Abstract

We present experimental evidence of the optical spring effect in a silica microtoroid resonator. The variation of the measured mechanical resonant frequency as a function of optical power, optical coupling, and optical detuning is in very good agreement with a model for radiation-pressure-induced rigidity in a silica microtoroid.

© 2007 Optical Society of America

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  1. V. B. Braginsky and S. P. Vyatchanin, Phys. Lett. A 293, 228 (2002).
    [CrossRef]
  2. T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Phys. Rev. Lett. 95, 033901 (2005).
    [CrossRef] [PubMed]
  3. H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 12, 96 (2006).
    [CrossRef]
  4. M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, Phys. Rev. A 74, 023813 (2006).
    [CrossRef]
  5. A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
    [CrossRef]
  6. S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
    [CrossRef] [PubMed]
  7. T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
    [CrossRef]
  8. B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, Phys. Rev. A 69, 051801(R) (2004).
    [CrossRef]
  9. S. W. Schediwy, C. Zhao, L. Ju, and D. G. Blair, Class. Quantum Grav. 21, 1253 (2004).
    [CrossRef]
  10. S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, Phys. Rev. Lett. 88, 120401 (2002).
    [CrossRef] [PubMed]

2006 (5)

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 12, 96 (2006).
[CrossRef]

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, Phys. Rev. A 74, 023813 (2006).
[CrossRef]

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[CrossRef]

2005 (1)

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

2004 (2)

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, Phys. Rev. A 69, 051801(R) (2004).
[CrossRef]

S. W. Schediwy, C. Zhao, L. Ju, and D. G. Blair, Class. Quantum Grav. 21, 1253 (2004).
[CrossRef]

2002 (2)

S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, Phys. Rev. Lett. 88, 120401 (2002).
[CrossRef] [PubMed]

V. B. Braginsky and S. P. Vyatchanin, Phys. Lett. A 293, 228 (2002).
[CrossRef]

Aspelmeyer, M.

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Bauerle, D.

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Blair, D. G.

S. W. Schediwy, C. Zhao, L. Ju, and D. G. Blair, Class. Quantum Grav. 21, 1253 (2004).
[CrossRef]

Blaser, F.

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Bohm, H. R.

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Braginsky, V. B.

V. B. Braginsky and S. P. Vyatchanin, Phys. Lett. A 293, 228 (2002).
[CrossRef]

Carmon, T.

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 12, 96 (2006).
[CrossRef]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

Chen, Y.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[CrossRef]

Corbitt, T.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[CrossRef]

Del'Haye, P.

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

Gigan, S.

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Giovannetti, V.

S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, Phys. Rev. Lett. 88, 120401 (2002).
[CrossRef] [PubMed]

Gray, M. B.

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, Phys. Rev. A 69, 051801(R) (2004).
[CrossRef]

Hajimiri, A.

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, Phys. Rev. A 74, 023813 (2006).
[CrossRef]

Hertzberg, J. B.

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Hossein-Zadeh, M.

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, Phys. Rev. A 74, 023813 (2006).
[CrossRef]

Ju, L.

S. W. Schediwy, C. Zhao, L. Ju, and D. G. Blair, Class. Quantum Grav. 21, 1253 (2004).
[CrossRef]

Khalili, F.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[CrossRef]

Kippenberg, T. J.

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 12, 96 (2006).
[CrossRef]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

Langer, G.

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Mancini, S.

S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, Phys. Rev. Lett. 88, 120401 (2002).
[CrossRef] [PubMed]

Mavalvala, N.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[CrossRef]

McClelland, D. E.

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, Phys. Rev. A 69, 051801(R) (2004).
[CrossRef]

Mow-Lowry, C. M.

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, Phys. Rev. A 69, 051801(R) (2004).
[CrossRef]

Nooshi, N.

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

Ottaway, D.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[CrossRef]

Paternostro, M.

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Rokhsari, H.

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, Phys. Rev. A 74, 023813 (2006).
[CrossRef]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 12, 96 (2006).
[CrossRef]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

Schediwy, S. W.

