Abstract

We show that eigenmodes of dielectric optical waveguides exert surface dilation forces on waveguide boundaries owing to radiation pressure, and we develop an exact scaling law relating modal dispersion of an arbitrary dielectric waveguide to the magnitude of optical forces generated by radiation pressure. This result points to highly dispersive waveguides as an optimal choice for the generation of large optical forces in nano-optomechanical systems. Exact agreement with ab initio calculations is demonstrated.

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Povinelli, M. Loncar, M. Ibanescu, E. Smythe, S. Johnson, F. Capasso, and J. Joannopoulos, Opt. Lett. 30, 3042 (2005).
    [CrossRef] [PubMed]
  2. A. Mizrahi and L. Schachter, Opt. Lett. 32, 692 (2007).
    [CrossRef] [PubMed]
  3. M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photon. 1, 416 (2007).
    [CrossRef]
  4. P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photon. 1, 658 (2007).
    [CrossRef]
  5. M. Li, W. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. Tang, Nature 456, 480 (2008).
    [CrossRef] [PubMed]
  6. J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, Nat. Nanotechnol. 4, 510 (2009).
    [CrossRef] [PubMed]
  7. P. T. Rakich, M. A. Popovic, and Z. Wang, Opt. Express 17, 18116 (2009).
    [CrossRef] [PubMed]
  8. P. T. Rakich, P. Davids, and Z. Wang, Opt. Express 18, 14439 (2010).
    [CrossRef] [PubMed]
  9. M. Tomes and T. Carmon, Phys. Rev. Lett. 102, 113601 (2009).
    [CrossRef] [PubMed]
  10. P. Dainese, P. Russell, N. Joly, J. Knight, G. S. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, Nat. Phys. 2, 388 (2006).
    [CrossRef]
  11. E. M. Lifshitz, D. Landau, and L. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, 1984).
  12. M. Mansuripur, Opt. Express 12, 5375 (2004).
    [CrossRef] [PubMed]
  13. J. D. Joannopoulos, S. Johnson, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton, 2008).

2010 (1)

2009 (3)

M. Tomes and T. Carmon, Phys. Rev. Lett. 102, 113601 (2009).
[CrossRef] [PubMed]

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

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

2008 (1)

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

2007 (3)

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

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

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

2006 (1)

P. Dainese, P. Russell, N. Joly, J. Knight, G. S. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, Nat. Phys. 2, 388 (2006).
[CrossRef]

2005 (1)

2004 (1)

Baehr-Jones, T.

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

Baets, R.

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

Capasso, F.

Carmon, T.

M. Tomes and T. Carmon, Phys. Rev. Lett. 102, 113601 (2009).
[CrossRef] [PubMed]

Dainese, P.

P. Dainese, P. Russell, N. Joly, J. Knight, G. S. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, Nat. Phys. 2, 388 (2006).
[CrossRef]

Davids, P.

De Vlaminck, I.

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

Eichenfield, M.

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

Fragnito, H.

P. Dainese, P. Russell, N. Joly, J. Knight, G. S. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, Nat. Phys. 2, 388 (2006).
[CrossRef]

Hochberg, M.

M. Li, W. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. 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. Photon. 1, 658 (2007).
[CrossRef]

Joannopoulos, J.

Joannopoulos, J. D.

J. D. Joannopoulos, S. Johnson, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton, 2008).

Johnson, S.

M. Povinelli, M. Loncar, M. Ibanescu, E. Smythe, S. Johnson, F. Capasso, and J. Joannopoulos, Opt. Lett. 30, 3042 (2005).
[CrossRef] [PubMed]

J. D. Joannopoulos, S. Johnson, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton, 2008).

Joly, N.

P. Dainese, P. Russell, N. Joly, J. Knight, G. S. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, Nat. Phys. 2, 388 (2006).
[CrossRef]

Khelif, A.

P. Dainese, P. Russell, N. Joly, J. Knight, G. S. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, Nat. Phys. 2, 388 (2006).
[CrossRef]

Knight, J.

P. Dainese, P. Russell, N. Joly, J. Knight, G. S. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, Nat. Phys. 2, 388 (2006).
[CrossRef]

Lagae, L.

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

Landau, D.

