Dynamic Phonon Manipulation by Optomechanically InducedStrong Coupling between Two Distinct Mechanical ResonatorsJianguo Huang,†,‡,§ Lip Ket Chin,‡ Hong Cai,§ Huan Li,∥ Jiu Hui Wu,† Tianning Chen,† Mo Li,∥

and Ai-Qun Liu*,‡

†School of Mechanical Engineering, Xi’an Jiaotong University and State Key Laboratory for Strength and Vibration of MechanicalStructures, Xi’an 710049, China‡School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore§Institute of Microelectronics, A*STAR (Agency for Science, Technology and Research), 2 Fusionopolis Way, #08-02 InnovisTower, Singapore 138634, Singapore∥Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota 55455, United States

*S Supporting Information

ABSTRACT: Optical information storage is essential foroptical and quantum computation and communication, whichcan be implemented with various media including atoms, ions,and phonons. The main challenge lies in implementing arobust control to drastically slow down, store and transportultrafast optical signals. Cavity optomechanics enableinformation storage by converting photons into acousticphonons in mechanical resonators. However, fast andcontrollable effective coupling between multiple mechanicalresonators remains elusive for dynamic phonon manipulationand information transfer. This study considers dynamic phonon manipulation via optomechanically induced strong couplingbetween two distinct mechanical resonators. When the two resonators within an optical cavity are excited to optomechanicalself-oscillation, strong coupling is observed when a parametric pump laser compensates for their mechanical frequencymismatch. The strong and controllable coupling between the mechanical resonators demonstrated on the fully integratednanoscale optomechanical device is promising for dynamic phonon manipulation and robust optical information storage.KEYWORDS: strong coupling, optomechanics, phonon manipulation, parametric amplification, optical modulation

Optical information storage is essential for optical andquantum computing,1 optical communications,2 and

signal processing,3,4 which requires a robust ability todrastically slow down, store, and transport optical signals.5,6

The fast speed of optical signals poses a challenge for signaldelay and storage. Various approaches have been demonstratedto store optical information, such as using electronicresonances in atomic mediums,7,8 cavity resonances in opticalsystems,9,10 rare earth ion in nanoscale optical resonators11 andacoustic phonons in optical12 and optomechanical devi-ces.13−15 The breakthrough development of cavity optome-chanics enables the storage of optical information byconverting photons into acoustic phonons using the inter-action between the optical cavity and the mechanicalresonators. The retarded optical force within an optical cavityis used to drive the mechanical nanostructures, for example,spheres,16 toroids,17 cantilevers,18 and membranes,19 into theexcited phonon state. The technology and concept to storeoptical information into optomechanical devices will enablemany promising applications, such as radio frequencyoptomechanical oscillators,20 nonvolatile optical memory,21

wavelength conversion,22 and tunable wavelength routers.23

Although optical information storage in the form of acousticphonons has been demonstrated in optomechanical sys-tems,13−15 one of the main challenges remaining is therealization of dynamic phonon manipulation between distinctmechanical resonators in these systems. In practicalapplications of optical communications and informationprocessing, it is essential to couple distributed mechanicalresonators and enable them to communicate with each otherand exchange the stored information. One approach aims tocouple the distributed mechanical resonators to a commonoptical field, whereby the former form the local informationprocessing units and the latter plays the role of acommunication data bus to transport the phonons.24,25 Strongcoupling between mechanical resonators is necessary toovercome leakage during phonon manipulation, and thecoupling rate must exceed the damping rate of the mechanicalresonators. Although optical cavities have been used tosynchronize and hybridize distributed mechanical resona-tors,26−29 the coupling between two mechanical resonators

Received: April 26, 2019Published: July 8, 2019

Letter

pubs.acs.org/journal/apchd5Cite This: ACS Photonics 2019, 6, 1855−1862

© 2019 American Chemical Society 1855 DOI: 10.1021/acsphotonics.9b00618ACS Photonics 2019, 6, 1855−1862

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due to the static optical coupling has not been able todynamically control the mechanical resonators for phononmanipulation, which limits the prospect of practical applica-tions in optical information storage.30−33

