Abstract

This paper demonstrates the optical nonlinearity in opto-mechanical ring resonators that consist of a bus waveguide and two ring resonators, which is induced by the optical gradient force and characterized by the Kerr-like coefficient. Each ring resonator has a free-hanging arc that is perpendicularly deformable by an optical gradient force and subsequently this deformation changes the effective refractive index (ERI) of the ring resonator. The change of the ERI induces optical nonlinearity into the system, which is described by an equivalent Kerr coefficient (Kerr-like coefficient). Based on the experimental results, the Kerr-like coefficient of the ring resonator system falls in the range from 7.64 × 10−12 to 2.01 × 10−10 m2W−1, which is at least 6-order higher than the silicon’s Kerr coefficient. The dramatically improved optical nonlinearity in the opto-mechanical ring resonators promises potential applications in low power optical signal processing, modulation and bio-sensing.

© 2012 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  24. S. Pamidighantam, R. Puers, K. Baert, and H. A. C. Tilmans, “Pull-in voltage analysis of electrostatically actuated beam structures with fixed-fixed and fixed-free end conditions,” J. Micromech. Microeng.12(4), 458–464 (2002).
    [CrossRef]
  25. Z. Bor, K. Osvay, B. Racz, and G. Szabo, “Group refractive-index measurement by michelson interferometer,” Opt. Commun.78(2), 109–112 (1990).
    [CrossRef]
  26. H. Rokhsari and K. J. Vahala, “Observation of Kerr nonlinearity in microcavities at room temperature,” Opt. Lett.30(4), 427–429 (2005).
    [CrossRef] [PubMed]

2012

H. Cai, K. J. Xu, A. Q. Liu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Nano-opto-mechanical actuator driven by gradient optical force,” Appl. Phys. Lett.100(1), 013108 (2012).
[CrossRef]

J. F. Tao, J. Wu, H. Cai, Q. X. Zhang, J. M. Tsai, J. T. Lin, and A. Q. Liu, “A nanomachined optical logic gate driven by gradient optical force,” Appl. Phys. Lett.100(11), 113104 (2012).
[CrossRef]

2011

2009

S. Manipatruni, J. T. Robinson, and M. Lipson, “Optical Nonreciprocity in Optomechanical Structures,” Phys. Rev. Lett.102(21), 213903 (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. Express17(3), 1806–1816 (2009).
[CrossRef] [PubMed]

I. S. Grudinin and K. J. Vahala, “Thermal instability of a compound resonator,” Opt. Express17(16), 14088–14097 (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]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
[CrossRef]

2008

2007

2006

2005

2002

S. Pamidighantam, R. Puers, K. Baert, and H. A. C. Tilmans, “Pull-in voltage analysis of electrostatically actuated beam structures with fixed-fixed and fixed-free end conditions,” J. Micromech. Microeng.12(4), 458–464 (2002).
[CrossRef]

1990

Z. Bor, K. Osvay, B. Racz, and G. Szabo, “Group refractive-index measurement by michelson interferometer,” Opt. Commun.78(2), 109–112 (1990).
[CrossRef]

Andreani, L. C.

Arcizet, O.

R. Rivière, S. Deléglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A83(6), 063835 (2011).
[CrossRef]

Baert, K.

S. Pamidighantam, R. Puers, K. Baert, and H. A. C. Tilmans, “Pull-in voltage analysis of electrostatically actuated beam structures with fixed-fixed and fixed-free end conditions,” J. Micromech. Microeng.12(4), 458–464 (2002).
[CrossRef]

Baets, R.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
[CrossRef]

G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhout, G. Morthier, and R. Baets, “Optical bistability and pulsating behaviour in Silicon-On-Insulator ring resonator structures,” Opt. Express13(23), 9623–9628 (2005).
[CrossRef] [PubMed]

Biaggio, I.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
[CrossRef]

Bogaerts, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
[CrossRef]

G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhout, G. Morthier, and R. Baets, “Optical bistability and pulsating behaviour in Silicon-On-Insulator ring resonator structures,” Opt. Express13(23), 9623–9628 (2005).
[CrossRef] [PubMed]

Bor, Z.

Z. Bor, K. Osvay, B. Racz, and G. Szabo, “Group refractive-index measurement by michelson interferometer,” Opt. Commun.78(2), 109–112 (1990).
[CrossRef]

Brosi, J. M.

Cai, H.

