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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 9, Iss. 3 — Mar. 6, 2014
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Aerostatically tunable optomechanical oscillators

Kewen Han, Jun Hwan Kim, and Gaurav Bahl  »View Author Affiliations


Optics Express, Vol. 22, Issue 2, pp. 1267-1276 (2014)
http://dx.doi.org/10.1364/OE.22.001267


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Abstract

Recently, the first microfluidic optomechanical device was demonstrated, capable of operating with non-solid states of matter (viscous fluids, bioanalytes). These devices exhibit optomechanical oscillation in both the 10–20 MHz and 10–12 GHz regimes, driven by radiation pressure (RP) and stimulated Brillouin scattering (SBS) respectively. In this work, we experimentally investigate aerostatic tuning of these hollow-shell oscillators, enabled by geometry, stress, and temperature effects. We also demonstrate for the first time the simultaneous actuation of RP-induced breathing mechanical modes and SBS-induced whispering gallery acoustic modes, through a single pump laser. Our result is a step towards completely self-referenced optomechanical sensor technologies.

© 2014 Optical Society of America

1. Introduction

Optomechanical microresonators enable strong-coupling between their photon modes and phonon modes through photothermal effects [1

1. J. Mertz, O. Marti, and J. Mlynek, “Regulation of a microcantilever response by force feedback,” Appl. Phys. Lett. 62, 2344–2346 (1993). [CrossRef]

3

3. C. Metzger, M. Ludwig, C. Neuenhahn, A. Ortlieb, I. Favero, K. Karrai, and F. Marquardt, “Self-induced oscillations in an optomechanical system driven by bolometric backaction,” Phys. Rev. Lett. 101, 133903 (2008). [CrossRef] [PubMed]

], radiation pressure force [4

4. T. Carmon, H. Rokhsari, L. Yang, T. Kippenberg, and K. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005). [CrossRef] [PubMed]

10

10. R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A 83, 063835 (2011). [CrossRef]

], optical gradient force [11

11. M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett. 30, 3042–3044 (2005). [CrossRef] [PubMed]

14

14. Q. Lin, J. Rosenberg, X. Jiang, K. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009). [CrossRef] [PubMed]

], and electrostriction mechanisms [15

15. I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102, 043902 (2009). [CrossRef]

21

21. G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat. Commun. 4, 1994 (2013). [CrossRef] [PubMed]

]. This capability has been harnessed for many fundamental experiments including optomechanical cooling [5

5. O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–74 (2006). [CrossRef] [PubMed]

7

7. D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444, 75–78 (2006). [CrossRef] [PubMed]

,19

19. G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8, 203–207 (2012). [CrossRef]

], induced transparency [22

22. S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010). [CrossRef] [PubMed]

, 23

23. C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Transient optomechanically induced transparency in a silica microsphere,” Phys. Rev. A 87, 055802 (2013). [CrossRef]

], and dark modes [24

24. C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012). [CrossRef] [PubMed]

]. Efforts have also been made towards sensing applications such as accelerometers [25

25. A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6, 768–772 (2012). [CrossRef]

, 26

26. D. N. Hutchison and S. A. Bhave, “Z-axis optomechanical accelerometer,” in Proceedings of IEEE Conference on Micro Electro Mechanical Systems (IEEE, New York, 2012), pp. 615–619.

], mass sensors [27

27. F. Liu and M. Hossein-Zadeh, “Mass sensing with optomechanical oscillation,” IEEE Sensors J. 13, 146–147 (2013). [CrossRef]

, 28

28. F. Liu and M. Hossein-Zadeh, “On the spectrum of radiation pressure driven optomechanical oscillator and its application in sensing,” Opt. Commun. 294, 338–343 (2013). [CrossRef]

], and force sensors [29

29. E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7, 509–514 (2012). [CrossRef] [PubMed]

, 30

30. Y. Liu, H. Miao, V. Aksyuk, and K. Srinivasan, “Integrated cavity optomechanical sensors for atomic force microscopy,” in Proceedings of IEEE Conference on Microsystems for Measurement and Instrumentation (IEEE, New York, 2012).

]. Recently, the first microfluidic optomechanical devices capable of operating with liquids and targeted towards bio-applications [18

18. G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403 (2011). [CrossRef] [PubMed]

, 31

31. K. H. Kim, G. Bahl, W. Lee, J. Liu, M. Tomes, X. Fan, and T. Carmon, “Cavity optomechanics on a microfluidic resonator with water and viscous liquids,” to appear in Light Sci. Appl. (2013), arXiv.org:1205.5477.

] were demonstrated, enabling optomechanics with non-solid states of matter. Indeed, while individual optomechanical devices can operate at multiple oscillation frequencies [18

18. G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403 (2011). [CrossRef] [PubMed]

, 21

21. G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat. Commun. 4, 1994 (2013). [CrossRef] [PubMed]

], these frequencies are discrete and the spectral gaps cannot easily be filled. Achieving complete spectral coverage with a single device can provide frequency-on-demand capability that is extremely important for frequency-hopping and cognitive oscillator applications in communication systems. Enhanced tuning also helps align optical and mechanical modes to ‘phase match’ fundamental light-matter interaction processes that employ optomechanics [19

19. G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8, 203–207 (2012). [CrossRef]

, 22

22. S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010). [CrossRef] [PubMed]

24

24. C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012). [CrossRef] [PubMed]

].