Here, we demonstrate dynamic phonon manipulation viaoptomechanically induced strong coupling between twodistinct mechanical resonators in a racetrack optical resonator.A light with a constant power is coupled into the cavity toexcite the two mechanical resonators into self-oscillation andbuild an optical connection between them. When themechanical frequency mismatch is compensated by anotheramplitude periodically modulated light, the coupled mechan-ical resonators reach the strong coupling regime. In contrastwith traditional static optical connection via perturbation ofthe optical cavity through mechanical displacement, we

establish a new dynamic coupling between two mechanicalresonators via parametric modulation. Our work focuses on thecoherent control of phonon manipulation and presents animportant step toward achieving the strong coupling betweenmechanical resonators in integrated photonic circuits, in whicha wealth of fascinating phonon dynamics and practicalapplications can be explored.

■ RESULTS

Optical Racetrack Resonator and Mechanical Reso-nators. The optical racetrack resonator for dynamic phononmanipulation is shown in Figure 1a. A bus waveguide isdesigned to couple light into the optical racetrack resonator.Two mechanical resonators are located in the two straightsections of the optical racetrack resonator, which are clamped−

Figure 1. Dynamic phonon manipulation by strong coupling between two individual mechanical resonators. (a) Schematic of two mechanicalresonators on an optical racetrack resonator. The two mechanical resonators are mechanically isolated and coupled through the optical field in thecavity. (b) SEM of the mechanical resonators (scale bar: 2 μm). (c) Schematic of the coupled mechanical resonators in the optomechanicalsystems. The drive light with a wavelength λd is coupled into the cavity to excite the mechanical resonators with frequency ω1 and ω2 into self-oscillation, and a modulated pump light with a wavelength λp is pumped to transport the phonons with a rate of g through strong coupling. (d)Sideband generation due to the pump light. When the frequency mismatch is compensated by ωp, the frequencies ω1 and ω2 are split into ω1−, ω1+and ω2−, ω2+, respectively, which is the normal mode splitting.

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clamped beams that are released from the substrate with a 300nm gap underneath. The two clamped−clamped beams havethe same cross-sectional dimension of 0.45 × 0.22 μm, butdifferent lengths (L1 = 15 μm and L2 = 10 μm), such that thetwo mechanical resonators resonate at different frequencies. Inaddition, the two mechanical resonators are isolated 30 μmapart, such that only optical connection exists. Figure 1b showsa scanning electron microscope (SEM) image of the actualdevice. A blue detuned drive light (λd) related to the opticalresonance frequency (λod) at constant power Pdc is coupledinto the optical racetrack resonator to generate the opticalforce on the two mechanical resonators. The optical forceresults in optical spring (k0) and optical damping (c0) effects.

34

In this case, the optical spring k0 increases the resonancefrequency of the mechanical resonators, while the opticaldamping c0 decreases the mechanical damping, thus, amplifyingthe mechanical motions. Above a certain threshold power, theoptical damping totally compensates for the mechanicaldamping, and the two mechanical resonators evolve into self-oscillation with frequencies ω1 and ω2.Subsequently, an amplitude modulated pump light of

wavelength λp at power Pac with the modulation frequencyωp is coupled into the optical racetrack resonator to modulatethe resonance frequencies of the two mechanical resonatorsthrough the optical spring effect, as shown in Figure 1c. Theequations of the coupled mechanical resonators can beexpressed as

μ α ω ω − − + + Λ =x x x x t x F(1 ) cos( )1 1 12

1 12

1 1 p 2 th (1a)

μ α ω ω − − + + Λ =x x x x t x F(1 ) cos( )2 2 22

2 22

2 2 p 1 th

(1b)

where xi (i = 1, 2) is the displacement of mechanical resonatorsI and II, μ and αi is factor related to the nonlinear damping, ωiis the modified mechanical frequency, Λi are the intermodalcoupling factors, and Fth is the thermal force (SupportingInformation). The terms containing Λ represent the dynamicphonon transfer between the two mechanical resonators. Theparametric modulation of the mechanical spring results in thegeneration of sidebands ω1 ± ωp and ω2 ± ωp, as shown inFigure 1d. When the modulation frequency ωp ≈ ω2 − ω1compensates for the frequency mismatch between the twomechanical resonators, the phonons in the mechanicalresonator I are transferred to mechanical resonator II throughsideband ω1 + ωp. Simultaneously, the phonons in mechanicalresonator II are transferred to mechanical resonator I throughsideband ω2 − ωp. The interaction energy becomes sufficientlylarge, such that it is no longer possible to distinguish theenergy flow direction between the two mechanical resonators,in which the ω1 + ωp from mechanical resonator I and ω2 − ωpfrom mechanical resonator II result in the normal modesplitting, which is shown schematically in Figure 1d.