E. M. Lifshitz, D. Landau, and L. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, 1984).

Laude, V.

P. Dainese, P. Russell, N. Joly, J. Knight, G. S. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, Nat. Phys. 2, 388 (2006).
[CrossRef]

Li, M.

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

Lifshitz, E. M.

E. M. Lifshitz, D. Landau, and L. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, 1984).

Loncar, M.

Maes, B.

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

Mansuripur, M.

Michael, C. P.

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

Mizrahi, A.

Painter, O.

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

Perahia, R.

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

Pernice, W.

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

Pitaevskii, L.

E. M. Lifshitz, D. Landau, and L. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, 1984).

Popovic, M. A.

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

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

Povinelli, M.

Rakich, P. T.

Roels, J.

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

Russell, P.

P. Dainese, P. Russell, N. Joly, J. Knight, G. S. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, Nat. Phys. 2, 388 (2006).
[CrossRef]

Schachter, L.

Smythe, E.

Soljacic, M.

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

Tang, H.

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

Tomes, M.

M. Tomes and T. Carmon, Phys. Rev. Lett. 102, 113601 (2009).
[CrossRef] [PubMed]

Van Thourhout, D.

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

Wang, Z.

Wiederhecker, G. S.

P. Dainese, P. Russell, N. Joly, J. Knight, G. S. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, Nat. Phys. 2, 388 (2006).
[CrossRef]

Winn, J.

J. D. Joannopoulos, S. Johnson, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton, 2008).

Xiong, C.

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

Nat. Nanotechnol. (1)

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

Nat. Photon. (2)

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

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

Nat. Phys. (1)

P. Dainese, P. Russell, N. Joly, J. Knight, G. S. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, Nat. Phys. 2, 388 (2006).
[CrossRef]

Nature (1)

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

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

M. Tomes and T. Carmon, Phys. Rev. Lett. 102, 113601 (2009).
[CrossRef] [PubMed]

Other (2)

J. D. Joannopoulos, S. Johnson, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton, 2008).

E. M. Lifshitz, D. Landau, and L. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, 1984).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

(a) Circular and (d) rectangular waveguide cross sections; (b) and (e) are computed E x components of TE-like modes; (c) and (f) are computed magnitude of the normalized optical force densities.

Fig. 2
Fig. 2

Boundary displacements coinciding with variation in scale factor ( δ β ). For (a) circular, (b) rectangular, and (c) hexagonal cross sections, the transformation corresponds to ( a , b ) ( a , b ) , r r , and c c ; (d)–(f) show the orientation of radiation pressure on waveguides.

Fig. 3
Fig. 3

Radiation pressures of (a) circular and (b) rectangular waveguides computed via Maxwell stress tensor (circles) and the analytical scaling laws (solid curve).

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

T i j = ϵ o ϵ [ E i E j 1 2 δ i j | E | 2 ] + μ o μ [ H i H j 1 2 δ i j | H | 2 ] .
δ U EM = w g p · r δ β d S .
δ U EM = P i ω · ( ϕ ( q ) q ) ω · δ q .
δ U EM L = P i c · n p β · δ β = P i c k n p r k r k β · δ β .
P i c · n p ( β ) β = w g p · r d l .
[ ( c / ω ) 2 2 ϵ ( r ) ] E m ( r ) = n p 2 E m ( r ) .
[ ( c / ω ¯ ) 2 · ¯ 2 ϵ ¯ ( r ¯ ) ] E m ( r ¯ · s ) = n p 2 E m ( r ¯ · s ) .
n p ( ϵ ( r ) , ω ) = n p ( ϵ ¯ ( r ) , ω ¯ ) = n p ( ϵ ( r · s ) , ω · s ) .
k n p r k r k β = n p ω ω β .
P i c n p ω ω = P i c ( n g n p ) = P i [ 1 v g 1 v p ] = w g p · r d l .
p ¯ r = 1 2 · ( n g n p ) · [ P i / ( c · A w g ) ] .
( p ¯ x + p ¯ y ) = ( n g n p ) · [ P i / ( c · A w g ) ] .
k = 1 N p ¯ k = ( n g n p ) · [ P i / ( c · A w g ) ] · N / 2.

Metrics