Till date, continuous tuning of the discrete optomechanical oscillation frequencies is primarily achieved through direct temperature control [32

32. M. Zhang, G. S. Wiederhecker, S. Manipatruni, A. Barnard, P. McEuen, and M. Lipson, “Synchronization of micromechanical oscillators using light,” Phys. Rev. Lett. 109, 233906 (2012). [CrossRef]

] or by managing the dropped power [33

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

,34

34. G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Characterization of surface acoustic wave optomechanical oscillators,” in Proceedings of IEEE Conference on Frequency Control and the European Frequency and Time Forum (IEEE, New York, 2011).

]. However, tuning by means of temperature is often impractical since low phonon occupation and specific laser power coupling are often desirable, especially for single-phonon experiments in the quantum regime. For this reason aerostatic tuning, i.e. tuning through air pressure, is an alternative that can provide improved tuning capability with greater spectral coverage. Aerostatic tuning has been successfully employed with hollow microbubble resonators [35

35. A. Watkins, J. Ward, Y. Wu, and S. Nic Chormaic, “Single-input spherical microbubble resonator,” Opt. Lett. 36, 2113–2115 (2011). [CrossRef] [PubMed]

,36

36. R. Henze, T. Seifert, J. Ward, and O. Benson, “Tuning whispering gallery modes using internal aerostatic pressure,” Opt. Lett. 36, 4536–4538 (2011). [CrossRef] [PubMed]

], optofluidic ring resonators (OFRR) [37

37. S. Lacey, I. M. White, Y. Sun, S. I. Shopova, J. M. Cupps, P. Zhang, and X. Fan, “Versatile opto-fluidic ring resonator lasers with ultra-low threshold,” Opt. Express 15, 15523–15530 (2007). [CrossRef] [PubMed]

], and ring resonators on flexible membranes [38

38. X. Zhao, J. M. Tsai, H. Cai, X. M. Ji, J. Zhou, M. H. Bao, Y. P. Huang, D. L. Kwong, and A. Q. Liu, “A nano-opto-mechanical pressure sensor via ring resonator,” Opt. Express 20, 8535–8542 (2012). [CrossRef] [PubMed]

]. Another deformation-based strategy involves the use of stretchable polymer microspheres and achieves THz range tuning [39

39. R. Madugani, Y. Yang, J. M. Ward, J. D. Riordan, S. Coppola, V. Vespini, S. Grilli, A. Finizio, P. Ferraro, and S. Nic Chormaic, “Terahertz tuning of whispering gallery modes in a PDMS stand-alone, stretchable microsphere,” Opt. Lett. 37, 4762–4764 (2012). [CrossRef] [PubMed]

]. However, these extremely-tunable devices have not yet been employed for optomechanics, and the tuning of mechanical modes in conjunction with tuning of optical modes has not been studied previously. We have developed an OFRR-derived opto-mechanofluidic resonator (OMFR) platform [21

21. G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat. Commun. 4, 1994 (2013). [CrossRef] [PubMed]

, 31

31. K. H. Kim, G. Bahl, W. Lee, J. Liu, M. Tomes, X. Fan, and T. Carmon, “Cavity optomechanics on a microfluidic resonator with water and viscous liquids,” to appear in Light Sci. Appl. (2013), arXiv.org:1205.5477.

] that employs optical radiation pressure (RP) and stimulated Brillouin scattering (SBS) to actuate mechanical vibrations spanning the frequency ranges of 2 MHz – 1 GHz and 10 GHz – 12 GHz. In this study, we experimentally investigate the aerostatic tuning of these OMFR devices and we show the simultaneous actuation and tuning of multiple modes and mechanisms of optomechanical oscillation.

2. Setup and working principle

Fig. 1 Experimental overview (a) Colorized scanning electron micrograph of a hollow-core fused-silica optomechanical resonator with radius modulated by design. Resonator wall thickness can be varied as needed. (b) 1.5 μm light is coupled to the ultra-high-Q optical modes by means of a tapered fiber placed in contact to minimize vibrational issues. The optical pump and the scattered light are made to interfere on high speed photodetectors in both forward and backward directions, thus generating beat notes at the mechanical vibration frequency. (c) Radiation pressure (RP) drives “breathing mode” optomechanical oscillators (OMOs) that generate both upper and lower sidebands of the input optical signal. (d) Stimulated Brillouin scattering (SBS) excites traveling whispering gallery acoustic modes (WGAMs) that generate only a single Stokes shifted sideband in the backscattering direction.

Centrifugal radiation pressure induced optomechanical oscillations (OMOs) (Fig. 1(c)), described previously in [4

4. T. Carmon, H. Rokhsari, L. Yang, T. Kippenberg, and K. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005). [CrossRef] [PubMed]

, 46

46. H. Rokhsari, T. Kippenberg, T. Carmon, and K. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13, 5293–5301 (2005). [CrossRef] [PubMed]

, 47

47. T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95, 033901 (2005). [CrossRef] [PubMed]

], result in the actuation of ‘breathing’ mechanical eigenmodes ΩRP of the resonator and the generation of modulation sidebands to the pump. We measure these sidebands when they interfere with the pump on a photodetector in the forward propagation direction on the tapered fiber.