Optical Coupling and Phonons Preparation. Theracetrack optical resonator and mechanical resonators arefirst characterized using a low power (10 ± 2 μW) probe light.The transmission spectrum of the racetrack optical resonatorexhibits a high quality factor Qopt = 1.10 × 105 with an opticalline width κ/2π = 1.72 GHz at a resonance wavelength λod =1586.54 nm. Two different optical resonance wavelengths ofthe cavity, λod = 1586.54 nm for the drive light and λop =

Figure 2. Optical coupling and mechanical state preparation. (a) Mechanical line width of mechanical resonators I (black curve) and II (red curve)as a function of the wavelength detuning. (b) Mechanical frequency shift of mechanical resonators I (black curve) and II (red curve) as a functionof the wavelength detuning. (c) Experimental results demonstrating the measured power spectral density in the frequency domain when sweepingthe wavelength detuning at Pdc = 200 μW. (d) P−λ phase diagram of the self-oscillation regions for the two resonators with the fitting lines. Theblack pentagram marker corresponds to the strong coupling operating region and blue marker for parametric amplification.

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1595.32 nm for the pump light, are used in the experiment. Forthe two mechanical resonators, the thermomechanical motionmodulates the transmission power of the probe light, which isdetected as resonances at the mechanical frequency in thenoise power spectrum. Two mechanical resonances areobserved at ω1′/2π = 7.66 MHz with a mechanical qualityfactor Qm1 = 2.55 × 103 and a line width κm1/2π = 3.0 kHz andat ω2′/2π = 8.44 MHz with a mechanical quality factor Qm2 =2.64 × 103 and a line width κm2/2π = 3.2 kHz, whichcorrespond to the fundamental modes of the two mechanicalresonators. In addition, the optomechanical coupling coef-ficients for mechanical resonators I and II are gom1/2π = 183MHz/nm and gom2/2π = 146 MHz/nm, respectively.To investigate the static optical connection and prepare the

two mechanical resonators into a high phonon population, ablue detuned drive light (λd) with a constant power Pdc is

injected into the racetrack optical resonator. Figure 2a showsthe mechanical line width of mechanical resonators I and II asa function of the wavelength difference of drive light (Δλd = λd− λod). Due to the thermo-optical effect, the original resonancewavelength of the optical cavity, λod = 1586.54 nm, is red-shifted to the final wavelength, λod = 1586.81 nm, as sweepingthe wavelength λd from 1586.51 to 1586.81 nm, leading to awavelength difference Δλd of −300 to 0 pm. Mechanicalresonator I steps into self-oscillation in the region from −230to −100 pm (A + B region), and mechanical resonator II stepsinto self-oscillation in the region from −170 to −40 pm (B + Cregion). When the mechanical resonators step into self-oscillation, the mechanical line width is significantly reduceddue to the optical damping effect. When sweeping thewavelength λd, the optical spring effect changes the resonantfrequencies of the mechanical resonators, as shown in Figure

Figure 3. Mode splitting in the strong coupling regime. (a) Experimental confirmation of the sideband generation ω1 + ωp and ω2 − ωp, labeled asblack and blue lines, respectively (logarithmic scale). (b) Normalized mode splitting in mechanical resonator II in the frequency domain whensweeping ωp/2π from 0.754 to 0.794 MHz (linear scale). (c) The representative results of g, measured with different AC powers 0, 300, 400, and500 μW, at a fixed wavelength detuning at Δλp = −160 pm. (d) The coupling rate reaches 2π × 11.5 kHz when Pac is 500 μW and the modesplitting is generated at an efficiency of 22.8 Hz/μW. (e) The representative results of g measured with different detuning wavelengths −180, −160,−140, and −120 pm. (f) The coupling rate reaches 2π × 12.2 kHz when Δλp is −120 pm, which shows that the mode splitting is generated at anefficiency of 110 Hz/pm.

