Abstract

We propose a set of principles to tailor and enhance optical forces between parallel, periodic dielectric waveguides by molding the eigen-mode field distribution via the combined effects of highly symmetric slow light modes and waveguide morphology. The geometries here considered are amenable to standard lithographic techniques and possess strong repulsive and attractive optical forces that can be enhanced via slow-light band edge modes. This new methodology should enable the fabrication of optomechanical devices for applications in sensing, switching and nano-optomechanical systems.

© 2012 OSA

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  1. J. D. Jackson, Classical Electrodynamics, 3rd ed (Wiley, New York, 1998).
  2. D. V. Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force”, Nat. Photonics4, 211–217 (2010).
    [CrossRef]
  3. M. Bagheri, M. Poot, M. Li, W. Pernice, and H. Tang, “Dynamic manipulation of mechanical resonators in the high amplitude regime through optical backaction”, Nature Nanotechnology6, 726–732 (2011).
    [CrossRef] [PubMed]
  4. M. Aspelmeyer, S. Groblacher, K. Hammerer, and N. Kiesel, “Quantum optomechanics–throwing a glance”, J. Opt. Soc. Am. B27, 189–197 (2010).
    [CrossRef]
  5. J. Ma and M. Povinelli, “Applications of optomechanical effects for on-chip manipulation of light signals”, Curr. Opin. Sol. State Mater. Sci16, 82–90 (2012).
    [CrossRef]
  6. M. Povinelli, M. Loncar, M. Ibanescu, E. Smythe, S. Johnson, F. Capasso, and J. Joannopoulos, “Evanescent-wave bonding between optical waveguides”, Opt. Lett.30, 3042–3044 (2005).
    [CrossRef] [PubMed]
  7. M. Li, W. Pernice, and H. Tang, “Tunable bipolar optical interactions between guided lightwaves”, Nat. Photonics3, 464–469 (2009).
    [CrossRef]
  8. A. Oskooi, P. Favuzzi, Y. Kawakami, and S. Noda, “Tailoring repulsive optical forces in nanophotonic waveguides”, Opt. Lett.36, 4638–4640 (2011).
    [CrossRef] [PubMed]
  9. M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, “Optomechanical crystals”, Nature462, 78–82 (2009).
    [CrossRef] [PubMed]
  10. J. Ma and M. Povinelli, “Effect of periodicity on optical forces between a one-dimensional periodic photonic-crystal waveguide and an underlying substrate”, Appl. Phys. Lett.97 (2010).
    [CrossRef]
  11. J. D. Joannopoulos, S. G. Johnson, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd ed (Princeton Univ. Press, 2008).
  12. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis”, Opt. Express8, 173–190 (2001).
    [CrossRef] [PubMed]
  13. V. Almeida, Q. Xu, C. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure”, Opt. Lett.29, 1209–1211 (2004).
    [CrossRef] [PubMed]
  14. E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity”, Phys. Rev. Lett.106, 203902 (2011).
    [CrossRef] [PubMed]
  15. M. Tinkham, Group Theory and Quantum Meachanics, 2nd ed (Dover, 1992).

2012

J. Ma and M. Povinelli, “Applications of optomechanical effects for on-chip manipulation of light signals”, Curr. Opin. Sol. State Mater. Sci16, 82–90 (2012).
[CrossRef]

2011

M. Bagheri, M. Poot, M. Li, W. Pernice, and H. Tang, “Dynamic manipulation of mechanical resonators in the high amplitude regime through optical backaction”, Nature Nanotechnology6, 726–732 (2011).
[CrossRef] [PubMed]

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity”, Phys. Rev. Lett.106, 203902 (2011).
[CrossRef] [PubMed]

A. Oskooi, P. Favuzzi, Y. Kawakami, and S. Noda, “Tailoring repulsive optical forces in nanophotonic waveguides”, Opt. Lett.36, 4638–4640 (2011).
[CrossRef] [PubMed]

2010

D. V. Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force”, Nat. Photonics4, 211–217 (2010).
[CrossRef]

J. Ma and M. Povinelli, “Effect of periodicity on optical forces between a one-dimensional periodic photonic-crystal waveguide and an underlying substrate”, Appl. Phys. Lett.97 (2010).
[CrossRef]

M. Aspelmeyer, S. Groblacher, K. Hammerer, and N. Kiesel, “Quantum optomechanics–throwing a glance”, J. Opt. Soc. Am. B27, 189–197 (2010).
[CrossRef]

2009

M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, “Optomechanical crystals”, Nature462, 78–82 (2009).
[CrossRef] [PubMed]

M. Li, W. Pernice, and H. Tang, “Tunable bipolar optical interactions between guided lightwaves”, Nat. Photonics3, 464–469 (2009).
[CrossRef]

2005

2004

2001

Almeida, V.

Arcizet, O.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity”, Phys. Rev. Lett.106, 203902 (2011).
[CrossRef] [PubMed]

Aspelmeyer, M.

M. Aspelmeyer, S. Groblacher, K. Hammerer, and N. Kiesel, “Quantum optomechanics–throwing a glance”, J. Opt. Soc. Am. B27, 189–197 (2010).
[CrossRef]

Bagheri, M.

