Abstract

We demonstrate and characterize a thermo-optomechanical oscillator based on a PMMA-coated silica microtoroid and employ it as a sensor. The observed thermo-optomechanical oscillation has a unique waveform that consists of fast and slow oscillation periods. A model based on thermal and optical dynamics of the cavity is used to describe the bi-frequency oscillation and experiments are conducted to validate the theoretical model in order to explore the origin of the two oscillatory phenomena. As opposed to previously shown hybrid toroidal microcavities, the excessive PMMA coating boosts the thermo-mechanical (expansion) effect that results in bi-frequency oscillation when coupled with the thermo-optical effect. The influences of the input power, quality factor, and wavelength detuning on oscillation frequencies are studied experimentally and verified theoretically. Finally the application of this oscillator as a sensor is explored by demonstrating the sensitivity of oscillation frequency to humidity changes.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]

2012

2010

2009

2008

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods5(7), 591–596 (2008).
[CrossRef] [PubMed]

L. He, Y.-F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett.93(20), 201102 (2008).
[CrossRef]

2007

2006

2005

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A71(1), 013817 (2005).
[CrossRef]

2004

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity,” Phys. Rev. Lett.93(8), 083904 (2004).
[CrossRef] [PubMed]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express12(20), 4742–4750 (2004).
[CrossRef] [PubMed]

H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett.85(15), 3029–3031 (2004).
[CrossRef]

2003

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421(6926), 925–928 (2003).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003).
[CrossRef] [PubMed]

L. Yang, D. K. Armani, and K. J. Vahala, “Fiber-coupled erbium microlasers on a chip,” Appl. Phys. Lett.83(5), 825–826 (2003).
[CrossRef]

1999

1998

1992

V. S. Ilchenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys.2, 1004–1009 (1992).

1989

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A137(7–8), 393–397 (1989).
[CrossRef]

Armani, A. M.

H.-S. Choi and A. M. Armani, “Thermal non-linear effects in hybrid optical microresonators,” Appl. Phys. Lett.97(22), 223306 (2010).
[CrossRef]

H. S. Choi, X. Zhang, and A. M. Armani, “Hybrid silica-polymer ultra-high-Q microresonators,” Opt. Lett.35(4), 459–461 (2010).
[CrossRef] [PubMed]

Armani, D. K.

L. Yang, D. K. Armani, and K. J. Vahala, “Fiber-coupled erbium microlasers on a chip,” Appl. Phys. Lett.83(5), 825–826 (2003).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Arnold, S.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods5(7), 591–596 (2008).
[CrossRef] [PubMed]

Baets, R.

Baker, C.

Borselli, M.

Braginsky, V. B.

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A137(7–8), 393–397 (1989).
[CrossRef]

Carmon, T.

Chen, D.-R.

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics4(1), 46–49 (2010).
[CrossRef]

Choi, H. S.

Choi, H.-S.

H.-S. Choi and A. M. Armani, “Thermal non-linear effects in hybrid optical microresonators,” Appl. Phys. Lett.97(22), 223306 (2010).
[CrossRef]

Dong, C.

L. He, Y.-F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett.93(20), 201102 (2008).
[CrossRef]

Dong, C. H.

C. H. Dong, L. He, Y. F. Xiao, V. Goddam, S. K. Ozdemir, Z. F. Han, G. C. Guo, and L. Yang, “Fabrication of high-Q PDMS optical microspheres with applications towards thermal sensing,” Appl. Phys. Lett.94(23), 231119 (2009).
[CrossRef]

Ducci, S.

Favero, I.

Gaddam, V.

L. He, Y.-F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett.93(20), 201102 (2008).
[CrossRef]

Goddam, V.

C. H. Dong, L. He, Y. F. Xiao, V. Goddam, S. K. Ozdemir, Z. F. Han, G. C. Guo, and L. Yang, “Fabrication of high-Q PDMS optical microspheres with applications towards thermal sensing,” Appl. Phys. Lett.94(23), 231119 (2009).
[CrossRef]

Goh, K. W.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A71(1), 013817 (2005).
[CrossRef]

Gorodetskii, M. L.

V. S. Ilchenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys.2, 1004–1009 (1992).

Gorodetsky, M. L.

M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optical coupling to high-Q whispering-gallery-modes,” J. Opt. Soc. Am. B16(1), 147 (1999).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A137(7–8), 393–397 (1989).
[CrossRef]

Grudinin, I. S.