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2b. The optical spring effect is used to modulate thefrequencies of the two mechanical resonators and is essentialto reach the strong coupling regime. The discontinuity of themechanical frequency is attributed to the intrinsic andoptomechanically induced mechanical Duffing nonlinearity,19

which becomes more pronounced due to the abrupt changes ofthe vibration amplitude induced by the self-oscillation. Formechanical resonator I (black curve), the abrupt changes at theleft edges of regions A and C are due to the self-oscillation ofthe systems. As for the mechanical resonator II (red curve), wecan also observe the same effect at the right edges of regions Aand C, which are both induced by the self-oscillation. Whenthe input wavelength approaches the resonance wavelength ofthe cavity, the thermo-optical effect becomes stronger and thewavelength of the optical cavity is red-shifted, resulting indifferent self-oscillating regions for the two mechanicalresonators.When the optical power Pdc is maintained at 200 ± 2 μW,

the power spectral density in the frequency domain ismeasured by changing the wavelength difference from −250to −20 ± 5 pm, as shown in Figure 2c. With a wavelengthdifference of −250 pm (i), neither mechanical resonator stepsinto self-oscillation. When the wavelength difference isdecreased to −195 pm (ii), only mechanical resonator Isteps into self-oscillation. When the wavelength difference isfurther reduced to −130 pm (iii), both mechanical resonatorsstep into self-oscillation. Subsequently, only mechanicalresonator II steps into self-oscillation when the wavelengthdifference is reduced to −80 pm (iv), and neither mechanicalresonator steps into self-oscillation with a wavelength differ-ence of −20 pm (v). Because the self-oscillation is dependenton the power and wavelength detuning of the drive light, theregion of self-oscillation as a function of the power P andwavelength difference (λd − λod) is illustrated in the P−λ phasediagram, as shown in Figure 2d, with conditions (i)−(v)highlighted. Mechanical resonator I steps into self-oscillationwith any combination of optical power Pdc and wavelengthdifferences in regions A and B. Furthermore, mechanicalresonator II steps into self-oscillation in regions B and C only.The black triangles (red dots) correspond to the combinationof power and wavelength detuning, which are required for themechanical resonator I (II) to step into self-oscillation. Thethreshold power required for mechanical resonators I and II tostep into self-oscillation is experimentally determined as Pth1 =103 μW and Pth2 = 171 μW, respectively. As a result, byselecting the power and wavelength of the blue detuned drivelight, the preparation of the coupled mechanical resonatorswith high phonon occupation in region B will provide sufficientphonons for dynamic phonon manipulation between the twomechanical resonators.Controllable Dynamic Phonon Manipulation. The

dynamic phonon manipulation is realized by applyingamplitude modulated pump light (λp = 1595.30 nm) withpeak-to-peak amplitude in power Pac = 500 ± 2 μW (meanpower is 250 μW) into the racetrack optical resonator. With adrive light (the wavelength detuning is −200 pm) at power Pdc= 500 ± 2 μW, the mechanical resonance frequencies formechanical resonators I and II are ω1/2π = 7.643 MHz andω2/2π = 8.417 MHz, respectively. When the pump lightmodulated at frequency ωp/2π = 0.70 MHz is applied,sidebands are observed in the noise power spectrum, as shownin Figure 3a. The red curve is the noise of background. Theblack curve represents the mechanical resonance ω1 and