M. Bagheri, M. Poot, M. Li, W. Pernice, and H. Tang, “Dynamic manipulation of mechanical resonators in the high amplitude regime through optical backaction”, Nature Nanotechnology6, 726–732 (2011).
[CrossRef] [PubMed]

Barrios, C.

Beveratos, A.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity”, Phys. Rev. Lett.106, 203902 (2011).
[CrossRef] [PubMed]

Braive, R.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity”, Phys. Rev. Lett.106, 203902 (2011).
[CrossRef] [PubMed]

Camacho, R.

M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, “Optomechanical crystals”, Nature462, 78–82 (2009).
[CrossRef] [PubMed]

Capasso, F.

Chan, J.

M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, “Optomechanical crystals”, Nature462, 78–82 (2009).
[CrossRef] [PubMed]

Eichenfield, M.

M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, “Optomechanical crystals”, Nature462, 78–82 (2009).
[CrossRef] [PubMed]

Favuzzi, P.

Gavartin, E.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity”, Phys. Rev. Lett.106, 203902 (2011).
[CrossRef] [PubMed]

Groblacher, S.

M. Aspelmeyer, S. Groblacher, K. Hammerer, and N. Kiesel, “Quantum optomechanics–throwing a glance”, J. Opt. Soc. Am. B27, 189–197 (2010).
[CrossRef]

Hammerer, K.

M. Aspelmeyer, S. Groblacher, K. Hammerer, and N. Kiesel, “Quantum optomechanics–throwing a glance”, J. Opt. Soc. Am. B27, 189–197 (2010).
[CrossRef]

Ibanescu, M.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed (Wiley, New York, 1998).

Joannopoulos, J.

Joannopoulos, J. D.

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis”, Opt. Express8, 173–190 (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. Press, 2008).

Johnson, S.

Johnson, S. G.

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis”, Opt. Express8, 173–190 (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. Press, 2008).

Kawakami, Y.

Kiesel, N.

M. Aspelmeyer, S. Groblacher, K. Hammerer, and N. Kiesel, “Quantum optomechanics–throwing a glance”, J. Opt. Soc. Am. B27, 189–197 (2010).
[CrossRef]

Kippenberg, T. J.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity”, Phys. Rev. Lett.106, 203902 (2011).
[CrossRef] [PubMed]

Li, M.

M. Bagheri, M. Poot, M. Li, W. Pernice, and H. Tang, “Dynamic manipulation of mechanical resonators in the high amplitude regime through optical backaction”, Nature Nanotechnology6, 726–732 (2011).
[CrossRef] [PubMed]

M. Li, W. Pernice, and H. Tang, “Tunable bipolar optical interactions between guided lightwaves”, Nat. Photonics3, 464–469 (2009).
[CrossRef]

Lipson, M.

Loncar, M.

Ma, J.

J. Ma and M. Povinelli, “Applications of optomechanical effects for on-chip manipulation of light signals”, Curr. Opin. Sol. State Mater. Sci16, 82–90 (2012).
[CrossRef]

J. Ma and M. Povinelli, “Effect of periodicity on optical forces between a one-dimensional periodic photonic-crystal waveguide and an underlying substrate”, Appl. Phys. Lett.97 (2010).
[CrossRef]

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. Press, 2008).

Noda, S.

Oskooi, A.

Painter, O.

M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, “Optomechanical crystals”, Nature462, 78–82 (2009).
[CrossRef] [PubMed]

Pernice, W.

M. Bagheri, M. Poot, M. Li, W. Pernice, and H. Tang, “Dynamic manipulation of mechanical resonators in the high amplitude regime through optical backaction”, Nature Nanotechnology6, 726–732 (2011).
[CrossRef] [PubMed]

M. Li, W. Pernice, and H. Tang, “Tunable bipolar optical interactions between guided lightwaves”, Nat. Photonics3, 464–469 (2009).
[CrossRef]

Poot, M.

M. Bagheri, M. Poot, M. Li, W. Pernice, and H. Tang, “Dynamic manipulation of mechanical resonators in the high amplitude regime through optical backaction”, Nature Nanotechnology6, 726–732 (2011).
[CrossRef] [PubMed]

Povinelli, M.

J. Ma and M. Povinelli, “Applications of optomechanical effects for on-chip manipulation of light signals”, Curr. Opin. Sol. State Mater. Sci16, 82–90 (2012).
[CrossRef]

J. Ma and M. Povinelli, “Effect of periodicity on optical forces between a one-dimensional periodic photonic-crystal waveguide and an underlying substrate”, Appl. Phys. Lett.97 (2010).
[CrossRef]

M. Povinelli, M. Loncar, M. Ibanescu, E. Smythe, S. Johnson, F. Capasso, and J. Joannopoulos, “Evanescent-wave bonding between optical waveguides”, Opt. Lett.30, 3042–3044 (2005).
[CrossRef] [PubMed]

Robert-Philip, I.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity”, Phys. Rev. Lett.106, 203902 (2011).
[CrossRef] [PubMed]

Roels, J.

