Abstract

We study the optical force in a micro ring resonator coupled to a bus waveguide, using the coupled mode theory and a numerical Finite Element Method. We show that the resonance enhancement of the force is diminished by the opposing contributions of the attractive and the repulsive forces related to the symmetric and the anti symmetric modes in the coupling region. We show that this limiting factor can be removed by adding asymmetry to the system, e.g. by modifying one of the waveguides. Furthermore, we study for the first time a combined system in which the micro ring resonator is coupled to a one dimensional photonic crystal waveguide. This modified geometry allows further enhancement of the optical force via the combination of optical resonances and slow light effect.

© 2011 OSA

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    [CrossRef] [PubMed]
  31. J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17(5), 3802–3817 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2011 (1)

2010 (10)

Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nature Photonics 4(4), 236–242 (2010).
[CrossRef]

Y. G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81(12), 121101 (2010).
[CrossRef]

T. P. M. Alegre, R. Perahia, and O. Painter, “Optomechanical zipper cavity lasers: theoretical analysis of tuning range and stability,” Opt. Express 18(8), 7872–7885 (2010).
[CrossRef] [PubMed]

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97(18), 181106 (2010).
[CrossRef]

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4(4), 211–217 (2010).
[CrossRef]

S. Huang and G. S. Agarwal, “reactive Coupling Induced Normal Mode Splittings in Microdisk Resonators Coupled to Waveguides,” Phys. Rev. A 81(5), 053810 (2010).
[CrossRef]

C. Huang and L. Zhu, “Enhanced optical forces in 2D hybrid and plasmonic waveguides,” Opt. Lett. 35(10), 1563–1565 (2010).
[CrossRef] [PubMed]

W. H. P. Pernice, M. Li, D. Garcia-Sanchez, and H. X. Tang, “Analysis of short range forces in opto-mechanical devices with a nanogap,” Opt. Express 18(12), 12615–12621 (2010).
[CrossRef] [PubMed]

J. Ma and M. L. Povinelli, “Effect of periodicity on optical forces between a one-dimensional periodic photonic crystal waveguide and an underlying substrate,” Appl. Phys. Lett. 97(15), 151102 (2010).
[CrossRef]

R. Zhao, P. Tassin, T. Koschny, and C. M. Soukoulis, “Optical forces in nanowire pairs and metamaterials,” Opt. Express 18(25), 25665–25676 (2010).
[CrossRef] [PubMed]

2009 (17)

W. H. P. Pernice, M. Li, and H. X. Tang, “Theoretical investigation of the transverse optical force between a silicon nanowire waveguide and a substrate,” Opt. Express 17(3), 1806–1816 (2009).
[CrossRef] [PubMed]

W. H. P. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009).
[CrossRef] [PubMed]

L. Zhu, “Frequency dependence of the optical force between two coupled waveguides,” Opt. Lett. 34(18), 2870–2872 (2009).
[CrossRef] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “A mechanical kerr effect in deformable photonic media,” Appl. Phys. Lett. 95(12), 123507 (2009).
[CrossRef]

J. Ma and M. L. Povinelli, “Large tuning of birefringence in two strip silicon waveguides via optomechanical motion,” Opt. Express 17(20), 17818–17828 (2009).
[CrossRef] [PubMed]

P. T. Rakich, M. A. Popović, and Z. Wang, “General treatment of optical forces and potentials in mechanically variable photonic systems,” Opt. Express 17(20), 18116–18135 (2009).
[CrossRef] [PubMed]

A. Mizrahi, K. Ikeda, F. Bonomelli, V. Lomakin, and Y. Fainman, “Self-alignment and instability of waveguides induced by optical forces,” Phys. Rev. A 80(4), 041804 (2009).
[CrossRef]

V. Liu, M. Povinelli, and S. Fan, “Resonance-enhanced optical forces between coupled photonic crystal slabs,” Opt. Express 17(24), 21897–21909 (2009).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103(22), 223901 (2009).
[CrossRef] [PubMed]