H. Cai, K. J. Xu, A. Q. Liu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Nano-opto-mechanical actuator driven by gradient optical force,” Appl. Phys. Lett.100(1), 013108 (2012).
[CrossRef]

J. F. Tao, J. Wu, H. Cai, Q. X. Zhang, J. M. Tsai, J. T. Lin, and A. Q. Liu, “A nanomachined optical logic gate driven by gradient optical force,” Appl. Phys. Lett.100(11), 113104 (2012).
[CrossRef]

Chen, L.

Chen, T.

Chetrit, Y.

Chin, M. K.

Y. M. Landobasa, S. Darmawan, and M. K. Chin, “Matrix analysis of 2-D microresonator lattice optical filters,” IEEE J. Quantum Electron.41(11), 1410–1418 (2005).
[CrossRef]

Ciftcioglu, B.

Cohen, O.

Darmawan, S.

Y. M. Landobasa, S. Darmawan, and M. K. Chin, “Matrix analysis of 2-D microresonator lattice optical filters,” IEEE J. Quantum Electron.41(11), 1410–1418 (2005).
[CrossRef]

Deléglise, S.

R. Rivière, S. Deléglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A83(6), 063835 (2011).
[CrossRef]

Diederich, F.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
[CrossRef]

Dumon, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
[CrossRef]

G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhout, G. Morthier, and R. Baets, “Optical bistability and pulsating behaviour in Silicon-On-Insulator ring resonator structures,” Opt. Express13(23), 9623–9628 (2005).
[CrossRef] [PubMed]

Esembeson, B.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
[CrossRef]

Fang, A.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005).
[CrossRef] [PubMed]

Fang, Q.

H. Cai, K. J. Xu, A. Q. Liu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Nano-opto-mechanical actuator driven by gradient optical force,” Appl. Phys. Lett.100(1), 013108 (2012).
[CrossRef]

Freude, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
[CrossRef]

J. M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, “High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide,” Opt. Express16(6), 4177–4191 (2008).
[CrossRef] [PubMed]

Gavartin, E.

R. Rivière, S. Deléglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A83(6), 063835 (2011).
[CrossRef]

Grudinin, I.

Grudinin, I. S.

Hak, D.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005).
[CrossRef] [PubMed]

Izhaky, N.

Jones, R.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005).
[CrossRef] [PubMed]

Kippenberg, T. J.

R. Rivière, S. Deléglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A83(6), 063835 (2011).
[CrossRef]

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: Back-action at the mesoscale,” Science321(5893), 1172–1176 (2008).
[CrossRef] [PubMed]

Koos, C.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
[CrossRef]

J. M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, “High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide,” Opt. Express16(6), 4177–4191 (2008).
[CrossRef] [PubMed]

Kuo, Y. H.

Kwong, D. L.

H. Cai, K. J. Xu, A. Q. Liu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Nano-opto-mechanical actuator driven by gradient optical force,” Appl. Phys. Lett.100(1), 013108 (2012).
[CrossRef]

Landobasa, Y. M.

Y. M. Landobasa, S. Darmawan, and M. K. Chin, “Matrix analysis of 2-D microresonator lattice optical filters,” IEEE J. Quantum Electron.41(11), 1410–1418 (2005).
[CrossRef]

Lee, H.

Leuthold, J.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
[CrossRef]

J. M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, “High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide,” Opt. Express16(6), 4177–4191 (2008).
[CrossRef] [PubMed]

Li, M.

Liao, L.

Lin, J. T.

J. F. Tao, J. Wu, H. Cai, Q. X. Zhang, J. M. Tsai, J. T. Lin, and A. Q. Liu, “A nanomachined optical logic gate driven by gradient optical force,” Appl. Phys. Lett.100(11), 113104 (2012).
[CrossRef]

Lipson, M.

Liu, A.

Liu, A. Q.

H. Cai, K. J. Xu, A. Q. Liu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Nano-opto-mechanical actuator driven by gradient optical force,” Appl. Phys. Lett.100(1), 013108 (2012).
[CrossRef]

J. F. Tao, J. Wu, H. Cai, Q. X. Zhang, J. M. Tsai, J. T. Lin, and A. Q. Liu, “A nanomachined optical logic gate driven by gradient optical force,” Appl. Phys. Lett.100(11), 113104 (2012).
[CrossRef]

Liu, Y.

H. K. Tsang and Y. Liu, “Nonlinear optical properties of silicon waveguides,” Semicond. Sci. Technol.23(6), 064007 (2008).
[CrossRef]

Lo, G. Q.

H. Cai, K. J. Xu, A. Q. Liu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Nano-opto-mechanical actuator driven by gradient optical force,” Appl. Phys. Lett.100(1), 013108 (2012).
[CrossRef]

Ma, C. S.