sideband ω1 + ωp, while the blue curve represents themechanical resonance ω2 and sideband ω2 − ωp. Othersidebands, such as ω1 + ωp, ω2 − ωp, and higher harmonics,are not shown in the figure. When the pump light’s modulationfrequency reaches the resonance frequency difference betweenthe two mechanical resonators, that is, ωp = ω2 − ω1, thephonon transport between the two mechanical resonatorsoccurs. The phonons in mechanical resonator I, generated bythe photons in the optical cavity, are transported to mechanicalresonator II via a radio frequency absorption process, that is,ℏω1 + ℏωp → ℏω2. The phonons in mechanical resonator IIare simultaneously transported to mechanical resonator I via aradio frequency emission process, that is, ℏω2 − ℏωp → ℏω1.A characteristic feature of the dynamic phonon manipulationsystem in strong coupling regime is normal mode splitting,which is observed in the experiment. The measured powerspectral density of mechanical resonator II when sweeping ωp/2π from 0.754 to 0.794 MHz is shown in Figure 3b. At ωp/2π= 0.754 MHz, sideband (ω1 + ωp)/2π = 8.397 MHz isobserved together with the mechanical resonance peak ofmechanical resonator II (ω2/2π = 8.417 MHz). When thesideband approaches ω2 by increasing ωp, mode splittingoccurs, splitting the resonance into ω2

+ and ω2−. For instance,

at ωp/2π = 0.774 MHz, the mode is split into ω2+/2π = 8.421

MHz and ω2−/2π = 8.4210 MHz. When ωp is further increased

to exceed the resonance frequency difference between the twomechanical resonators, the resonance frequency ω2 is restoredwith a sideband at ω1 + ωp. This shows the strong couplingbetween the two mechanical resonators.To investigate the strength of the controllable coupling

between the two mechanical resonators for dynamic phonontransport, we theoretically and experimentally examine the

coupling rate. The coupling rate is described by ≈ω ω

Λ Λg13

1 2

1 2,

where ω1 and ω2 are the renormalized frequencies ofmechanical resonators I and II, respectively (SupportingInformation). Different from the conventional power-depend-ent coupling rate, Λ can also be tuned by the wavelengthdifference of pump light Δλp = λp − λop, which providesanother degree of freedom to control the coupling between thetwo mechanical resonators. The coupling rate is firstcharacterized by varying the power of the modulated pumplight (Pac). The coupling rate g can be determined based on theseparation between the split peaks, that is, g = ω1

+ − ω1− = ω2

+

− ω2−. Figure 3c shows the measured power spectral densities

of mechanical resonator II after changing Pac from 0 to 300,400, and 500 μW at a fixed wavelength detuning of Δλp =−160 pm, and the modulation frequency is ωp/2π = 0.774MHz. We observe a threshold behavior in the mode splittingbecause the coupling rate must exceed the line width of twomechanical resonators before it can be observed. When Pac =300 μW, mode splitting is observed, indicating the occurrenceof dynamic phonon manipulation between the two mechanicalresonators. The coupling rate increases approximately linearlyin relation to Pac, as shown in Figure 3d, because the coefficientof Λ Λ1 2 is proportional to Pac. The coupling rate reaches 2π× 11.5 kHz when Pac is 500 μW. The mode splitting increaseslinearly with the input power above 300 μW and is generatedat an efficiency of 22.8 Hz μW1−. Subsequently, the couplingrate or mode splitting is controlled by the wavelengthdifference Δλp = λp − λop. It should be noted that the originalresonance wavelength of the optical cavity λop = 1595.32 nm is

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also red-shifted to the final wavelength λop = 1595.52 nm.Figure 3e presents the measured power spectral densities ofmechanical resonator II by changing Δλp from −180 to −160,−140, and −120 pm at a fixed Pac of 400 μW. Decreasing thewavelength detuning increases the coupling rate, as shown inFigure 3f, for the optical spring increases as the wavelengthdetuning decreases. It is noted that the power and wavelengthof the pump light is limited, because an improper pump lightwill increase the resonance wavelength of the optical cavity dueto the thermo-optical effect, resulting in the mechanicaloscillators stepping out of the self-oscillation. The strongcoupling requires a careful detuning of pump light to maintainthe mechanical oscillators in the self-oscillation regime.We further demonstrate the parametric amplification