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17(5), 3802–3817 (2009).
[CrossRef] [PubMed]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nature Photonics 3(8), 464–468 (2009).
[CrossRef]

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
[CrossRef] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “Optomechanical coupling in photonic crystal supported nanomechanical waveguides,” Opt. Express 17(15), 12424–12432 (2009).
[CrossRef] [PubMed]

J. Rosenberg, Q. Lin, and O. Painter, “Static and dynamic wavelength routing via the gradient optical force,” Nature Photonics 3(8), 478–483 (2009).
[CrossRef]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[CrossRef] [PubMed]

2008 (3)

D. Goldring, U. Levy, I. E. Dotan, A. Tsukernik, M. Oksman, I. Rubin, Y. David, and D. Mendlovic, “Experimental measurement of quality factor enhancement using slow light modes in one dimensional photonic crystal,” Opt. Express 16(8), 5585–5595 (2008).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[CrossRef] [PubMed]

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, “Radiation induced force between two planar waveguides,” Eur. Phys. J. D 46(1), 157–164 (2008).
[CrossRef]

2007 (3)

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1(7), 416–422 (2007).
[CrossRef]

A. Mizrahi and L. Schächter, “Two-slab all-optical spring,” Opt. Lett. 32(6), 692–694 (2007).
[CrossRef] [PubMed]

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, “Trapping, corralling and spectral bonding of optical resonances through optically induced potentials,” Nat. Photonics 1(11), 658–665 (2007).
[CrossRef]

2005 (4)

Agarwal, G. S.

S. Huang and G. S. Agarwal, “reactive Coupling Induced Normal Mode Splittings in Microdisk Resonators Coupled to Waveguides,” Phys. Rev. A 81(5), 053810 (2010).
[CrossRef]

Alegre, T. P. M.

T. P. M. Alegre, R. Perahia, and O. Painter, “Optomechanical zipper cavity lasers: theoretical analysis of tuning range and stability,” Opt. Express 18(8), 7872–7885 (2010).
[CrossRef] [PubMed]

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97(18), 181106 (2010).
[CrossRef]

Antezza, M.

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, “Radiation induced force between two planar waveguides,” Eur. Phys. J. D 46(1), 157–164 (2008).
[CrossRef]

Baehr-Jones, T.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[CrossRef] [PubMed]

Baets, R.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
[CrossRef] [PubMed]

Bonomelli, F.

A. Mizrahi, K. Ikeda, F. Bonomelli, V. Lomakin, and Y. Fainman, “Self-alignment and instability of waveguides induced by optical forces,” Phys. Rev. A 80(4), 041804 (2009).
[CrossRef]

Camacho, R.

Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nature Photonics 4(4), 236–242 (2010).
[CrossRef]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17(5), 3802–3817 (2009).
[CrossRef] [PubMed]

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[CrossRef] [PubMed]

Capasso, F.

Carusotto, I.

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, “Radiation induced force between two planar waveguides,” Eur. Phys. J. D 46(1), 157–164 (2008).
[CrossRef]

Chan, C. T.

Chan, J.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[CrossRef] [PubMed]

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17(5), 3802–3817 (2009).
[CrossRef] [PubMed]

Chang, D.

Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nature Photonics 4(4), 236–242 (2010).
[CrossRef]

Chen, L.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[CrossRef] [PubMed]

David, Y.

De Vlaminck, I.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
[CrossRef] [PubMed]

Dotan, I. E.

Eichenfield, M.

Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nature Photonics 4(4), 236–242 (2010).
[CrossRef]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[CrossRef] [PubMed]

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17(5), 3802–3817 (2009).
[CrossRef] [PubMed]

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1(7), 416–422 (2007).
[CrossRef]

Fainman, Y.

A. Mizrahi, K. Ikeda, F. Bonomelli, V. Lomakin, and Y. Fainman, “Self-alignment and instability of waveguides induced by optical forces,” Phys. Rev. A 80(4), 041804 (2009).
[CrossRef]

Fan, S.

Fong, K. Y.

