Integrated waveguide-DBR microcavity opto - OSA Publishing

Integrated waveguide-DBR microcavity optomechanical system Marcel W. Pruessner,1,* Todd H. Stievater,1,* Jacob B. Khurgin,2 and William S. Rabinovich1,* 2

1 Naval Research Laboratory, Washington, DC 20375, USA Johns Hopkins University, Baltimore, Maryland 21218, USA * [email protected]

Abstract: Cavity opto-mechanics exploits optical forces acting on mechanical structures. Many opto-mechanics demonstrations either require extensive alignment of optical components for probing and measurement, which limits the number of opto-mechanical devices on-chip; or the approaches limit the ability to control the opto-mechanical parameters independently. In this work, we propose an opto-mechanical architecture incorporating a waveguide-DBR microcavity coupled to an in-plane microbridge resonator, enabling large-scale integration on-chip with the ability to individually tune the optical and mechanical designs. We experimentally characterize our device and demonstrate mechanical resonance damping and amplification, including the onset of coherent oscillations. The resulting collapse of the resonance linewidth implies a strong increase in effective mechanical quality-factor, which is of interest for high-resolution sensing. ©2011 Optical Society of America OCIS codes: (200.4880) Optomechanics; (230.4685) Optical microelectromechanical devices; (140.3945) Microcavities; (280.4788) Optical sensing and sensors.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008). I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3(4), 201–205 (2009). F. Marquardt and S. Girvin, “Optomechanics,” Physics 2, 40 (2009). 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(7221), 480–484 (2008). M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009). J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009). C. H. Metzger and K. Karrai, “Cavity cooling of a microlever,” Nature 432(7020), 1002–1005 (2004). S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444(7115), 67–70 (2006). O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444(7115), 71–74 (2006). M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, “Autoparametric optical drive for micromechanical oscillators,” Appl. Phys. Lett. 79(5), 695–697 (2001). 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(3), 033901 (2005). H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13(14), 5293–5301 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX13-14-5293. T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressureinduced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005). A. Schliesser, P. Del’Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, “Radiation pressure cooling of a micromechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 97(24), 243905 (2006). S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold microoptomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5(7), 485–488 (2009).

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Received 20 Jun 2011; revised 6 Sep 2011; accepted 30 Sep 2011; published 21 Oct 2011