Stimulated Brillouin scattering is an acousto-optical nonlinearity [48

48. R. Chiao, C. Townes, and B. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12, 592–595 (1964). [CrossRef]

51

51. G. Bahl and T. Carmon, “Brillouin optomechanics” (2013), arxiv.org:1309.2828.

] that has been recently used for generating high frequency acoustic waves in various resonant and nonresonant systems [15

15. I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102, 043902 (2009). [CrossRef]

21

21. G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat. Commun. 4, 1994 (2013). [CrossRef] [PubMed]

, 34

34. G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Characterization of surface acoustic wave optomechanical oscillators,” in Proceedings of IEEE Conference on Frequency Control and the European Frequency and Time Forum (IEEE, New York, 2011).

, 40

40. K. Han, K. H. Kim, J. Kim, W. Lee, J. Liu, X. Fan, T. Carmon, and G. Bahl, “Fabrication and testing of microfluidic optomechanical oscillators,” J. Vis. Exp., in review (2013).

, 45

45. G. Bahl, X. Fan, and T. Carmon, “Acoustic whispering-gallery modes in optomechanical shells,” New J. Phys. 14, 115026 (2012). [CrossRef]

, 52

52. H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013). [CrossRef] [PubMed]

] (Fig. 1(d)). SBS is caused by photoelastic scattering of input (pump) light from acoustic perturbations in the material, and coherently amplifies these acoustic perturbations through positive feedback from electrostrictive pressure generated by the scattered light and the pump light [50

50. R. Boyd, “Stimulated Brillouin and stimulated Rayleigh scattering,” in Nonlinear Optics (Academic, 1992).

]. This process is ‘phase matched’ when the energy and momentum of the two photon modes (pump mode and scattered ‘Stokes’ mode) are separated precisely by the energy and momentum of the phonon mode (acoustic mode) under consideration. This phase matching occurs near 11 GHz for a 1550 nm pump laser in silica material. However, we note that the optical mode separation in a resonator strongly affects the precise frequency obtained [16

16. M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett. 102, 113601 (2009). [CrossRef] [PubMed]

]. By monitoring back-scattered light through a circulator, we can measure the temporal interference of the pump laser and the scattered Stokes optical signal which occurs at the acoustic frequency ΩSBS (Fig. 1(d)).

Multiple phenomena can contribute to the pressure response of the RP- and SBS-driven OMOs in a hollow optomechanical system, namely (1) geometric effect, (2) stress effect, and (3) temperature effect, as shown in Fig. 2. The deformation of the resonator geometry by the application of differential pressure ΔP = PintPamb, will affect the mechanical frequency ΩM directly. This can be modeled via the resonant frequency equation for the breathing mechanical modes of an annular resonator [53

53. S. Timoshenko, D. H. Young, and W. Weaver, “Beams of elastic bodies,” in “Vibration Problems in Engineering” (John Wiley, 1974), pp. 455–477.

] of radius R.
ΩM=12πREρ
(1)
where, E is the modulus of elasticity and ρ is the mass density. The stiffness of the resonator decreases as the radius of the annulus increases. For a radius R of 67.5 μm and a wall thickness of 12 μm (Fig. 1(a)), the change of radius of the resonator with respect to ΔP can be calculated through finite element analysis in COMSOL Multiphysics [54

54. Comsol Group, “COMSOL Multiphysics,” http://www.comsol.com/.

] to provide dR/dΔP = 3.82 × 10−12 m/kPa. Similarly, the mechanical frequency due to geometry perturbation can also be calculated to get dΩM/dR = −0.19 × 1012 Hz/m. Here, we define a new quantity, the pressure coefficient of frequency, PCf = dΩM/dΔP = dΩM/dR × dR/dΔP = −0.736 Hz/kPa caused by geometry change alone.

Fig. 2 Aerostatic tuning mechanisms: Increasing the internal aerostatic pressure (Pint) causes geometry change (radius, dR) and increases the stress (S) in the resonator shell, both of which cause the mechanical frequency to shift. Geometry and stress effects also modify the optical modes, which changes the laser power coupling and thus energy dissipation in the resonator, modifying the device temperature. Since the mechanical modulii of a material are temperature-dependent, this also induces a change in the mechanical frequency of the OMO.

Circumferential stress (S) is also developed on the resonator when pressure is applied. Stress-induced stiffening effects are well-understood, and have been previously studied in the case of beams as described by equation (5.144) of [53

53. S. Timoshenko, D. H. Young, and W. Weaver, “Beams of elastic bodies,” in “Vibration Problems in Engineering” (John Wiley, 1974), pp. 455–477.

] and in the case of curved beams and annular resonators in [55

55. P. Chidamparam and A. W. Leissa, “Vibrations of planar curved beams, rings, and arches,” Appl. Mech. Rev. 46, 467–483 (1993). [CrossRef]

]. In general, higher tensile stress (such as that caused due to pressure exerting an outward force on a hollow tube) causes mechanical resonance frequencies to increase [55

55. P. Chidamparam and A. W. Leissa, “Vibrations of planar curved beams, rings, and arches,” Appl. Mech. Rev. 46, 467–483 (1993). [CrossRef]

].