Garcia-Sanchez, D.

Goldring, D.

Gondarenko, A.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[CrossRef] [PubMed]

Hochberg, M.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[CrossRef] [PubMed]

Huang, C.

Huang, S.

S. Huang and G. S. Agarwal, “reactive Coupling Induced Normal Mode Splittings in Microdisk Resonators Coupled to Waveguides,” Phys. Rev. A 81(5), 053810 (2010).
[CrossRef]

Ibanescu, M.

Ikeda, K.

A. Mizrahi, K. Ikeda, F. Bonomelli, V. Lomakin, and Y. Fainman, “Self-alignment and instability of waveguides induced by optical forces,” Phys. Rev. A 80(4), 041804 (2009).
[CrossRef]

Ippen, E. P.

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, “Trapping, corralling and spectral bonding of optical resonances through optically induced potentials,” Nat. Photonics 1(11), 658–665 (2007).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Koschny, T.

Kuramochi, E.

Y. G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81(12), 121101 (2010).
[CrossRef]

Lagae, L.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
[CrossRef] [PubMed]

Lee, S.

Levy, U.

Li, M.

W. H. P. Pernice, M. Li, D. Garcia-Sanchez, and H. X. Tang, “Analysis of short range forces in opto-mechanical devices with a nanogap,” Opt. Express 18(12), 12615–12621 (2010).
[CrossRef] [PubMed]

W. H. P. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009).
[CrossRef] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “A mechanical kerr effect in deformable photonic media,” Appl. Phys. Lett. 95(12), 123507 (2009).
[CrossRef]

W. H. P. Pernice, M. Li, and H. X. Tang, “Theoretical investigation of the transverse optical force between a silicon nanowire waveguide and a substrate,” Opt. Express 17(3), 1806–1816 (2009).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103(22), 223901 (2009).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nature Photonics 3(8), 464–468 (2009).
[CrossRef]

W. H. P. Pernice, M. Li, and H. X. Tang, “Optomechanical coupling in photonic crystal supported nanomechanical waveguides,” Opt. Express 17(15), 12424–12432 (2009).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[CrossRef] [PubMed]

Lin, Q.

Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nature Photonics 4(4), 236–242 (2010).
[CrossRef]

J. Rosenberg, Q. Lin, and O. Painter, “Static and dynamic wavelength routing via the gradient optical force,” Nature Photonics 3(8), 478–483 (2009).
[CrossRef]

Lin, Z.

Lipson, M.

G. S. Wiederhecker, S. Manipatruni, S. Lee, and M. Lipson, “Broadband tuning of optomechanical cavities,” Opt. Express 19(3), 2782–2790 (2011).
[CrossRef] [PubMed]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[CrossRef] [PubMed]

Liu, V.

Lomakin, V.

A. Mizrahi, K. Ikeda, F. Bonomelli, V. Lomakin, and Y. Fainman, “Self-alignment and instability of waveguides induced by optical forces,” Phys. Rev. A 80(4), 041804 (2009).
[CrossRef]

Loncar, M.

Ma, J.

J. Ma and M. L. Povinelli, “Effect of periodicity on optical forces between a one-dimensional periodic photonic crystal waveguide and an underlying substrate,” Appl. Phys. Lett. 97(15), 151102 (2010).
[CrossRef]

J. Ma and M. L. Povinelli, “Large tuning of birefringence in two strip silicon waveguides via optomechanical motion,” Opt. Express 17(20), 17818–17828 (2009).
[CrossRef] [PubMed]

Maes, B.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
[CrossRef] [PubMed]

Manipatruni, S.

Matsuo, S.

Y. G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81(12), 121101 (2010).
[CrossRef]

Mendlovic, D.

Michael, C. P.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1(7), 416–422 (2007).
[CrossRef]

Mizrahi, A.

Ng, J.

Notomi, M.

Y. G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81(12), 121101 (2010).
[CrossRef]

Oksman, M.

Painter, O.