24 October 2011 / Vol. 19, No. 22 / OPTICS EXPRESS 21904

16. G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009). 17. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009). 18. L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nanooptomechanical disk resonator,” Phys. Rev. Lett. 105(26), 263903 (2010). 19. K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11(2), 791–797 (2011). 20. M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “In-plane microelectromechanical resonator with integrated Fabry–Pérot cavity,” Appl. Phys. Lett. 92(8), 081101 (2008). 21. P. Yeh, Optical Waves in Layered Media, B.E. Saleh, ed., (Wiley, 1998), Chapter 5. 22. C. Metzger, I. Favero, A. Ortlieb, and K. Karrai, “Optical self cooling of a deformable Fabry-Perot cavity in the classical limit,” Phys. Rev. B 78(3), 035309 (2008). 23. U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” IEEE Photon. Technol. Lett. 8(5), 647–648 (1996). 24. M. W. Pruessner, J. B. Khurgin, T. H. Stievater, and W. S. Rabinovich, “an optically pumped phonon laser in a silicon micromechanical oscillator,” Conf. on Lasers and Electro-Optics (CLEO), May 1–6, 2011, Baltimore, MD. Technical Digest (CD) (Optical Society of America, 2011), paper QWI3. http://www.opticsinfobase.org/abstract.cfm?URI=QELS-2011-QWI3. 25. K. L. Ekinci and M. L. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum. 76(6), 061101 (2005). 26. N. V. Lavrik, M. J. Sepaniak, and P. G. Datskos, “Cantilever transducers as a platform for chemical and biological sensors,” Rev. Sci. Instrum. 75(7), 2229–2253 (2004). 27. T. H. Stievater, W. S. Rabinovich, N. A. Papanicolaou, R. Bass, and J. B. Boos, “Measured limits of detection based on thermal-mechanical frequency noise in micromechanical sensors,” Appl. Phys. Lett. 90(5), 051114 (2007). 28. M. W. Pruessner, T. H. Stievater, M. S. Ferraro, W. S. Rabinovich, J. L. Stepnowski, and R. A. McGill, “Waveguide micro-opto-electro-mechanical resonant chemical sensors,” Lab Chip 10(6), 762–768 (2010). 29. B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectromechanical oscillators,” J. Appl. Phys. 95(7), 3694–3703 (2004). 30. U. Krishnamoorthy, R. H. Olsson III, G. R. Bogart, M. S. Baker, D. W. Carr, T. P. Swiler, and P. J. Clews, “Inplane MEMS-based nano-g accelerometer with sub-wavelength optical resonant sensor,” Sens. Actuators A Phys. 145–146, 283–290 (2008). 31. T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, Jr., J. Cole, S. Rashleigh, and R. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. 18(4), 626–665 (1982). 32. G. A. Cranch, G. M. H. Flockhart, and C. K. Kirkendall, “High-resolution distributed-feedback fiber laser dc magnetometer based on the Lorentzian force,” Meas. Sci. Technol. 20(3), 034023 (2009). 33. F. Keplinger, S. Kvasnica, A. Jachimowicz, F. Kohl, J. Steurer, and H. Hauser, “Lorentz force based magnetic field sensor with optical readout,” Sens. Actuators A Phys. 110(1-3), 112–118 (2004). 34. D. F. Edwards, Handbook of Optical Constants of Solids (Academic Press, 1985), Chapter: Silicon (Si), p. 547. 35. http://www.ioffe.ru/SVA/NSM/Semicond/Si/mechanic.html (accessed on November 23, 2010). 36. F. R. Blom, S. Bouwstra, M. Elwenspoek, and J. H. J. Fluitman, “Dependence of the quality factor of micromachined silicon beam resonators on pressure and geometry,” J. Vac. Sci. Technol. B 10(1), 19–26 (1992). 37. M. Bao, H. Yang, H. Yin, and Y. Sun, “Energy transfer model for squeeze-film air damping in low vacuum,” J. Micromech. Microeng. 12(3), 341–346 (2002). 38. C. Gui, R. Legtenberg, M. Elwenspoek, and J. H. Fluitman, “Q-factor dependence of one-port encapsulated polysilicon resonator on reactive sealing pressure,” J. Micromech. Microeng. 5(2), 183–185 (1995). 39. M. W. Pruessner, T. H. Stievater, M. S. Ferraro, and W. S. Rabinovich, “Thermo-optic tuning and switching in SOI waveguide Fabry-Perot microcavities,” Opt. Express 15(12), 7557–7563 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7557. 40. T. H. Stievater, W. S. Rabinovich, H. S. Newman, R. Mahon, P. G. Goetz, J. L. Ebel, and D. J. McGee, “Measurement of thermal-mechanical noise in microelectromechanical systems,” Appl. Phys. Lett. 81(10), 1779–1781 (2002).

1. Introduction It is well known that light exerts a force [1–3] on macro-scale objects. The emergence of micro-electro-mechanical systems (MEMS) makes such forces appreciable when considering the small mass and large compliance achievable in micro-scale devices [4–6]. The light intensity and resulting force is enhanced by optical cavities, e.g. linear Fabry-Perot [7–9] or circular micro-ring/disk/toroids [10–14]. In addition to amplifying the optical force, a cavity results in coupling between the optical and mechanical systems. The resulting feedback [2] enables mechanical amplification/damping via wavelength tuning across the cavity mode [7]. Following initial demonstrations of opto-mechanical interaction in micro-scale resonators [7,10], much work has focused on increasingly sophisticated experiments for achieving quantum mechanical ground state cooling [8,9,14,15]. While impressive results were