3. Experimental results

Our experiment is capable of testing over a wide differential pressure range (ΔP = −90 kPa to 1000 kPa). However, in order to avoid optical and mechanical mode hopping, we experimentally measure the behavior of the RP- and SBS-driven OMOs over a smaller pressure range. As described above, the PCf is the fractional shift of oscillation frequency for a change in ΔP. As shown in Fig. 3, the mechanical vibration frequency is tuned through internally applied pressure. The sensitivity is measured to be PCf = −3.1 Hz/kPa without any control applied to the coupled optical power. As we described above, when pressure is increased inside the resonator, the geometric deformation and the temperature effect both act to decrease the mechanical frequency. However, the stress effect simultaneously acts to increase the mechanical frequency. A study of these three effects separately is necessary to verify our hypothesis. However, decoupling the geometric effect and stress effect is not feasible. Nevertheless, one can apply feedback control on the coupled optical power in order to at least eliminate the temperature effect. With such feedback applied (Fig. 3), the PCf without the temperature effect is measured to be +4.4 Hz/kPa. Since the geometrical effect is small as calculated (PCf = −0.736 Hz/kPa), this positive PCf verifies the strong influence of the additional stress-tuning effect. The reversed sign of PCf indicates that the temperature effect is a major influence in determining sensitivity of this high-Q OMO.

Fig. 3 Aerostatic tuning of a 13.07 MHz RP-driven OMO. We characterize aerostatic tuning of the OMO using a fixed-frequency pump laser, observing a negative pressure coefficient of frequency (PCf) caused by lowering of the temperature of the device due to the optical mode shift. When feedback control is applied on the laser (to track the shifting optical mode) the amount of power coupling into the device does not change. Thus the temperature effect is eliminated and the net positive PCf indicates that the OMO frequency is dominated by the increasing stress in the resonator shell.

In contrast to the RP-driven OMO, the SBS-driven 11 GHz OMO requires two optical modes and one acoustic mode that are mutually phase matched (this can also be understood as a momentum and energy conservation requirement) [21

21. G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat. Commun. 4, 1994 (2013). [CrossRef] [PubMed]

,31

31. K. H. Kim, G. Bahl, W. Lee, J. Liu, M. Tomes, X. Fan, and T. Carmon, “Cavity optomechanics on a microfluidic resonator with water and viscous liquids,” to appear in Light Sci. Appl. (2013), arXiv.org:1205.5477.

]. At such high frequencies, the WGAMs are part of a continuum, and thus do not restrict a specific operational frequency. As a result, pressure tuning of SBS-driven OMOs is highly sensitive to the separation between the two optical modes involved, which are known to exhibit a wide variety of slopes in their dispersion behavior [58

58. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Strekalov, and L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76, 023816 (2007). [CrossRef]

, 59

59. T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008). [CrossRef] [PubMed]

]. Our experimental data provides evidence for this argument by demonstrating both positive (Fig. 4(a)) and negative (Fig. 4(b)) PCf for different 11 GHz OMOs on the same resonator. We find that for any specific optomechanical coupling mode the SBS-based sensor demonstrates very large absolute pressure sensitivity (up to |PCf| = 55 kHz/kPa) and is repeatable.

Fig. 4 Aerostatic tuning of 11.2 GHz SBS-driven OMOs: Both (a) negative and (b) positive PCf are observed in multiple trials, exhibiting large absolute pressure sensitivity. The red line is a linear fit to the data.

Finally, we note that on a low stiffness shell-type resonator that we explore here, it is easy to actuate SBS-driven oscillation simultaneously with RP-driven oscillation. A representative experimental spectrogram demonstrating such dual-mode operation is shown in Fig. 5. The SBS oscillation (ΩSBS ≈ 11.2 GHz) is modulated by the RP oscillation (ΩRP ≈ 16 MHz) resulting in sidebands that are separated by ΩRP. This modulation occurs because the resonator geometry is being modified by the radiation pressure oscillation, resulting in coupling between the two oscillation modes. As the internal pressure is changed from 1 atm (∼101 kPa) to 5 atm (∼500 kPa), both ΩRP and ΩSBS are tuned (Fig. 5). The tuning of the two modes can be quantified accurately by interferometric measurement of the forward and backward scattered optical signals as explained previously. A representative result is shown in Fig. 6. The frequency shift data are presented in parts-per-million (ppm) since the absolute sensitivity of the SBS oscillator is four orders-of-magnitude greater than the RP oscillator. Such multimode operation enables the future possibility of self-referencing the pressure sensor without need for additional amplitude or wavelength references.

Fig. 5 RP and SBS oscillations can be simultaneously actuated on a single device as evidenced in this spectrogram. Experimentally, the ΩRP = 11 GHz oscillation shows multiple sidebands separated by ΩRP = 16 MHz. As internal pressure is changed from 1 atm (∼101 kPa) to 5 atm (∼500 kPa), both the 11 GHz OMO and the 16 MHz OMO are tuned. CF, center frequency.
Fig. 6 Aerostatic tuning experiment with simultaneous RP (15.2 MHz) and SBS oscillation (11 GHz) on a device. Fractional mechanical frequency shift is recorded in parts-per-million (ppm) for convenient comparison since the SBS OMO absolute sensitivity is four order-of-magnitude higher.