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97(18), 181106 (2010).
[CrossRef]

T. P. M. Alegre, R. Perahia, and O. Painter, “Optomechanical zipper cavity lasers: theoretical analysis of tuning range and stability,” Opt. Express 18(8), 7872–7885 (2010).
[CrossRef] [PubMed]

Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nature Photonics 4(4), 236–242 (2010).
[CrossRef]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[CrossRef] [PubMed]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17(5), 3802–3817 (2009).
[CrossRef] [PubMed]

J. Rosenberg, Q. Lin, and O. Painter, “Static and dynamic wavelength routing via the gradient optical force,” Nature Photonics 3(8), 478–483 (2009).
[CrossRef]

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1(7), 416–422 (2007).
[CrossRef]

Perahia, R.

T. P. M. Alegre, R. Perahia, and O. Painter, “Optomechanical zipper cavity lasers: theoretical analysis of tuning range and stability,” Opt. Express 18(8), 7872–7885 (2010).
[CrossRef] [PubMed]

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1(7), 416–422 (2007).
[CrossRef]

Pernice, W. H. P.

W. H. P. Pernice, M. Li, D. Garcia-Sanchez, and H. X. Tang, “Analysis of short range forces in opto-mechanical devices with a nanogap,” Opt. Express 18(12), 12615–12621 (2010).
[CrossRef] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “A mechanical kerr effect in deformable photonic media,” Appl. Phys. Lett. 95(12), 123507 (2009).
[CrossRef]

W. H. P. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009).
[CrossRef] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “Theoretical investigation of the transverse optical force between a silicon nanowire waveguide and a substrate,” Opt. Express 17(3), 1806–1816 (2009).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103(22), 223901 (2009).
[CrossRef] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “Optomechanical coupling in photonic crystal supported nanomechanical waveguides,” Opt. Express 17(15), 12424–12432 (2009).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nature Photonics 3(8), 464–468 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[CrossRef] [PubMed]

Popovic, M. A.

P. T. Rakich, M. A. Popović, and Z. Wang, “General treatment of optical forces and potentials in mechanically variable photonic systems,” Opt. Express 17(20), 18116–18135 (2009).
[CrossRef] [PubMed]

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, “Trapping, corralling and spectral bonding of optical resonances through optically induced potentials,” Nat. Photonics 1(11), 658–665 (2007).
[CrossRef]

Povinelli, M.

Povinelli, M. L.

Rakich, P. T.

P. T. Rakich, M. A. Popović, and Z. Wang, “General treatment of optical forces and potentials in mechanically variable photonic systems,” Opt. Express 17(20), 18116–18135 (2009).
[CrossRef] [PubMed]

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, “Trapping, corralling and spectral bonding of optical resonances through optically induced potentials,” Nat. Photonics 1(11), 658–665 (2007).
[CrossRef]

Recati, A.

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, “Radiation induced force between two planar waveguides,” Eur. Phys. J. D 46(1), 157–164 (2008).
[CrossRef]

Riboli, F.

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, “Radiation induced force between two planar waveguides,” Eur. Phys. J. D 46(1), 157–164 (2008).
[CrossRef]

Roels, J.

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4(4), 211–217 (2010).
[CrossRef]

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
[CrossRef] [PubMed]

Roh, Y. G.

Y. G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81(12), 121101 (2010).
[CrossRef]

Rosenberg, J.

Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nature Photonics 4(4), 236–242 (2010).
[CrossRef]

J. Rosenberg, Q. Lin, and O. Painter, “Static and dynamic wavelength routing via the gradient optical force,” Nature Photonics 3(8), 478–483 (2009).
[CrossRef]

Rubin, I.

Safavi-Naeini, A. H.

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97(18), 181106 (2010).
[CrossRef]

Sato, T.

Y. G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81(12), 121101 (2010).
[CrossRef]

Schächter, L.

Sheng, P.

Shinya, A.

Y. G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81(12), 121101 (2010).
[CrossRef]

Smythe, E. J.

Soljacic, M.