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achieved, the experimental systems required alignment of external optics for opto-mechanical excitation/damping and resonator motion readout [7–15]. The external optics generally limits the opto-mechanical system to a single device. Recently, integrated waveguide [4–6] cavity opto-mechanical devices were reported, in which the cavity itself forms a mechanical resonator [16–18]. This on-chip waveguide approach [4–6,16,19] paves the way for dense integration of many optical components on a single-chip. In order to take advantage of the dense integration enabled by the monolithic integration of optical waveguides with opto-mechanical structures, we propose and demonstrate a new versatile architecture for amplification and damping in a silicon opto-mechanical integrated circuit. Our approach features the self-aligned fabrication of a bus waveguide coupled to an opto-mechanical resonator. Specifically, a silicon microbridge is intersected by a waveguide cavity (Fig. 1). The suspended microbridge forms a mechanical resonator. We create a FabryPerot cavity using silicon/air distributed Bragg reflectors (DBR’s) [20]. One DBR is fixed; the second is etched into the microbridge center. Any in-plane bridge motion displaces the movable DBR and modulates the cavity transmittance enabling sensitive motion readout. Our architecture has several advantages. The cavity is co-fabricated with the mechanical resonator, avoiding the need for extensive optics alignment [7–10,14,15]. Furthermore, the waveguide-DBR cavity enables the integration of many opto-mechanical components on a common platform: a single fiber coupled to the chip enables the optical interconnection of many opto-mechanical devices via on-chip waveguides without the need for precise alignment to each component. Finally, the opto-mechanical designs are decoupled enabling independent control of optical properties (resonance wavelengths, optical Q-factor, finesse, photon lifetime) and mechanical properties (resonance frequency, mechanical Q-factor, thermal time constant). Having a large design freedom is essential to exploit cavity opto-mechanics for practical applications. For example, we design the microbridge with a high compliance to enable coherent mechanical oscillations with a large increase in effective mechanical Q-factor at low optical powers.

Fig. 1. Integrated waveguide-DBR microcavity opto-mechanical system. (a) Schematic showing optical waveguide, Fabry-Perot cavity consisting of one fixed and a second movable distributed Bragg reflector (DBR), a suspended micro-mechanical bridge resonator with spring constant KSpring, air gaps surrounding the movable DBR, and direction of optical forces (F-pt: photothermal pressure, F-rp: radiation pressure); the in-plane vibration of the movable DBR mirror modulates the Fabry-Perot cavity transmittance (out-of-plane beam motion can generally not be read out). (b) Fabricated silicon-on-insulator coupled opto-mechanical cavity with waveguide Fabry-Perot (red) and silicon microbridge mechanical resonator (green).

2. Device model 2.1 Optical model Our optical microcavity consists of two DBR mirrors separated by a waveguide of length LC = 3 µm. The DBR mirrors consist of three silicon slabs of length L = 25 µm, height H = 4.8 µm, and width dSi≈5λ/4nSi. The silicon slabs are separated by air gaps of width dair ≈λ/4. We #149575 - $15.00 USD

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modeled our microcavity using a one-dimensional transfer matrix [21]. This model was based on experimentally measured or well-known material parameters (Appendix Table A1) with the exception of: (i) the exact thickness of the silicon slab in the DBR; (ii) the exact thickness of the air gap in the DBR; (iii) the diffraction losses within the air gaps of the DBR; and (iv) the material absorption loss of our silicon device layer. The two thicknesses were constrained such that their sum was equal to the nominal DBR period (944 nm), leaving only three free parameters in our transfer matrix model. These three free parameters were then chosen so that the output finesse and cavity transmission of the model matched our measured values (Appendix Table A2). We added input and output waveguides on both sides of the DBR cavity to reproduce the measured etaloning from facet reflections. The measured transmission spectra are matched to the exact level of transmission at resonance in the model by adding input and output sample coupling factors. These factors (≈0.32) account for both coupling losses and Fresnel reflections from the vacuum cell windows. They are then used to convert the incident laser power on the vacuum cell to the forward optical power in the input waveguide (Popt) that is incident on the DBR cavity. The model finds an exact solution for the optical fields at various wavelengths and positions in the cavity. It also enables us to find the various cavity penetration factors, βi, which describe the decrease in field intensity with optical penetration into the DBR mirror. Figure 2a shows the calculated square of the electric field with the wavelength set to the cavity resonance. In order to obtain the cavity penetration factors, we calculate the forward and backward optical power flow in the structure (Fig. 2b). The ratio of the power flowing in a particular DBR layer N (PDBR-N) to that in the cavity (PCav) gives the penetration factors: β1 ≈ β2 = 0.28, β3 ≈ β4 = 0.08, β5 ≈ β6 = 0.02, and β7 = 0.005. (We note that a similar definition also holds for a single DBR mirror, where “PCav” is replaced by the incident power hitting the DBR). The penetration factors are critical for proper scaling of the optical force – the DBR mirror makes our structure and its analysis fundamentally different from previous Fabry-Perot opto-mechanical structures [7].