Guo, G. C.

C. H. Dong, L. He, Y. F. Xiao, V. Goddam, S. K. Ozdemir, Z. F. Han, G. C. Guo, and L. Yang, “Fabrication of high-Q PDMS optical microspheres with applications towards thermal sensing,” Appl. Phys. Lett.94(23), 231119 (2009).
[CrossRef]

Han, Q.

Han, Z. F.

C. H. Dong, L. He, Y. F. Xiao, V. Goddam, S. K. Ozdemir, Z. F. Han, G. C. Guo, and L. Yang, “Fabrication of high-Q PDMS optical microspheres with applications towards thermal sensing,” Appl. Phys. Lett.94(23), 231119 (2009).
[CrossRef]

He, L.

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics4(1), 46–49 (2010).
[CrossRef]

L. He, Y.-F. Xiao, J. Zhu, S. K. Ozdemir, and L. Yang, “Oscillatory thermal dynamics in high-Q PDMS-coated silica toroidal microresonators,” Opt. Express17(12), 9571–9581 (2009).
[CrossRef] [PubMed]

C. H. Dong, L. He, Y. F. Xiao, V. Goddam, S. K. Ozdemir, Z. F. Han, G. C. Guo, and L. Yang, “Fabrication of high-Q PDMS optical microspheres with applications towards thermal sensing,” Appl. Phys. Lett.94(23), 231119 (2009).
[CrossRef]

L. He, Y.-F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett.93(20), 201102 (2008).
[CrossRef]

Hens, Z.

Ilchenko, V. S.

M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optical coupling to high-Q whispering-gallery-modes,” J. Opt. Soc. Am. B16(1), 147 (1999).
[CrossRef]

D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, “High-Q measurements of fused-silica microspheres in the near infrared,” Opt. Lett.23(4), 247–249 (1998).
[CrossRef] [PubMed]

V. S. Ilchenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys.2, 1004–1009 (1992).

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A137(7–8), 393–397 (1989).
[CrossRef]

Johnson, T. J.

Kim, C. W.

Kimble, H. J.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A71(1), 013817 (2005).
[CrossRef]

D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, “High-Q measurements of fused-silica microspheres in the near infrared,” Opt. Lett.23(4), 247–249 (1998).
[CrossRef] [PubMed]

Kippenberg, T. J.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A71(1), 013817 (2005).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity,” Phys. Rev. Lett.93(8), 083904 (2004).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Lan, X.

Leo, G.

Li, L.

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics4(1), 46–49 (2010).
[CrossRef]

Li, M.

Lommens, P.

Mabuchi, H.

Ozdemir, S. K.

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics4(1), 46–49 (2010).
[CrossRef]

L. He, Y.-F. Xiao, J. Zhu, S. K. Ozdemir, and L. Yang, “Oscillatory thermal dynamics in high-Q PDMS-coated silica toroidal microresonators,” Opt. Express17(12), 9571–9581 (2009).
[CrossRef] [PubMed]

C. H. Dong, L. He, Y. F. Xiao, V. Goddam, S. K. Ozdemir, Z. F. Han, G. C. Guo, and L. Yang, “Fabrication of high-Q PDMS optical microspheres with applications towards thermal sensing,” Appl. Phys. Lett.94(23), 231119 (2009).
[CrossRef]

Painter, O.

Park, Y. S.

Parrain, D.

Pernice, W. H.

Rokhsari, H.

H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett.85(15), 3029–3031 (2004).
[CrossRef]

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A71(1), 013817 (2005).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity,” Phys. Rev. Lett.93(8), 083904 (2004).
[CrossRef] [PubMed]

H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett.85(15), 3029–3031 (2004).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Stapfner, S.

Streed, E. W.

Tang, H. X.

Vahala, K. J.

I. S. Grudinin and K. J. Vahala, “Thermal instability of a compound resonator,” Opt. Express17(16), 14088–14097 (2009).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A71(1), 013817 (2005).
[CrossRef]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express12(20), 4742–4750 (2004).
[CrossRef] [PubMed]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity,” Phys. Rev. Lett.93(8), 083904 (2004).
[CrossRef] [PubMed]

H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett.85(15), 3029–3031 (2004).
[CrossRef]

K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003).
[CrossRef] [PubMed]

L. Yang, D. K. Armani, and K. J. Vahala, “Fiber-coupled erbium microlasers on a chip,” Appl. Phys. Lett.83(5), 825–826 (2003).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Vernooy, D. W.