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, “Trapping, corralling and spectral bonding of optical resonances through optically induced potentials,” Nat. Photonics 1(11), 658–665 (2007).
[CrossRef]

Soukoulis, C. M.

Tanabe, T.

Y. G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81(12), 121101 (2010).
[CrossRef]

Tang, H. X.

W. H. P. Pernice, M. Li, D. Garcia-Sanchez, and H. X. Tang, “Analysis of short range forces in opto-mechanical devices with a nanogap,” Opt. Express 18(12), 12615–12621 (2010).
[CrossRef] [PubMed]

W. H. P. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009).
[CrossRef] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “A mechanical kerr effect in deformable photonic media,” Appl. Phys. Lett. 95(12), 123507 (2009).
[CrossRef]

W. H. P. Pernice, M. Li, and H. X. Tang, “Theoretical investigation of the transverse optical force between a silicon nanowire waveguide and a substrate,” Opt. Express 17(3), 1806–1816 (2009).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103(22), 223901 (2009).
[CrossRef] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “Optomechanical coupling in photonic crystal supported nanomechanical waveguides,” Opt. Express 17(15), 12424–12432 (2009).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nature Photonics 3(8), 464–468 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[CrossRef] [PubMed]

Taniyama, H.

Y. G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81(12), 121101 (2010).
[CrossRef]

Tassin, P.

Tsukernik, A.

Vahala, K. J.

Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nature Photonics 4(4), 236–242 (2010).
[CrossRef]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[CrossRef] [PubMed]

Van Thourhout, D.

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4(4), 211–217 (2010).
[CrossRef]

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
[CrossRef] [PubMed]

Wang, Z.

Wiederhecker, G. S.

G. S. Wiederhecker, S. Manipatruni, S. Lee, and M. Lipson, “Broadband tuning of optomechanical cavities,” Opt. Express 19(3), 2782–2790 (2011).
[CrossRef] [PubMed]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[CrossRef] [PubMed]

Winger, M.

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97(18), 181106 (2010).
[CrossRef]

Xiong, C.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[CrossRef] [PubMed]

Zhao, R.

Zhu, L.

Appl. Phys. Lett. (3)

W. H. P. Pernice, M. Li, and H. X. Tang, “A mechanical kerr effect in deformable photonic media,” Appl. Phys. Lett. 95(12), 123507 (2009).
[CrossRef]

J. Ma and M. L. Povinelli, “Effect of periodicity on optical forces between a one-dimensional periodic photonic crystal waveguide and an underlying substrate,” Appl. Phys. Lett. 97(15), 151102 (2010).
[CrossRef]

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97(18), 181106 (2010).
[CrossRef]

Eur. Phys. J. D (1)

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, “Radiation induced force between two planar waveguides,” Eur. Phys. J. D 46(1), 157–164 (2008).
[CrossRef]

Nat. Nanotechnol. (1)

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
[CrossRef] [PubMed]

Nat. Photonics (3)

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, “Trapping, corralling and spectral bonding of optical resonances through optically induced potentials,” Nat. Photonics 1(11), 658–665 (2007).
[CrossRef]

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4(4), 211–217 (2010).
[CrossRef]

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1(7), 416–422 (2007).
[CrossRef]

Nature (4)

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[CrossRef] [PubMed]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[CrossRef] [PubMed]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[CrossRef] [PubMed]

Nature Photonics (3)

Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nature Photonics 4(4), 236–242 (2010).
[CrossRef]

J. Rosenberg, Q. Lin, and O. Painter, “Static and dynamic wavelength routing via the gradient optical force,” Nature Photonics 3(8), 478–483 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nature Photonics 3(8), 464–468 (2009).
[CrossRef]

Opt. Express (14)

W. H. P. Pernice, M. Li, and H. X. Tang, “Optomechanical coupling in photonic crystal supported nanomechanical waveguides,” Opt. Express 17(15), 12424–12432 (2009).
[CrossRef] [PubMed]