4. Conclusions

We have experimentally demonstrated and characterized the first aerostatically-tunable optomechanical oscillators driven by both radiation pressure as well as stimulated Brillouin scattering. Potential applications of this system include pressure sensing in extremely harsh conditions, particularly in high temperature environments. Understanding the pressure-sensitivity of these deformable devices is also important for future optomechanics experiments with liquid-phase media such as viscous liquids, bioanalytes [21

21. G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat. Commun. 4, 1994 (2013). [CrossRef] [PubMed]

, 31

31. K. H. Kim, G. Bahl, W. Lee, J. Liu, M. Tomes, X. Fan, and T. Carmon, “Cavity optomechanics on a microfluidic resonator with water and viscous liquids,” to appear in Light Sci. Appl. (2013), arXiv.org:1205.5477.

], and superfluids [60

60. L. A. DeLorenzo and K. C. Schwab, “Superfluid optomechanics: Coupling of a superfluid to a superconducting condensate” (2013),arXiv.org:1308.2164.

]. We note that multimode oscillators with different coefficients-of-frequency have been employed widely in quartz [61

61. J. Vig, “Dual-mode oscillators for clocks and sensors,” in Proceedings of IEEE Ultrasonics Symposium (IEEE, New York, 1999), pp. 859–868.

] and MEMS [62

62. J. C. Salvia, R. Melamud, S. A. Chandorkar, S. F. Lord, and T. W. Kenny, “Real-time temperature compensation of MEMS oscillators using an integrated micro-oven and a phase-locked loop,” J. Microelectromech. Syst. 19, 192–201 (2010). [CrossRef]

] resonator technology to provide reference-free operation for timing reference and sensor applications. Finally, we note that this coupled system involves a MHz regime mechanical oscillator, a GHz regime mechanical oscillator, and a 200 THz regime optical oscillator. This presents a unique and exciting opportunity to explore coupled oscillator dynamics over extremely broad timescales, and to study the coupling of fields and signals spanning radio-frequency, microwave, and optical regimes.

Acknowledgments

Funding for this research was provided through a University of Illinois Startup Grant. We would like to acknowledge stimulating discussions and guidance from Prof. Tal Carmon, Prof. Xudong Fan, Prof. William P. King, Prof. Randy Ewoldt, Prof. Taher Saif, Prof. Rashid Bashir, Prof. Kimani Toussaint, Prof. Lynford Goddard, and Sandeep Anand.

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5.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–74 (2006). [CrossRef] [PubMed]

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D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444, 75–78 (2006). [CrossRef] [PubMed]

8.

J. Thompson, B. Zwickl, A. Jayich, F. Marquardt, S. Girvin, and J. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008). [CrossRef] [PubMed]

9.

J. Chan, T. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011). [CrossRef] [PubMed]

10.

R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A 83, 063835 (2011). [CrossRef]

11.

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett. 30, 3042–3044 (2005). [CrossRef] [PubMed]

12.

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, 480–484 (2008). [CrossRef] [PubMed]

13.

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

14.

Q. Lin, J. Rosenberg, X. Jiang, K. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009). [CrossRef] [PubMed]

15.

I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102, 043902 (2009). [CrossRef]

16.

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett. 102, 113601 (2009). [CrossRef] [PubMed]

17.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Surface acoustic wave opto-mechanical oscillator and frequency comb generator,” Opt. Lett. 36, 3338–3340 (2011). [CrossRef] [PubMed]

18.

G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403 (2011). [CrossRef] [PubMed]

19.

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8, 203–207 (2012). [CrossRef]

20.

P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).

21.

G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat. Commun. 4, 1994 (2013). [CrossRef] [PubMed]

22.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010). [CrossRef] [PubMed]

23.

C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Transient optomechanically induced transparency in a silica microsphere,” Phys. Rev. A 87, 055802 (2013). [CrossRef]

24.

C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012). [CrossRef] [PubMed]

25.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6, 768–772 (2012). [CrossRef]

26.

D. N. Hutchison and S. A. Bhave, “Z-axis optomechanical accelerometer,” in Proceedings of IEEE Conference on Micro Electro Mechanical Systems (IEEE, New York, 2012), pp. 615–619.

27.

F. Liu and M. Hossein-Zadeh, “Mass sensing with optomechanical oscillation,” IEEE Sensors J. 13, 146–147 (2013). [CrossRef]

28.

F. Liu and M. Hossein-Zadeh, “On the spectrum of radiation pressure driven optomechanical oscillator and its application in sensing,” Opt. Commun. 294, 338–343 (2013). [CrossRef]

29.

E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7, 509–514 (2012). [CrossRef] [PubMed]

30.

Y. Liu, H. Miao, V. Aksyuk, and K. Srinivasan, “Integrated cavity optomechanical sensors for atomic force microscopy,” in Proceedings of IEEE Conference on Microsystems for Measurement and Instrumentation (IEEE, New York, 2012).

31.

