Abstract

We report stable thermo-optomechanical oscillations in high-Q-spherical ZBLAN microcavities. The oscillations are manifested as a complex combination of fast and slow oscillation periods. This behavior appears to be a consequence of the interplay between the negative thermo-optic effect, thermal expansion, and the Kerr effect. We have characterized the oscillatory behavior and measured the corresponding frequencies as a function of input power, wavelength detuning, and loaded optical quality factor. Our analysis shows that, as a gas sensor in the mid-IR spectral region, this thermo-optomechanical oscillator is two orders of magnitude more sensitive than previously demonstrated hybrid microtoroidal oscillators operating in the near-IR spectral region.

© 2013 Optical Society of America

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2013 (1)

2012 (3)

2009 (1)

2008 (1)

F. Vollmer and S. Arnold, Nat. Methods 5, 591 (2008).
[CrossRef]

2007 (1)

2006 (2)

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

T. J. Johnson, M. Borselli, and O. Painter, Opt. Express 14, 817 (2006).
[CrossRef]

2005 (1)

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, Phys. Rev. A 71, 013817 (2005).
[CrossRef]

2004 (2)

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef]

T. Carmon, L. Yang, and K. Vahala, Opt. Express 12, 4742 (2004).
[CrossRef]

2003 (2)

L. Yang, D. K. Armani, and K. J. Vahala, Appl. Phys. Lett. 83, 825 (2003).
[CrossRef]

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef]

1999 (1)

1992 (1)

V. S. Ilchenko and M. L. Gorodetskii, Laser Phys. 2, 1004 (1992).

1989 (1)

J. M. Parker, Annu. Rev. Mater. Sci. 19, 21 (1989).
[CrossRef]

Armani, D. K.

L. Yang, D. K. Armani, and K. J. Vahala, Appl. Phys. Lett. 83, 825 (2003).
[CrossRef]

Arnold, S.

F. Vollmer and S. Arnold, Nat. Methods 5, 591 (2008).
[CrossRef]

Baker, C.

Borselli, M.

Carmon, T.

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

T. Carmon, L. Yang, and K. Vahala, Opt. Express 12, 4742 (2004).
[CrossRef]

Deng, Y.

Ducci, S.

Favero, I.

Goh, K. W.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, Phys. Rev. A 71, 013817 (2005).
[CrossRef]

Gorodetskii, M. L.

V. S. Ilchenko and M. L. Gorodetskii, Laser Phys. 2, 1004 (1992).

Gorodetsky, M. L.

He, L.

Hossein-Zadeh, M.

Ilchenko, V. S.

M. L. Gorodetsky and V. S. Ilchenko, J. Opt. Soc. Am. B 16, 147 (1999).
[CrossRef]

V. S. Ilchenko and M. L. Gorodetskii, Laser Phys. 2, 1004 (1992).

Jain, R. K.

Johnson, T. J.

Kimble, H. J.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, Phys. Rev. A 71, 013817 (2005).
[CrossRef]

Kippenberg, T. J.

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

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, Phys. Rev. A 71, 013817 (2005).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef]

Kito, C.

Leo, G.

Leseman, Z. C.

Liao, M.

Liu, F.

Miyoshi, S.

Ohishi, Y.

Ozdemir, S. K.

Painter, O.

Park, Y. S.

Parker, J. M.

J. M. Parker, Annu. Rev. Mater. Sci. 19, 21 (1989).
[CrossRef]

Parrain, D.

Rokhsari, H.

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

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, Phys. Rev. A 71, 013817 (2005).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef]

Stapfner, S.

Suzuki, T.

Vahala, K.

Vahala, K. J.

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

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, Phys. Rev. A 71, 013817 (2005).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef]

L. Yang, D. K. Armani, and K. J. Vahala, Appl. Phys. Lett. 83, 825 (2003).
[CrossRef]

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef]

Vollmer, F.

F. Vollmer and S. Arnold, Nat. Methods 5, 591 (2008).
[CrossRef]

Wang, H.

Way, B.

Weig, E. M.

Wilcut, E.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, Phys. Rev. A 71, 013817 (2005).
[CrossRef]

Xiao, Y.-F.

Yan, X.

Yang, L.

Zhu, J.

Annu. Rev. Mater. Sci. (1)

J. M. Parker, Annu. Rev. Mater. Sci. 19, 21 (1989).
[CrossRef]

Appl. Phys. Lett. (1)

L. Yang, D. K. Armani, and K. J. Vahala, Appl. Phys. Lett. 83, 825 (2003).
[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]

J. Opt. Soc. Am. B (2)

Laser Phys. (1)

V. S. Ilchenko and M. L. Gorodetskii, Laser Phys. 2, 1004 (1992).

Nat. Methods (1)

F. Vollmer and S. Arnold, Nat. Methods 5, 591 (2008).
[CrossRef]

Nature (1)

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef]

Opt. Express (5)

Opt. Lett. (2)

Phys. Rev. A (1)

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, Phys. Rev. A 71, 013817 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of the experimental configuration.

Fig. 2.
Fig. 2.

Experimentally observed, self-sustained oscillations of the optical power transmitted through the fiber taper coupled to the ZBLAN microsphere. The laser wavelength was redshifted (detuned) by 68 pm from the WGM resonant wavelength (λres) and kept at 1557.1 nm. The input power was 13 mW. (a) The measured temporal behavior of the optical power transmitted through the fiber taper coupled to the microresonator. (b) Enlarged view of the fast oscillation cycles. fL and fH are frequencies of the slow (10–200 Hz range) and fast (0.1–2 MHz range) oscillations, respectively. The absence of positively directed transients (transmission>1) for each pulsation in the upper trace [Fig. 2(a)] is simply attributable to “sampling error” caused by the low temporal resolution of the digital oscilloscope at the slower time scale settings. In reality, every “macropulsation” consists of a series of upward- and downward-going transients, as evident from the high resolution measurement near a dip [see Fig. 2(b)].

Fig. 3.
Fig. 3.

Simulated temporal oscillation of the transmitted optical power using Eqs. (1)–(4). The optical quality factor, the laser detuning and input optical power used for these simulations are identical to those used for the experimental results depicted in Fig. 2. The transmission is defined as Ttrans(t)=|E0(t)|2/|Ein(t)|2. For this calculation, η=99%, neff=1.496, n2=5.4×1020m2/W [15], Aeff=1.1×1011m2. γth,1=2.9×103Hz, γth,2=58.1Hz, γabs,1=305K/J, and γabs,2=9.8K/J. These values are estimated using finite element modeling (COMSOL multiphysics).

Fig. 4.
Fig. 4.

Plots of the fast and slow thermo-optomechanical oscillation frequencies in a ZBLAN microsphere as a function of (a) optical input power, when the optical total Q is 8.3×106 and wavelength detuning is 80 pm, (b) loaded optical-Q, when the input optical power is 12.83 mW and the wavelength detuning is 90 pm, and (c) detuning, when the input optical power is 13 mW and Qtot=8.2×106. The points indicate measured data, and the solid lines represent simulation results (based on the aforementioned physical model). Note that the resonant wavelength (λr) is measured at ultralow input powers to avoid thermally induced shifts.

Equations (4)

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Δω(t)ω0=[ηneffdndTΔT1(t)+α·ΔT2(t)+n2neff AeffEc2(t)τr],
dΔTm(t)dt=γth,mΔTm(t)+γabs,mEc2(t)τr,
dEc(t)dt=[δ0(t)+δc(t)+iΔω(t)]Ec(t)+iκτrEin,
Eo(t)=1κ2Ein+iκEc(t),

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