R. Zhao, P. Tassin, T. Koschny, and C. M. Soukoulis, “Optical forces in nanowire pairs and metamaterials,” Opt. Express 18(25), 25665–25676 (2010).
[CrossRef] [PubMed]

W. H. P. Pernice, M. Li, D. Garcia-Sanchez, and H. X. Tang, “Analysis of short range forces in opto-mechanical devices with a nanogap,” Opt. Express 18(12), 12615–12621 (2010).
[CrossRef] [PubMed]

G. S. Wiederhecker, S. Manipatruni, S. Lee, and M. Lipson, “Broadband tuning of optomechanical cavities,” Opt. Express 19(3), 2782–2790 (2011).
[CrossRef] [PubMed]

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery- mode resonators,” Opt. Express 13(20), 8286–8295 (2005).
[CrossRef] [PubMed]

W. H. P. Pernice, M. Li, and H. X. Tang, “Theoretical investigation of the transverse optical force between a silicon nanowire waveguide and a substrate,” Opt. Express 17(3), 1806–1816 (2009).
[CrossRef] [PubMed]

W. H. P. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009).
[CrossRef] [PubMed]

J. Ma and M. L. Povinelli, “Large tuning of birefringence in two strip silicon waveguides via optomechanical motion,” Opt. Express 17(20), 17818–17828 (2009).
[CrossRef] [PubMed]

P. T. Rakich, M. A. Popović, and Z. Wang, “General treatment of optical forces and potentials in mechanically variable photonic systems,” Opt. Express 17(20), 18116–18135 (2009).
[CrossRef] [PubMed]

A. Mizrahi and L. Schächter, “Mirror manipulation by attractive and repulsive forces of guided waves,” Opt. Express 13(24), 9804–9811 (2005).
[CrossRef] [PubMed]

V. Liu, M. Povinelli, and S. Fan, “Resonance-enhanced optical forces between coupled photonic crystal slabs,” Opt. Express 17(24), 21897–21909 (2009).
[CrossRef] [PubMed]

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17(5), 3802–3817 (2009).
[CrossRef] [PubMed]

T. P. M. Alegre, R. Perahia, and O. Painter, “Optomechanical zipper cavity lasers: theoretical analysis of tuning range and stability,” Opt. Express 18(8), 7872–7885 (2010).
[CrossRef] [PubMed]

D. Goldring, U. Levy, I. E. Dotan, A. Tsukernik, M. Oksman, I. Rubin, Y. David, and D. Mendlovic, “Experimental measurement of quality factor enhancement using slow light modes in one dimensional photonic crystal,” Opt. Express 16(8), 5585–5595 (2008).
[CrossRef] [PubMed]

Opt. Lett. (5)

Phys. Rev. A (2)

S. Huang and G. S. Agarwal, “reactive Coupling Induced Normal Mode Splittings in Microdisk Resonators Coupled to Waveguides,” Phys. Rev. A 81(5), 053810 (2010).
[CrossRef]

A. Mizrahi, K. Ikeda, F. Bonomelli, V. Lomakin, and Y. Fainman, “Self-alignment and instability of waveguides induced by optical forces,” Phys. Rev. A 80(4), 041804 (2009).
[CrossRef]

Phys. Rev. B (1)

Y. G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81(12), 121101 (2010).
[CrossRef]

Phys. Rev. Lett. (1)

M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103(22), 223901 (2009).
[CrossRef] [PubMed]

Other (3)

J. D. Jackson, “Classical Electrodynamics”, 3rd ed. (Wiley, 1998), Chap. 6.7.

K. Okamoto, “fundamentals of optical waveguides”, 2nd ed. (Elsevier, 2006), Chap. 2.2.

H. Kogelnik, “Topics in Applied Physics” (Springer-Verlag, 1975), Vol. 7, Chap. 2.

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of the investigated structure. The system consists of an MRR coupled to a bus WG. The substrate under the bus WG is etched to create a free standing mechanical beam. For simplicity we perform a 2-D analysis but we keep the 3-D picture representation for visualization purposes.