K. H. Kim, G. Bahl, W. Lee, J. Liu, M. Tomes, X. Fan, and T. Carmon, “Cavity optomechanics on a microfluidic resonator with water and viscous liquids,” to appear in Light Sci. Appl. (2013), arXiv.org:1205.5477.

32.

M. Zhang, G. S. Wiederhecker, S. Manipatruni, A. Barnard, P. McEuen, and M. Lipson, “Synchronization of micromechanical oscillators using light,” Phys. Rev. Lett. 109, 233906 (2012). [CrossRef]

33.

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

34.

G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Characterization of surface acoustic wave optomechanical oscillators,” in Proceedings of IEEE Conference on Frequency Control and the European Frequency and Time Forum (IEEE, New York, 2011).

35.

A. Watkins, J. Ward, Y. Wu, and S. Nic Chormaic, “Single-input spherical microbubble resonator,” Opt. Lett. 36, 2113–2115 (2011). [CrossRef] [PubMed]

36.

R. Henze, T. Seifert, J. Ward, and O. Benson, “Tuning whispering gallery modes using internal aerostatic pressure,” Opt. Lett. 36, 4536–4538 (2011). [CrossRef] [PubMed]

37.

S. Lacey, I. M. White, Y. Sun, S. I. Shopova, J. M. Cupps, P. Zhang, and X. Fan, “Versatile opto-fluidic ring resonator lasers with ultra-low threshold,” Opt. Express 15, 15523–15530 (2007). [CrossRef] [PubMed]

38.

X. Zhao, J. M. Tsai, H. Cai, X. M. Ji, J. Zhou, M. H. Bao, Y. P. Huang, D. L. Kwong, and A. Q. Liu, “A nano-opto-mechanical pressure sensor via ring resonator,” Opt. Express 20, 8535–8542 (2012). [CrossRef] [PubMed]

39.

R. Madugani, Y. Yang, J. M. Ward, J. D. Riordan, S. Coppola, V. Vespini, S. Grilli, A. Finizio, P. Ferraro, and S. Nic Chormaic, “Terahertz tuning of whispering gallery modes in a PDMS stand-alone, stretchable microsphere,” Opt. Lett. 37, 4762–4764 (2012). [CrossRef] [PubMed]

40.

K. Han, K. H. Kim, J. Kim, W. Lee, J. Liu, X. Fan, T. Carmon, and G. Bahl, “Fabrication and testing of microfluidic optomechanical oscillators,” J. Vis. Exp., in review (2013).

41.

W. Lee, Y. Sun, H. Li, K. Reddy, M. Sumetsky, and X. Fan, “A quasi-droplet optofluidic ring resonator laser using a micro-bubble,” Appl. Phys. Lett. 99, 091102 (2011). [CrossRef]

42.

M. N. M. Nasir, M. Ding, G. S. Murugan, and M. N. Zervas, “Microtaper fiber excitation effects in bottle microresonators,” Proc. SPIE LASE 8600, 860020 (2013). [CrossRef]

43.

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131 (1997). [CrossRef] [PubMed]

44.

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12, 4742–4750 (2004). [CrossRef] [PubMed]

45.

G. Bahl, X. Fan, and T. Carmon, “Acoustic whispering-gallery modes in optomechanical shells,” New J. Phys. 14, 115026 (2012). [CrossRef]

46.

H. Rokhsari, T. Kippenberg, T. Carmon, and K. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13, 5293–5301 (2005). [CrossRef] [PubMed]

47.

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95, 033901 (2005). [CrossRef] [PubMed]

48.

R. Chiao, C. Townes, and B. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12, 592–595 (1964). [CrossRef]

49.

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137, A1787–A1805 (1965). [CrossRef]

50.

R. Boyd, “Stimulated Brillouin and stimulated Rayleigh scattering,” in Nonlinear Optics (Academic, 1992).

51.

G. Bahl and T. Carmon, “Brillouin optomechanics” (2013), arxiv.org:1309.2828.

52.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013). [CrossRef] [PubMed]

53.

S. Timoshenko, D. H. Young, and W. Weaver, “Beams of elastic bodies,” in “Vibration Problems in Engineering” (John Wiley, 1974), pp. 455–477.

54.

Comsol Group, “COMSOL Multiphysics,” http://www.comsol.com/.

55.

P. Chidamparam and A. W. Leissa, “Vibrations of planar curved beams, rings, and arches,” Appl. Mech. Rev. 46, 467–483 (1993). [CrossRef]

56.

D. N. Nikogosyan, Properties of Optical and Laser-Related Materials: A Handbook (John Wiley, 1997).

57.

R. Melamud, B. Kim, S. A. Chandorkar, M. A. Hopcroft, M. Agarwal, C. M. Jha, and T. W. Kenny, “Temperature-compensated high-stability silicon resonators,” Appl. Phys. Lett. 90, 244107 (2007). [CrossRef]

58.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Strekalov, and L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76, 023816 (2007). [CrossRef]

59.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008). [CrossRef] [PubMed]

60.

L. A. DeLorenzo and K. C. Schwab, “Superfluid optomechanics: Coupling of a superfluid to a superconducting condensate” (2013),arXiv.org:1308.2164.

61.

J. Vig, “Dual-mode oscillators for clocks and sensors,” in Proceedings of IEEE Ultrasonics Symposium (IEEE, New York, 1999), pp. 859–868.