Vollmer, F.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods5(7), 591–596 (2008).
[CrossRef] [PubMed]

Wang, H.

Wei, T.

Weig, E. M.

Wilcut, E.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A71(1), 013817 (2005).
[CrossRef]

Xiao, H.

Xiao, Y. F.

C. H. Dong, L. He, Y. F. Xiao, V. Goddam, S. K. Ozdemir, Z. F. Han, G. C. Guo, and L. Yang, “Fabrication of high-Q PDMS optical microspheres with applications towards thermal sensing,” Appl. Phys. Lett.94(23), 231119 (2009).
[CrossRef]

Xiao, Y.-F.

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics4(1), 46–49 (2010).
[CrossRef]

L. He, Y.-F. Xiao, J. Zhu, S. K. Ozdemir, and L. Yang, “Oscillatory thermal dynamics in high-Q PDMS-coated silica toroidal microresonators,” Opt. Express17(12), 9571–9581 (2009).
[CrossRef] [PubMed]

L. He, Y.-F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett.93(20), 201102 (2008).
[CrossRef]

Yang, L.

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics4(1), 46–49 (2010).
[CrossRef]

L. He, Y.-F. Xiao, J. Zhu, S. K. Ozdemir, and L. Yang, “Oscillatory thermal dynamics in high-Q PDMS-coated silica toroidal microresonators,” Opt. Express17(12), 9571–9581 (2009).
[CrossRef] [PubMed]

C. H. Dong, L. He, Y. F. Xiao, V. Goddam, S. K. Ozdemir, Z. F. Han, G. C. Guo, and L. Yang, “Fabrication of high-Q PDMS optical microspheres with applications towards thermal sensing,” Appl. Phys. Lett.94(23), 231119 (2009).
[CrossRef]

L. He, Y.-F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett.93(20), 201102 (2008).
[CrossRef]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express12(20), 4742–4750 (2004).
[CrossRef] [PubMed]

L. Yang, D. K. Armani, and K. J. Vahala, “Fiber-coupled erbium microlasers on a chip,” Appl. Phys. Lett.83(5), 825–826 (2003).
[CrossRef]

Yebo, N. A.

Yuan, L.

Zhang, X.

Zhu, J.

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics4(1), 46–49 (2010).
[CrossRef]

L. He, Y.-F. Xiao, J. Zhu, S. K. Ozdemir, and L. Yang, “Oscillatory thermal dynamics in high-Q PDMS-coated silica toroidal microresonators,” Opt. Express17(12), 9571–9581 (2009).
[CrossRef] [PubMed]

L. He, Y.-F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett.93(20), 201102 (2008).
[CrossRef]

Appl. Phys. Lett.

L. Yang, D. K. Armani, and K. J. Vahala, “Fiber-coupled erbium microlasers on a chip,” Appl. Phys. Lett.83(5), 825–826 (2003).
[CrossRef]

L. He, Y.-F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett.93(20), 201102 (2008).
[CrossRef]

C. H. Dong, L. He, Y. F. Xiao, V. Goddam, S. K. Ozdemir, Z. F. Han, G. C. Guo, and L. Yang, “Fabrication of high-Q PDMS optical microspheres with applications towards thermal sensing,” Appl. Phys. Lett.94(23), 231119 (2009).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

(a). SEM picture of the microtoroid before (left half) and after (right half) coating with PMMA. (b). Cross sectional profile of the TE polarized WG mode in a hybrid (silica/PMMA) toroidal microcavity. (c) Top: Measurement of the transmitted optical power through the fiber-taper coupled to the hybrid microtoroid at a fixed laser wavelength detuned by 62 pm from hot WGM resonant wavelength. The optical input power is 2.14 mW. t1 + t2 is the period of the low-speed oscillation. Bottom: enlarged view of the fast oscillation cycles. fL and fH are frequencies of the slow and fast oscillations respectively.

Fig. 2
Fig. 2

(a) FEM modeling of thermally induced deformation caused by expansion of residual PMMA (underneath the toroidal region). Here the input optical power is 1 mW (resulting in a circulating optical power of >1 W). The scale factor for the deformation is 200. The color represents the temperature distribution. (b) Schematic diagram summarizing the mutual interaction between circulating optical power (Pcirc) and the resonant wavelength (λr).