Fig. 2. Transfer matrix calculation of cavity optical field. (a) Cross-section of DBR mirrors and optical cavity showing calculated electric field squared profile on-resonance. (b) Calculated power flow, where Popt. is the incident power on the input DBR, Pcav. is the cavity power, and PDBR. is the power in the Nth- silicon slab of the DBR. The βN-factors indicate the power in each DBR region relative to Pcav. The absorbed power in each silicon region N is found from the difference between the power flow into region N and the flow out of that region, summed for both forward and backward power flows.

2.2 Optical forces The opto-mechanical forces arise from radiation- and photothermal pressure. In the absence of a cavity, the radiation pressure on the DBR microbridge is:

F0rp ≈  2 ( β1 − β 7 ) / c  ( K eff K p ) Popt ,

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(1)



where Keff is the effective distributed-load beam spring constant and Kp is the point-load spring constant. The factor β1 (β7) accounts for the decrease in power flow with penetration depth into the first (last) DBR air gap, with respect to the peak power flow in the cavity (Fig. 2). We note that in this equation β1>>β7 and the forward and backward power flows at the first DBR slab (PDBR-1) are almost identical indicating that the mirror reflectivity is R≈100%. A full treatment, however, considers all terms (ΣPDBR-N), which is what we have done in our analysis. The photothermal pressure results from nonuniform optical absorption and heating in the DBR due to the limited penetration of the field into the mirror (see Appendix Fig. A2). From Fig. 2b it is clear that most of the optical power is absorbed in the cavity and in the first silicon slab (i.e. PDBR-2 = β2PCav) and that the other silicon slabs (β4 and β6) contribute only minimally. In the absence of a cavity, absorption-induced heating, thermal expansion and beam bending produce an equivalent force:

F0pt ≈ − K eff (dz dPabs ) Pabs = − K eff (dz dPabs )  2 ( β 2 − β 6 ) α Si d Si  Popt ,

(2)

where Keff is the microbridge’s effective distributed-load spring constant, dz dPabs describes the beam bending with absorbed optical power (Pabs.), αSi is silicon’s absorption coefficient, and dSi is the DBR silicon slab width. The coefficient dz dPabs is essentially an optical absorption-displacement gain coefficient that is found from simulation assuming a unit heat distribution across the inner (first) DBR silicon slab and subsequent thermal expansion and beam bending. We note that the β2 factor in Eq. (2) emphasizes that the optical power drops significantly in the first DBR silicon slab compared to the power in the main part of the cavity (Fig. 2 and Appendix A2). Any heating in the outermost DBR silicon slab (β6) produces an opposite force and its contribution must be subtracted from the net photothermal force. Furthermore, the contribution of the first DBR silicon slab dominates, since β2>>β6 (i.e. the heating of the inner DBR slab is much greater than the heating of the outer DBR slab). The contribution of the middle slab (β4) can be neglected since any thermal expansion will not result in beam bending due to symmetry. For the optical powers considered here any absorption and heating in the cavity is minimal and does not lead to significant thermo-optic tuning of the optical resonances. We note that absorption, however, may limit the ultimate cavity finesse in any photothermal opto-mechanical device. 2.3 Optical spring An optical force changes a resonator’s spring constant by Kopt. = ∂Fopt./∂z. The net optical force is Fopt = F0χenhL(φ), where F0 is the force without a cavity, χ enh = f Tcav / π is the cavity optical power enhancement on resonance, f is the finesse, TCav. is the net power transmitted through the cavity on-resonance (and √TCav relates the power coupled into the cavity to the incident power), L(φ) is the normalized cavity lineshape, and φ is the phase of the cavity optical field. The optically induced change in spring constant for a Lorentzian lineshape is:

 f Tcav K opt = F0    π

   16 β1 f 2 ∆λ     λ FSR ( 2∆λ δλ ) 2 + 1  0

(

)