C. S. Ma, Y. Z. Xu, X. Yan, Z. K. Qin, and X. Y. Wang, “Optimization and analysis of series-coupled microring resonator arrays,” Opt. Commun.262(1), 41–46 (2006).
[CrossRef]

Ma, J.

Manipatruni, S.

S. Manipatruni, J. T. Robinson, and M. Lipson, “Optical Nonreciprocity in Optomechanical Structures,” Phys. Rev. Lett.102(21), 213903 (2009).
[CrossRef] [PubMed]

Michinobu, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
[CrossRef]

Morthier, G.

Nguyen, H.

Osvay, K.

Z. Bor, K. Osvay, B. Racz, and G. Szabo, “Group refractive-index measurement by michelson interferometer,” Opt. Commun.78(2), 109–112 (1990).
[CrossRef]

Pamidighantam, S.

S. Pamidighantam, R. Puers, K. Baert, and H. A. C. Tilmans, “Pull-in voltage analysis of electrostatically actuated beam structures with fixed-fixed and fixed-free end conditions,” J. Micromech. Microeng.12(4), 458–464 (2002).
[CrossRef]

Paniccia, M.

Pernice, W. H. P.

Povinelli, M. L.

Priem, G.

Puers, R.

S. Pamidighantam, R. Puers, K. Baert, and H. A. C. Tilmans, “Pull-in voltage analysis of electrostatically actuated beam structures with fixed-fixed and fixed-free end conditions,” J. Micromech. Microeng.12(4), 458–464 (2002).
[CrossRef]

Qin, Z. K.

C. S. Ma, Y. Z. Xu, X. Yan, Z. K. Qin, and X. Y. Wang, “Optimization and analysis of series-coupled microring resonator arrays,” Opt. Commun.262(1), 41–46 (2006).
[CrossRef]

Racz, B.

Z. Bor, K. Osvay, B. Racz, and G. Szabo, “Group refractive-index measurement by michelson interferometer,” Opt. Commun.78(2), 109–112 (1990).
[CrossRef]

Rivière, R.

R. Rivière, S. Deléglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A83(6), 063835 (2011).
[CrossRef]

Robinson, J. T.

S. Manipatruni, J. T. Robinson, and M. Lipson, “Optical Nonreciprocity in Optomechanical Structures,” Phys. Rev. Lett.102(21), 213903 (2009).
[CrossRef] [PubMed]

J. T. Robinson, L. Chen, and M. Lipson, “On-chip gas detection in silicon optical microcavities,” Opt. Express16(6), 4296–4301 (2008).
[CrossRef] [PubMed]

Rokhsari, H.

Rong, H.

Rubin, D.

Schliesser, A.

R. Rivière, S. Deléglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A83(6), 063835 (2011).
[CrossRef]

Sih, V.

Szabo, G.

Z. Bor, K. Osvay, B. Racz, and G. Szabo, “Group refractive-index measurement by michelson interferometer,” Opt. Commun.78(2), 109–112 (1990).
[CrossRef]

Tang, H. X.

Tao, J. F.

J. F. Tao, J. Wu, H. Cai, Q. X. Zhang, J. M. Tsai, J. T. Lin, and A. Q. Liu, “A nanomachined optical logic gate driven by gradient optical force,” Appl. Phys. Lett.100(11), 113104 (2012).
[CrossRef]

Tilmans, H. A. C.

S. Pamidighantam, R. Puers, K. Baert, and H. A. C. Tilmans, “Pull-in voltage analysis of electrostatically actuated beam structures with fixed-fixed and fixed-free end conditions,” J. Micromech. Microeng.12(4), 458–464 (2002).
[CrossRef]

Tsai, J. M.

J. F. Tao, J. Wu, H. Cai, Q. X. Zhang, J. M. Tsai, J. T. Lin, and A. Q. Liu, “A nanomachined optical logic gate driven by gradient optical force,” Appl. Phys. Lett.100(11), 113104 (2012).
[CrossRef]

Tsang, H. K.

H. K. Tsang and Y. Liu, “Nonlinear optical properties of silicon waveguides,” Semicond. Sci. Technol.23(6), 064007 (2008).
[CrossRef]

Vahala, K.

Vahala, K. J.

Vallaitis, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
[CrossRef]

Van Thourhout, D.

Vorreau, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
[CrossRef]

Waldow, M.

Wang, X. Y.