S. W. Schediwy, C. Zhao, L. Ju, and D. G. Blair, Class. Quantum Grav. 21, 1253 (2004).
[CrossRef]

Scherer, A.

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

Schliesser, A.

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

Schwab, K. C.

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Sheard, B. S.

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, Phys. Rev. A 69, 051801(R) (2004).
[CrossRef]

Tombesi, P.

S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, Phys. Rev. Lett. 88, 120401 (2002).
[CrossRef] [PubMed]

Vahala, K. J.

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 12, 96 (2006).
[CrossRef]

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, Phys. Rev. A 74, 023813 (2006).
[CrossRef]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

Vitali, D.

S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, Phys. Rev. Lett. 88, 120401 (2002).
[CrossRef] [PubMed]

Vyatchanin, S.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[CrossRef]

Vyatchanin, S. P.

V. B. Braginsky and S. P. Vyatchanin, Phys. Lett. A 293, 228 (2002).
[CrossRef]

Whitcomb, S.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[CrossRef]

Whitcomb, S. E.

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, Phys. Rev. A 69, 051801(R) (2004).
[CrossRef]

Zeilinger, A.

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Zhao, C.

S. W. Schediwy, C. Zhao, L. Ju, and D. G. Blair, Class. Quantum Grav. 21, 1253 (2004).
[CrossRef]

Class. Quantum Grav. (1)

S. W. Schediwy, C. Zhao, L. Ju, and D. G. Blair, Class. Quantum Grav. 21, 1253 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 12, 96 (2006).
[CrossRef]

Nature (1)

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).
[CrossRef] [PubMed]

Phys. Lett. A (1)

V. B. Braginsky and S. P. Vyatchanin, Phys. Lett. A 293, 228 (2002).
[CrossRef]

Phys. Rev. A (3)

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, Phys. Rev. A 74, 023813 (2006).
[CrossRef]

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev. A 73, 023801 (2006).
[CrossRef]

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, Phys. Rev. A 69, 051801(R) (2004).
[CrossRef]

Phys. Rev. Lett. (3)

S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, Phys. Rev. Lett. 88, 120401 (2002).
[CrossRef] [PubMed]

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

(a) Toroid offset with respect to support disk. (b) Coupling of the radiation-pressure-induced force ( F rad ) to the first eigenmechanical mode of the microtoroid.

Fig. 2
Fig. 2

(a) Top-view photograph of the silica microtoroid coupled to fiber taper. (b) Schematic diagram of the experimental configuration.

Fig. 3
Fig. 3

(a) Noise spectra of the eigenmechanical modes of the microtoroidal cavity in the RF spectrum of the detected optical power. The gray dots are the simulated values of the first three eigenfrequencies using finite element modeling (FEMLAB). (b) Cross-sectional diagram of the microtoroid structure and deformation associated with the first eigenmechanical mode.

Fig. 4
Fig. 4

(a) Measured mechanical resonant frequency plotted against optical input power at critical coupling ( Q L Q 0 = 0.5 ) and d = 0.5 . The solid line is a linear fit to the experimental data. (b) Measured value of η os plotted against optical detuning ( d ) for three different optical input powers ( P in ) at critical coupling ( Q L Q 0 = 0.5 ) . The solid curve is the theoretical prediction based on Eq. (3). Q 0 is about 6.5 × 10 6 for both measurements.

Fig. 5
Fig. 5

Measured value of η os plotted against Q L Q 0 at d = 0.5 for an optical mode with Q 0 = 1.2 × 10 7 . The solid curve is the theoretical prediction based on Eq. (3).

Equations (5)

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

f = f 0 ( 1 + η os P in ) .
k opt = d ( β × F opt ) d z = β ( d r d z ) d F opt d r ,
F opt = 2 π n c P circ ,
P circ = λ P in Q 0 4 π 2 n R 0 y ( 1 y ) d 2 + 0.25 ,
η os = β ( d r d z ) Ω 0 2 m eff ω 0 R 0 2 Q 0 2 ( y 2 y 3 ) d ( d 2 + 0.25 ) 2 .

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