2

   ,    

(3)

where Tcav = 4.6%, f = 140, ∆λ = λ-λ0 is the detuning, FSR = 112 nm is the free-spectral-range, and δλ = 0.80 nm is the optical resonance bandwidth (FWHM). Choosing an appropriate detuning makes Kopt positive or negative. While radiation pressure bends the beam to increase

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the cavity length, photothermal pressure bends the beam in the opposite direction (Fig. 3a) resulting in opposing Kopt (Fig. 3b). The resonant frequency (ν) and damping (Γ) in the presence of an optical force are [22]:



ν 2 = ν 0 2 1 +  

1 K eff

 Q Γ = Γ 0 1 − M  K eff 

∑

K opt ( N )

 , 2 ( 2πν 0τ opt ( N ) ) + 1

(4)

∑

K opt ( N )

 , 2 2 1 + πν τ ( 0 opt ( N ) ) 

(5)

Force ( N )

Force ( N )

1

2πν 0τ opt ( N )

where ν0 and Γ are the resonant frequency and damping, respectively, in the absence of optical forces, QM≈2 × 104 in the absence of optical forces and τopt(N) refers to the time constant of force N. For radiation pressure τopt(N) is the cavity photon lifetime, τrp = 1.7 ps. The photothermal time constant is found from simulation by applying a heat load to the mirror and calculating the thermal-temporal response, which is biexponential due to the microbridge geometry (Appendix Fig. A2 and Tables A3 and A4). The fast time constant describes the DBR slab heating (τpt-fast = 3 µs) while the slow time constant corresponds to the heat flow in the silicon microbridge, which has a larger thermal mass and responds slower (τpt-slow = 162 µs). The large discrepancy in time constants means that optically-induced changes to ν are dominated by radiation pressure, while changes to Γ are dominated by the photothermal pressure, predominantly the fast component (τpt-fast).

Fig. 3. Optical manipulation of a micro-mechanical spring. (a) Finite-element method simulation of radiation and photothermal pressure and resulting beam bending; the simulated images clearly show the opposing beam bending. (b) Calculated optical force modification of effective micro-mechanical spring constant (normalized by Keff) as a function of laser detuning for Popt = 370 µW. Radiation pressure and photothermal forces have opposite effect on Kopt. The solid lines in (b) are for the Fabry-Perot cavity only; the dashed lines include the effect of spurious cavities formed between the high reflectivity DBR mirrors and the cleaved waveguide facets at the sample input/output (see Fig. 4b inset).

2.4 Device fabrication The devices are fabricated from silicon-on-insulator wafers with 4.8 µm silicon device layer and 1 µm SiO2 buried oxide, similar to Ref [20]. We pattern the DBR mirrors and silicon microbridge resonator using a single electron-beam lithography exposure and subsequent development followed by cryogenic etching (SF6/O2) through the silicon device layer. The rib waveguides are patterned with contact lithography and a shallow cryogenic etch to a depth of ≈0.5 µm. We then thin the samples and cleave the waveguide facets for optical coupling. The silicon microbridge is released by etching the SiO2 layer in BHF followed by CO2 critical point drying to prevent stiction.