C. S. Ma, Y. Z. Xu, X. Yan, Z. K. Qin, and X. Y. Wang, “Optimization and analysis of series-coupled microring resonator arrays,” Opt. Commun.262(1), 41–46 (2006).
[CrossRef]

Weis, S.

R. Rivière, S. Deléglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A83(6), 063835 (2011).
[CrossRef]

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J. F. Tao, J. Wu, H. Cai, Q. X. Zhang, J. M. Tsai, J. T. Lin, and A. Q. Liu, “A nanomachined optical logic gate driven by gradient optical force,” Appl. Phys. Lett.100(11), 113104 (2012).
[CrossRef]

Xu, K. J.

H. Cai, K. J. Xu, A. Q. Liu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Nano-opto-mechanical actuator driven by gradient optical force,” Appl. Phys. Lett.100(1), 013108 (2012).
[CrossRef]

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[CrossRef]

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C. S. Ma, Y. Z. Xu, X. Yan, Z. K. Qin, and X. Y. Wang, “Optimization and analysis of series-coupled microring resonator arrays,” Opt. Commun.262(1), 41–46 (2006).
[CrossRef]

Yu, M. B.

H. Cai, K. J. Xu, A. Q. Liu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Nano-opto-mechanical actuator driven by gradient optical force,” Appl. Phys. Lett.100(1), 013108 (2012).
[CrossRef]

Zhang, Q. X.

J. F. Tao, J. Wu, H. Cai, Q. X. Zhang, J. M. Tsai, J. T. Lin, and A. Q. Liu, “A nanomachined optical logic gate driven by gradient optical force,” Appl. Phys. Lett.100(11), 113104 (2012).
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Appl. Phys. Lett.

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H. Cai, K. J. Xu, A. Q. Liu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Nano-opto-mechanical actuator driven by gradient optical force,” Appl. Phys. Lett.100(1), 013108 (2012).
[CrossRef]

J. F. Tao, J. Wu, H. Cai, Q. X. Zhang, J. M. Tsai, J. T. Lin, and A. Q. Liu, “A nanomachined optical logic gate driven by gradient optical force,” Appl. Phys. Lett.100(11), 113104 (2012).
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IEEE J. Quantum Electron.

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Nat. Photonics

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics3(4), 216–219 (2009).
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Nature

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005).
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Opt. Express

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. Express17(3), 1806–1816 (2009).
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A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express15(2), 660–668 (2007).
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R. Rivière, S. Deléglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A83(6), 063835 (2011).
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Figures (7)

Fig. 1
Fig. 1

(a) Schematic illustration of the opto-mechanical ring resonator system; and (b) demonstration of the deformation of the free-hanging arcs caused by the optical gradient forces.

Fig. 2
Fig. 2

Contour plot of (a) the effective refractive index and (b) the optical force in the gap-wavelength domain.

Fig. 3
Fig. 3

Optical force and mechanical force versus the deflection. The circles indicate the different deflections corresponding to different wavelengths.

Fig. 4
Fig. 4

(a) SEM image of the opto-mechanical ring resonator system with a released bus waveguide and two partially released ring resonators, and (b) the schematic of experimental setup.

Fig. 5
Fig. 5

Transmission spectrum of the opto-mechanical ring resonator system.

Fig. 6
Fig. 6

Shift of absorption peak of ring 1 under different control wavelengths.

Fig. 7
Fig. 7

(a) Effective input power for ring 1 versus the control wavelength; and (b) Kerr-like coefficient versus the effective input power.

Equations (10)

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

[ E 3 E 4 E 5 ]=[ t j r 1 j r 2 j r 1 t 1 0 j r 2 0 t 2 ][ E 0 E 1 E 2 ],
{ B 1 =| E 1 E 0 |=| j r 1 a 1 e j ϕ 1 1 t 1 a 1 e j ϕ 1 | B 2 =| E 2 E 0 |=| j r 2 a 2 e j ϕ 2 1 t 2 a 2 e j ϕ 2 | ,
E 3 E 0 =t r 1 2 a 1 e j ϕ 1 1 t 1 a 1 e j ϕ 1 r 2 2 a 2 e j ϕ 2 1 t 2 a 2 e j ϕ 2 .
I c = B 2 I 0 .
n 2 = Δ n eff Δ I c .
n 2 = Δ n eff Δ I a ,
I a = ( 1T( λ ) ) I 0 ( λ ) dλ,
F o = 1 n eff n eff g P c n g c ,
n 2 =A Δ n eff Δ P eff ,
n 2 =A Δ n eff Δ P c Δ P c Δ P eff .

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