Fig. 3
Fig. 3

Calculated temporal oscillation of the transmitted optical power using Eq. (2)-(6). (a) The detected waveform showing eight periods of slow oscillation. The dark regions are the fast oscillation regions. The transmission is defined as Ttrans(t) = |E0(t)|2/|Ein(t)|2. (b) Fast oscillations resolved by a larger temporal resolution. The input power is 2 mW. Δλ = 75 pm. Here Qtot = 1.75 × 106, αexp = 2.02 × 10−4, αben = −2.6 × 10−4, γth,1 = 3.56 × 104, γabs,1 = 2.96 × 104, γth,2 = 1.805 × 107, γabs,2 = 3.79 × 105, γth,3 = 26, gcon,3 = 18, γth,4 = 16, gcon4 = 24.

Fig. 4
Fig. 4

(a) Measured resonant wavelength shift as the input power is increased very slowly (~10 μW/sec). Here Qtot = 1.9 × 106. (b). Calculated change of the effective radius plotted against input power. FEM thermo-mechanical modeling is used to estimate ΔReff due to thermal expansion and resulted bending. The negative slope shows the magnitude of ΔReff is dominated by bending toward the center (see Fig. 2(a)).

Fig. 5
Fig. 5

Transmitted optical power through the fiber-taper coupled to a PMMA-coated microtoroid while the laser wavelength is scanned near WGM resonance at different speeds (a) 35nm/s, (b) 3.5nm/s, (c) 0.35nm/s and (d) 0 nm/s (at a fixed detuning). Here Qtot = 1.77 × 106.

Fig. 6
Fig. 6

(a). The fast and slow thermo-optomechanical oscillation frequencies plotted against optical input power. The markers are the measured data and the solid lines are the simulation results (based on the physical model defined in section 2). (b) Measured temporal variation of the detected power at different input powers. Solid lines are fitting curves. Qtot = 1.75 × 106 and Δλ = λr-hot− λlaser = 70pm. Here the resonator is in the under-coupled regime (Qext > Qint).

Fig. 7
Fig. 7

(a) The fast and slow thermo-optomechanical oscillation frequencies plotted against Qtot. The markers are the measured data and the solid lines are the simulation results (based on the physical model defined in 2). (b) Measured temporal variation of the detected power for different values of Qtot. The optical input power is 3.4 mW and Δλ = λr-hot− λlaser = 58 pm.

Fig. 8
Fig. 8

(a) The fast and slow thermo-optomechanical oscillation frequencies plotted against Δλ = λres-hot− λlaser. The markers are the measured data and the solid lines are the simulation results (based on the physical model defined in 2). (b) Measured temporal variation of the detected power for different values of Δλ. The input power is 3.1mW. Qtot = 1.65 × 106.

Fig. 9
Fig. 9

Schematic diagram of the experimental configuration used for measuring the sensitivity of fL and fH to humidity of the surrounding medium. The hybrid microtoroid and the fiber-taper are kept in a closed chamber and a nitrogen bubbler increases the number of water molecules in the chamber.

Fig. 10
Fig. 10

(a). The fast and slow thermo-optical frequencies plotted against relative humidity. The markers are the measured data and solid lines are the best fits. Here laser wavelength, coupling strength (κ) and optical input power are constant (b). Resonant wavelength shift (detuning change) induced by relative humidity change. The dots are the experimental data and the line is the linear fit to the measured data. Here Qtot = 1.65 × 106.

Equations (6)

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Δ λ r λ r = Δ n eff n eff + Δ R eff R eff
Δ ω r (t) ω r [ 1 n eff ( η 1 d n 1 dT Δ T 1 (t)+ η 2 d n 2 dT Δ T 2 (t) )+( α exp Δ T 3 (t) α ben Δ T 4 (t) ) ]
dΔ T m (t) dt = γ th,m Δ T m (t)+ γ abs,m E c 2 (t) τ r
dΔ T n (t) dt = γ th,n Δ T n (t)+ g con,n E c 2 (t) τ r
d E c (t) dt =[ δ 0 (t)+ δ c (t)+iΔω(t)] E c (t)+i κ τ r E in
E 0 (t)= 1 κ 2 E in +iκ E c (t)

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