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3. Experimental characterization 3.1 Experimental setup Our experimental setup in Fig. 4a uses a custom vacuum cell with sapphire windows and a rough pump to obtain a base pressure of 20 mTorr (measured with a thermocouple gauge). All measurements are performed at room temperature. The device is characterized in vacuum to minimize damping – the mechanical Q-factor (QM) is approximately 10 at one atmosphere and is >1×104 at 21 mTorr (Appendix Fig. A3). Light from a tunable laser is coupled to our sample using a NIR 100x long working distance objective. After passing through the device and vacuum cell windows, the light is collected with a 50x objective and measured with a custom InGaAs photodetector (2 MHz bandwidth) with an integrated transimpedance amplifier (gain=5×105 V/A) coupled to a digital multimeter. Although we use high-NA objectives to couple light to our device, future devices can be fiber-coupled with low loss [23] using existing packaging technology. First, the Fabry-Perot cavity modes are mapped by sweeping the laser wavelength and measuring the transmittance (Fig. 4b). Next, the mechanical resonances are measured by fixing the laser wavelength near the λ0=1593.75 nm cavity mode and detecting the modulated signal as the DBR vibrates using an electronic spectrum analyzer with 1 Hz resolution (16×averaging to eliminate noise) as the microbridge oscillates. The mechanical resonance spectra show a pronounced wavelength-dependence indicating a strong opto-mechanical interaction (Fig. 4c). Although we can detect several mechanical resonance modes (Appendix Fig. A3), we perform more detailed measurements on the λ0=101 kHz fundamental in-plane (M=0) mechanical resonance (Fig. 5 and Fig. 6). For both wavelength detuning and power dependence measurements we perform a Lorentzian curve fit to obtain ν and Γ.

Fig. 4. (a) Experimental setup. (b) Measured optical spectrum; inset: detail of resonance near λ0 = 1593.75 nm and Lorentzian fit; the high frequency oscillations (0.2-0.3 nm spacing) are due to reflections from the cleaved end-facets of the input/output waveguides. (c) Measured mechanical resonance for the fundamental in-plane resonance mode (M = 0) for red and blue detuned laser (∆λ =+0.38 nm [λ = 1594.13 nm] and ∆λ=−0.34 nm [1593.41 nm], respectively, both at Popt = 590 µW with effective QM ranging from 4.3×103 to >1×105; insets: detail of mechanical resonance for red (ν=101,139 Hz) and blue detuning (ν = 101,176 Hz) with Lorentzian fit. The displacement amplitude is ∆zRMS≈4.0 nm in (c) (red curve, ∆λ=+0.38 nm).

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3.2 Wavelength detuning measurements: fundamental in-plane mode (M=0) We performed experiments on the fundamental in-plane mode (M=0) in vacuum (P~20 mTorr) since this maximizes QM. To characterize our device we fixed the laser power and stepped λ across the Fabry-Perot mode. The measurements indicate a resonant frequency increase for blue detuning (∆λ0), in agreement with a radiation pressure based effect (Fig. 5a). While the photothermal pressure decreases ν slightly for blue detuning, this contribution is minimal since τpt-fast>>τrp. We observe an increase in Γ for blue detuning and a decrease for red detuning (Fig. 5b). From Eq. (5) and the slow photothermal response (τpt.slow/fast>>τrp) we expect that Γ is dominated by photothermal pressure. Indeed, a radiation pressure interaction suggests an increase in Γ for red- and a decrease for blue wavelength detuning [9], in contrast to our measurements. There is some oscillation in Fig. 5a and 5b (0.2-0.3 nm wavelength spacing), which is due to etaloning from the DBR mirrors and the uncoated waveguide facets (see the Fabry-Perot optical spectrum in Fig. 4b inset).

Fig. 5. Optical tuning of resonant frequency and damping. (a) Measured resonant frequency shift (ν-ν0) vs. detuning and theoretical shift. (b) Measured mechanical resonance width (Γ) vs. cavity detuning and theoretical linewidth. All measurements were performed at Popt = 370 µW. Frequency tuning is dominated by radiation pressure, while the linewidth Γ is determined entirely by photothermal forces. The vertical lines at ∆λ = −0.34 nm and + 0.38 nm (∆λ = −0.33 nm and + 0.34 nm) indicate the detuning for power dependent measurements (theory) in Fig. 6a, 6b, and 6c. The model includes the effect of the sample input/output waveguide facets. The scattering in Fig. 5b for ∆λ