Fig. 2
Fig. 2

Schematics of the 2-d system. (a) The notations of the EM fields in the bus WG and in the MRR as well as the phase accumulation in the MRR are shown. (b) The coupling region is sketched together with the two supermodes.

Fig. 3
Fig. 3

(a) Power enhancement and OF as a function of wavelength. A 250nm gap is assumed between two 400nm slab WGs with n=2.446 . The WGs are coupled along a coupling region of 4μm . The MRR properties are provided in the numerical section. (b) Zoom in on a specific resonance denoted by the rectangle.

Fig. 4
Fig. 4

The electric field distribution in the coupling region of the racetrack MRR is shown. Figure (a) [(b)] were calculated at wavelength in which the obtained force is maximal positive [negative], where the relative phase between the signals is close to π [0] . Figure (c) was calculated at a resonance wavelength in which the relative phase at the beginning of the coupling region is 3π /2 . The phase difference evolves and becomes π/2 at the output of the coupling region. For visualization purposes we modified the color scale between the 3 figures.

Fig. 5
Fig. 5

The force in an asymmetric MRR system as a function of the wavelength. The effective refractive index of the MRR is assumed to be 2.66. The separation gap is 250nm. These parameters corresponds to quality factor of Q10,000 .

Fig. 6
Fig. 6

Force as a function of wavelength for different gaps between the bus and the MRR. As can be seen, the Q factor grows with the increase of the separation gap. However, the magnitude of the force decreases with the increase in separation gap, because of the lower overlap between the mode and the WG. The inset shows the maximal force values normalized by the force that is obtained in the 2 slabs system for the same gap, as a function of the separation gap.

Fig. 7
Fig. 7

Tuning the MRR using the optomechanical effect. The power enhancement in the resonator near resonance is shown for the suggested device, at two power levels in the WG.

Fig. 8
Fig. 8

(a) The group index in the vicinity of the first band edge of the PhC WG as a function of wavelength. Two structures are considered as shown in the insets with the electric field mode superimposed: A single silicon WG with periodic perturbation of air holes (data can be found in the paper) and two coupled silicon WGs with periodic perturbation of holes. (b) The force obtained in the periodically perturbed double WG system, normalized by the value obtained in the equivalent unperturbed structure.

Fig. 9
Fig. 9

(a) drawing of the simulated structure, consisting of an MRR separated from a bus WG. Periodic perturbation of 30 air holes is embedded into the WG. The specific parameters are given in the text. (b) Transmission of light emerging from the structure of the MRR and a periodically perturbed bus WG as a function of the incident wavelength and the MRR refractive index. Red dotted line represents the shift in resonance wavelength as a function of variations in the MRR refractive index.

Fig. 10
Fig. 10

The transmission and the force acting on the WG, plotted against the wavelength in the region next to the band edge. The refractive index of the MRR WG is assumed to be n MRR =2.4572 .

Fig. 11
Fig. 11

The OF calculated for two Si (n = 3.45) WGs having identical cross sections of 400nm×300nm . The WGs are excited by an out of plane (TM) polarized, laser source at the wavelength of λ=1.55μm . The broken lines (solid lines) represent the force for an anti-symmetric (symmetric) mode excitation. The blue lines are the full three dimensional calculation, while the red lines refer to a two dimensional system, effectively two slabs of 400nm with n = 2.446.

Equations (9)

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F x = 1 4 [ ε 0 | E y | 2 + μ 0 ( | H x | 2 | H z | 2 )]
ψ=L+R
w= iα e iθ sin(κD) 1α e iθ cos(κD)
ψ=L+wR
( L R )=( a b c d )( S A )
a= L S * dx= R S * dx= c,b= L A * dx= R A * dx=d
F= a 2 (1+ | w | 2 +2{ w }) F sym + b 2 (1+ | w | 2 2{ w }) F antisym +2ab{ e iΔβz (1 | w | 2 +2i{ w })} F interference
F | resonance 1 4 (1+ | w | 2 )[ F sym + F asym ]
n g =c ( ω k ) 1

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