62.

J. C. Salvia, R. Melamud, S. A. Chandorkar, S. F. Lord, and T. W. Kenny, “Real-time temperature compensation of MEMS oscillators using an integrated micro-oven and a phase-locked loop,” J. Microelectromech. Syst. 19, 192–201 (2010). [CrossRef]

OCIS Codes
(290.5830) Scattering : Scattering, Brillouin
(140.3945) Lasers and laser optics : Microcavities
(120.4880) Instrumentation, measurement, and metrology : Optomechanics

ToC Category:
Optical Devices

History
Original Manuscript: October 31, 2013
Revised Manuscript: December 20, 2013
Manuscript Accepted: January 6, 2014
Published: January 13, 2014

Virtual Issues
Vol. 9, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Kewen Han, Jun Hwan Kim, and Gaurav Bahl, "Aerostatically tunable optomechanical oscillators," Opt. Express 22, 1267-1276 (2014)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-22-2-1267


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References

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  4. T. Carmon, H. Rokhsari, L. Yang, T. Kippenberg, K. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005). [CrossRef] [PubMed]
  5. O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–74 (2006). [CrossRef] [PubMed]
  6. S. Gigan, H. Bohm, M. Paternostro, F. Blaser, G. Langer, J. Hertzberg, K. Schwab, D. Bauerle, M. Aspelmeyer, A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006). [CrossRef] [PubMed]
  7. D. Kleckner, D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444, 75–78 (2006). [CrossRef] [PubMed]
  8. J. Thompson, B. Zwickl, A. Jayich, F. Marquardt, S. Girvin, J. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008). [CrossRef] [PubMed]
  9. J. Chan, T. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011). [CrossRef] [PubMed]
  10. R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, T. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A 83, 063835 (2011). [CrossRef]
  11. M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett. 30, 3042–3044 (2005). [CrossRef] [PubMed]
  12. M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008). [CrossRef] [PubMed]
  13. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459, 550–555 (2009). [CrossRef] [PubMed]
  14. Q. Lin, J. Rosenberg, X. Jiang, K. Vahala, O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009). [CrossRef] [PubMed]
  15. I. S. Grudinin, A. B. Matsko, L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102, 043902 (2009). [CrossRef]
  16. M. Tomes, T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett. 102, 113601 (2009). [CrossRef] [PubMed]
  17. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, L. Maleki, “Surface acoustic wave opto-mechanical oscillator and frequency comb generator,” Opt. Lett. 36, 3338–3340 (2011). [CrossRef] [PubMed]
  18. G. Bahl, J. Zehnpfennig, M. Tomes, T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403 (2011). [CrossRef] [PubMed]
  19. G. Bahl, M. Tomes, F. Marquardt, T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8, 203–207 (2012). [CrossRef]
  20. P. Rakich, C. Reinke, R. Camacho, P. Davids, Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).
  21. G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat. Commun. 4, 1994 (2013). [CrossRef] [PubMed]
  22. S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010). [CrossRef] [PubMed]
  23. C. Dong, V. Fiore, M. C. Kuzyk, H. Wang, “Transient optomechanically induced transparency in a silica microsphere,” Phys. Rev. A 87, 055802 (2013). [CrossRef]
  24. C. Dong, V. Fiore, M. C. Kuzyk, H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012). [CrossRef] [PubMed]
  25. A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6, 768–772 (2012). [CrossRef]
  26. D. N. Hutchison, S. A. Bhave, “Z-axis optomechanical accelerometer,” in Proceedings of IEEE Conference on Micro Electro Mechanical Systems (IEEE, New York, 2012), pp. 615–619.
  27. F. Liu, M. Hossein-Zadeh, “Mass sensing with optomechanical oscillation,” IEEE Sensors J. 13, 146–147 (2013). [CrossRef]
  28. F. Liu, M. Hossein-Zadeh, “On the spectrum of radiation pressure driven optomechanical oscillator and its application in sensing,” Opt. Commun. 294, 338–343 (2013). [CrossRef]
  29. E. Gavartin, P. Verlot, T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7, 509–514 (2012). [CrossRef] [PubMed]
  30. Y. Liu, H. Miao, V. Aksyuk, K. Srinivasan, “Integrated cavity optomechanical sensors for atomic force microscopy,” in Proceedings of IEEE Conference on Microsystems for Measurement and Instrumentation (IEEE, New York, 2012).
  31. K. H. Kim, G. Bahl, W. Lee, J. Liu, M. Tomes, X. Fan, T. Carmon, “Cavity optomechanics on a microfluidic resonator with water and viscous liquids,” to appear in Light Sci. Appl. (2013), arXiv.org:1205.5477.