D. V. Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force”, Nat. Photonics4, 211–217 (2010).
[CrossRef]

Sagnes, I.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity”, Phys. Rev. Lett.106, 203902 (2011).
[CrossRef] [PubMed]

Smythe, E.

Tang, H.

M. Bagheri, M. Poot, M. Li, W. Pernice, and H. Tang, “Dynamic manipulation of mechanical resonators in the high amplitude regime through optical backaction”, Nature Nanotechnology6, 726–732 (2011).
[CrossRef] [PubMed]

M. Li, W. Pernice, and H. Tang, “Tunable bipolar optical interactions between guided lightwaves”, Nat. Photonics3, 464–469 (2009).
[CrossRef]

Thourhout, D. V.

D. V. Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force”, Nat. Photonics4, 211–217 (2010).
[CrossRef]

Tinkham, M.

M. Tinkham, Group Theory and Quantum Meachanics, 2nd ed (Dover, 1992).

Vahala, K.

M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, “Optomechanical crystals”, Nature462, 78–82 (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. Press, 2008).

Xu, Q.

Appl. Phys. Lett.

J. Ma and M. Povinelli, “Effect of periodicity on optical forces between a one-dimensional periodic photonic-crystal waveguide and an underlying substrate”, Appl. Phys. Lett.97 (2010).
[CrossRef]

Curr. Opin. Sol. State Mater. Sci

J. Ma and M. Povinelli, “Applications of optomechanical effects for on-chip manipulation of light signals”, Curr. Opin. Sol. State Mater. Sci16, 82–90 (2012).
[CrossRef]

J. Opt. Soc. Am. B

M. Aspelmeyer, S. Groblacher, K. Hammerer, and N. Kiesel, “Quantum optomechanics–throwing a glance”, J. Opt. Soc. Am. B27, 189–197 (2010).
[CrossRef]

Nat. Photonics

D. V. Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force”, Nat. Photonics4, 211–217 (2010).
[CrossRef]

M. Li, W. Pernice, and H. Tang, “Tunable bipolar optical interactions between guided lightwaves”, Nat. Photonics3, 464–469 (2009).
[CrossRef]

Nature

M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, “Optomechanical crystals”, Nature462, 78–82 (2009).
[CrossRef] [PubMed]

Nature Nanotechnology

M. Bagheri, M. Poot, M. Li, W. Pernice, and H. Tang, “Dynamic manipulation of mechanical resonators in the high amplitude regime through optical backaction”, Nature Nanotechnology6, 726–732 (2011).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity”, Phys. Rev. Lett.106, 203902 (2011).
[CrossRef] [PubMed]

Other

M. Tinkham, Group Theory and Quantum Meachanics, 2nd ed (Dover, 1992).

J. D. Jackson, Classical Electrodynamics, 3rd ed (Wiley, New York, 1998).

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

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Figures (5)

Fig. 1
Fig. 1

(a) Schematics of the geometry in use. from (b) to (e): In-plane Eyz vector-field distribution (larger arrows mean more intense) with the total |E|2 in the background (darker is more intense) for the four fundamental modes of parallel waveguides with a semicircle profile (r = a/2) at an axial wave-vector of π/a and a fixed distance s = 0.05a. All arrows lengths and color scales share the same normalization.

Fig. 2
Fig. 2

(a) Normalized force per unit energy as a function of the waveguide-separation distance s/a of the four fundamental slow-light modes (kx = 0.98π/a) of two parallel-waveguides shown in inset (periodicity a, radius 0.3a). The inset also shows the dispersion diagram of the four studied modes. (b) Field distribution (y = 0 and y = 0.47a from the bottom) of the y-even/z-even and y-odd/z-even modes at the wavevector kx = 0.9π/a

Fig. 3
Fig. 3

(a) Waveguide’s unit cell. From (b) to (e): In plane Ezx vector-field distribution (larger arrows mean more intense) with the total |E|2 in the background (darker is more intense) for the four fundamental modes of parallel periodic waveguides (periodicity a, radius 0.3a, separation s/a = 0.05) cut along y = 0 and y = 0.47a at kx = 0.98π/a. Arrows and colors of all figures share the same normalization.

Fig. 4
Fig. 4

Normalized force per unit energy as a function of the waveguide-separation distance s/a for the four fundamental slow-light modes (kx = 0.98π/a) of two parallel-waveguides shown in inset (periodicity a, diameter d = 0.6a).The inset also shows the normalized force of the y-even/z-even mode for several different wavevectors.

Fig. 5
Fig. 5

(a): Waveguide’s unit cell. From (b) to (e): In plane Ezx vector-field distribution (larger arrows mean more intense) with the total |E|2 in the background (darker is more intense) for the four fundamental modes of parallel waveguides (periodicity a, radius 0.3a, separation s/a = 0.05) cut along y = 0 and y = 0.47a at kx = 0.98π/a. Arrows and colors of all the figures share the same normalization.

Equations (1)

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F U = A Δ ε 2 ( | E | | | 2 + 1 ε 1 ε 2 | D | 2 ) n d A V ε | E | 2 d V ,

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