang, Phys. Rev. Lett. 103, 223901 (2009).
[CrossRef]

Van Thourhout, D.

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

Wang, H.

A. Novitsky, C. Qiu, and H. Wang, Phys. Rev. Lett. 107, 203601 (2011).
[CrossRef]

Wang, Z.

Wiederhecker, G. S.

G. S. Wiederhecker, S. Manipatruni, S. Lee, and M. Lipson, Opt. Express 19, 2782 (2011).
[CrossRef]

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

Xiao, J. J.

J. J. Xiao, H. H. Zheng, Y. X. Sun, and Y. Yao, Opt. Lett. 35, 962 (2010).
[CrossRef]

J. J. Xiao, J. Ng, Z. F. Lin, and C. T. Chan, Appl. Phys. Lett. 94, 011102 (2009).
[CrossRef]

Yang, A. H. J.

Yao, Y.

Zemanek, P.

O. Brzobohaty, V. Karasek, M. Siler, L. Chvatal, T. Cizmar, and P. Zemanek, Nat. Photonics 7, 123 (2013).
[CrossRef]

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, New J. Phys. 8, 43 (2006).
[CrossRef]

Zheng, H. H.

Appl. Phys. Lett. (1)

J. J. Xiao, J. Ng, Z. F. Lin, and C. T. Chan, Appl. Phys. Lett. 94, 011102 (2009).
[CrossRef]

Light: Sci. Appl. (1)

Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, Light: Sci. Appl. 2, e64 (2013).
[CrossRef]

Nat. Photonics (5)

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

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

A. Dogariu, S. Sukhov, and J. J. Saenz, Nat. Photonics 7, 24 (2012).
[CrossRef]

O. Brzobohaty, V. Karasek, M. Siler, L. Chvatal, T. Cizmar, and P. Zemanek, Nat. Photonics 7, 123 (2013).
[CrossRef]

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

Nature (2)

S. M. Block, Nature 360, 493 (1992).
[CrossRef]

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

New J. Phys. (1)

T. Cizmar, V. Kollarova, Z. Bouchal, and P. Zemanek, New J. Phys. 8, 43 (2006).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. A (1)

V. Intaraprasonk and S. Fan, Phys. Rev. A 86, 063833 (2012).
[CrossRef]

Phys. Rev. Lett. (5)

M. Li, W. H. P. Pernice, and H. X. Tang, Phys. Rev. Lett. 103, 223901 (2009).
[CrossRef]

D. B. Ruffner and D. G. Grier, Phys. Rev. Lett. 109, 163903 (2012).
[CrossRef]

A. Novitsky, C. Qiu, and H. Wang, Phys. Rev. Lett. 107, 203601 (2011).
[CrossRef]

S. Sukhov and A. Dogariu, Phys. Rev. Lett. 107, 203602 (2011).
[CrossRef]

A. Ashkin and J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

Other (2)

V. Intaraprasonk and S. Fan, http://arxiv.org/abs/1306.2417 .

“Comsol Multiphysics,” www.comsol.com .

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Figures (4)

Fig. 1.
Fig. 1.

Schematics of a resonator–waveguide system, with the definition for the force in each direction on the resonator.

Fig. 2.
Fig. 2.

Modal field pattern of a waveguide with width 0.4a, permittivity of 12.1, at ω=0.65×2πc/a, in (a) the even mode and (b) the odd mode. The red (dark grey) and blue (light grey) represents positive and negative electric fields in the z direction. (c) Dispersion relation of the above waveguide for the even mode (dashed–dotted line) and the odd mode (dashed line). The solid line is the light line ω=ck.

Fig. 3.
Fig. 3.

Field pattern of the resonator–waveguide system. The resonator has permittivity of 12.1, outer radius of 4.3a, and inner radius of 3.9a. The gap between the resonator and waveguide has a width of 0.1a. The frequency is ω=0.65×2πc/a. The inputs are in the waveguide’s (a) even mode and (b) odd mode. The input direction is denoted with a black arrow. (c) Output power in each mode per input power (Pj/Pin) when the input is in the even mode. Solid lines denote the even mode output, dashed lines denote the odd mode output. (d) Same as (c) but with the input in the odd mode. Fx per input power as a function of ω for the input in the waveguide’s (e) even mode and (f) odd mode.

Fig. 4.
Fig. 4.

Field pattern of the resonator–waveguide system with the same parameters as Fig. 3, except that the ring has the inner radius of 3.3a instead. The input is in the waveguide’s odd mode. (a) First-order resonance at ω=0.6776×2πc/a. (b) Second-order resonance at ω=0.6747×2πc/a. The input direction is denoted with a black arrow. (c) U as a function of ω for the input in the waveguide’s odd mode. Light green arrows denote the first-order resonances, dark brown arrows denote the second-order resonances. (d) Fx×10 (dotted line) and Fy (solid line) per input power of the system at ω=0.6552×2πc/a.

Equations (5)

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F=1ωjPjdϕj,
F=1ωjPjxrϕj,
ϕj=kinxr+θjkj(Lxr),
F=1ωjPj(Δk)j,
F=jΦj(Δk)j.

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