  32. M. Zhang, G. S. Wiederhecker, S. Manipatruni, A. Barnard, P. McEuen, M. Lipson, “Synchronization of micromechanical oscillators using light,” Phys. Rev. Lett. 109, 233906 (2012). [CrossRef]
  33. J. Rosenberg, Q. Lin, O. Painter, “Static and dynamic wavelength routing via the gradient optical force,” Nat. Photonics 3, 478–483 (2009). [CrossRef]
  34. G. Bahl, J. Zehnpfennig, M. Tomes, T. Carmon, “Characterization of surface acoustic wave optomechanical oscillators,” in Proceedings of IEEE Conference on Frequency Control and the European Frequency and Time Forum (IEEE, New York, 2011).
  35. A. Watkins, J. Ward, Y. Wu, S. Nic Chormaic, “Single-input spherical microbubble resonator,” Opt. Lett. 36, 2113–2115 (2011). [CrossRef] [PubMed]
  36. R. Henze, T. Seifert, J. Ward, O. Benson, “Tuning whispering gallery modes using internal aerostatic pressure,” Opt. Lett. 36, 4536–4538 (2011). [CrossRef] [PubMed]
  37. S. Lacey, I. M. White, Y. Sun, S. I. Shopova, J. M. Cupps, P. Zhang, X. Fan, “Versatile opto-fluidic ring resonator lasers with ultra-low threshold,” Opt. Express 15, 15523–15530 (2007). [CrossRef] [PubMed]
  38. X. Zhao, J. M. Tsai, H. Cai, X. M. Ji, J. Zhou, M. H. Bao, Y. P. Huang, D. L. Kwong, A. Q. Liu, “A nano-opto-mechanical pressure sensor via ring resonator,” Opt. Express 20, 8535–8542 (2012). [CrossRef] [PubMed]
  39. R. Madugani, Y. Yang, J. M. Ward, J. D. Riordan, S. Coppola, V. Vespini, S. Grilli, A. Finizio, P. Ferraro, S. Nic Chormaic, “Terahertz tuning of whispering gallery modes in a PDMS stand-alone, stretchable microsphere,” Opt. Lett. 37, 4762–4764 (2012). [CrossRef] [PubMed]
  40. K. Han, K. H. Kim, J. Kim, W. Lee, J. Liu, X. Fan, T. Carmon, G. Bahl, “Fabrication and testing of microfluidic optomechanical oscillators,” J. Vis. Exp., in review (2013).
  41. W. Lee, Y. Sun, H. Li, K. Reddy, M. Sumetsky, X. Fan, “A quasi-droplet optofluidic ring resonator laser using a micro-bubble,” Appl. Phys. Lett. 99, 091102 (2011). [CrossRef]
  42. M. N. M. Nasir, M. Ding, G. S. Murugan, M. N. Zervas, “Microtaper fiber excitation effects in bottle microresonators,” Proc. SPIE LASE 8600, 860020 (2013). [CrossRef]
  43. J. C. Knight, G. Cheung, F. Jacques, T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131 (1997). [CrossRef] [PubMed]
  44. T. Carmon, L. Yang, K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12, 4742–4750 (2004). [CrossRef] [PubMed]
  45. G. Bahl, X. Fan, T. Carmon, “Acoustic whispering-gallery modes in optomechanical shells,” New J. Phys. 14, 115026 (2012). [CrossRef]
  46. H. Rokhsari, T. Kippenberg, T. Carmon, K. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13, 5293–5301 (2005). [CrossRef] [PubMed]
  47. T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95, 033901 (2005). [CrossRef] [PubMed]
  48. R. Chiao, C. Townes, B. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12, 592–595 (1964). [CrossRef]
  49. Y. R. Shen, N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137, A1787–A1805 (1965). [CrossRef]
  50. R. Boyd, “Stimulated Brillouin and stimulated Rayleigh scattering,” in Nonlinear Optics (Academic, 1992).
  51. G. Bahl, T. Carmon, “Brillouin optomechanics” (2013), arxiv.org:1309.2828.
  52. H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013). [CrossRef] [PubMed]
  53. S. Timoshenko, D. H. Young, W. Weaver, “Beams of elastic bodies,” in “Vibration Problems in Engineering” (John Wiley, 1974), pp. 455–477.
  54. Comsol Group, “COMSOL Multiphysics,” http://www.comsol.com/ .
  55. P. Chidamparam, A. W. Leissa, “Vibrations of planar curved beams, rings, and arches,” Appl. Mech. Rev. 46, 467–483 (1993). [CrossRef]
  56. D. N. Nikogosyan, Properties of Optical and Laser-Related Materials: A Handbook (John Wiley, 1997).
  57. R. Melamud, B. Kim, S. A. Chandorkar, M. A. Hopcroft, M. Agarwal, C. M. Jha, T. W. Kenny, “Temperature-compensated high-stability silicon resonators,” Appl. Phys. Lett. 90, 244107 (2007). [CrossRef]
  58. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Strekalov, L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76, 023816 (2007). [CrossRef]
  59. T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008). [CrossRef] [PubMed]
  60. L. A. DeLorenzo, K. C. Schwab, “Superfluid optomechanics: Coupling of a superfluid to a superconducting condensate” (2013),arXiv.org:1308.2164.
  61. J. Vig, “Dual-mode oscillators for clocks and sensors,” in Proceedings of IEEE Ultrasonics Symposium (IEEE, New York, 1999), pp. 859–868.
  62. J. C. Salvia, R. Melamud, S. A. Chandorkar, S. F. Lord, T. W. Kenny, “Real-time temperature compensation of MEMS oscillators using an integrated micro-oven and a phase-locked loop,” J. Microelectromech. Syst. 19, 192–201 (2010). [CrossRef]

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