between the two mechanical resonators. In region C describedin Figure 2d, the self-sustained mechanical resonator II isregarded as a phonon cavity,35,36 and the parametric couplinginduced by the blue-detuned modulated pump light is used toamplify the motion of mechanical resonator I. A drive light(wavelength detuning is −60 ± 5 pm) is used to excitemechanical resonator II into self-oscillation. Figure 4a showsthe frequency spectrum of the two mechanical resonators atthe pump frequency ωp = ω1 + ω2. The energy transportcaused by the parametric excitation of mechanical resonator Ican be considered as a generalized parametric amplification ofa single resonator. Figure 4b,c shows the measured powerspectral densities of mechanical resonator I by changing Pacfrom 0 to 600 μW in fine and coarse intervals at a fixedwavelength. When the power of the pump light increases, the

amplitude of resonator I is amplified, and the line widthdecreases because the parametric excitation of the pump lightcompensates the intrinsic mechanical damping rate ofresonator I, as shown in Figure 4d. In particular, the modulatedpump light can provide a tunable interaction strength betweentwo mechanical resonators. This provides a new means tomanipulate mechanical resonators in optomechanical systems,in which many interesting prospects such as squeezing, statetransferring, and information exchange between mechanicalresonators arise.37 More importantly, the strong coupling canalso be used for optomechanical information processing withphotons and phonons.38,39

■ DISCUSSION

The demonstrated dynamic phonon manipulation via strongcoupling between two distinct mechanical resonators in aracetrack optical resonator are mediated only by theoptomechanical modulation. It is unique and unprecedentedas strong coupling between two mechanical resonators havenot been realized in optomechanical systems. The concept ofoptomechanically induced strong coupling can be extended inmany other types of optomechanical configurations such ascoupled micro disk and photonic crystal cavities to achievemore sophisticated functions.As the first strong coupling optomechanical system, the

current device is still far from the sideband resolved regime.However, it is foreseeable that in other systems that hasreached the sideband resolved regime, such as optomechanicalcrystals, dynamic transport of a single phonon between distinct

Figure 4. Phonon manipulation by the parametric amplifying of the mechanical resonators. (a) Schematic of the spectrum at the pump ωp = ω1 +ω2. The motion of mechanical resonator I is parametrically amplified, and the energy is transported from mechanical resonator II to mechanicalresonator I. The response of mechanical resonator I at fine (b) and coarse (c) intervals of the pump power from 0 to 600 μW. (d) The amplitudeand mechanical line width as functions of the pump power due to the parametric amplification.

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mechanical resonators are within reach. In such a regime, thequantum computing and information processing can beexpected to emerge.Finally, the demonstrated dynamic phonon manipulation,

with its characteristic feature of normal mode splitting andparametric amplification between the two mechanical reso-nators could enables robust optical information storage basedon photon−phonon conversion in addition to dynamicphonon manipulation via strong coupling, presenting animportant step in integrated photonic circuits, in which awealth of fascinating phonon dynamics and practicalapplications can be explored.

■ METHODS

Materials and Device Fabrication. The device isfabricated on a silicon-on-insulator wafer with a structurelayer of 220 nm.40 The waveguide, ring resonator and gratingcoupler are patterned by deep UV lithography and etched byplasma dry etching. A 70 nm silicon dioxide hard mask isadopted to ensure the waveguide has a good profile andreduces optical loss, improving the mechanical and opticalperformance. The silicon structure is then covered by a layer ofSiO2 cladding (2 μm thick), which is deposited using plasma-enhanced chemical vapor deposition (PECVD). This processis designed to reduce optical loss and protect unreleasedstructures. Finally, a released window is opened by hydro-fluoric acid vapor to form the mechanical resonators.41,42 Thedesired gap between the silicon beam and substrate can beachieved by precisely controlling the etching time. The etchingrate for the substrate is about 30 nm/min.Experimental Setup. In the experiment, drive and pump

lights are pumped in the same direction while the probe light ispumped in the opposite direction to characterize themechanical resonators in the racetrack optical resonator. Thisarrangement can reduce effects of pump light on measurement.A wide spectrum light from a 12 dBm ASE light source(Amonics ALS-CL-13) is pumped into waveguide to measuretransmission spectrum of racetrack optical resonator. Thepower and polarization state of the two pump lights and aprobe light from a tunable laser (Santec TSL 510) arecontrolled using the fiber polarization controller and variableoptical attenuator. A pump light with 0 dBm modulated by theelectrical-optical modulator and frequency controlled by aprogrammable function generator (PM 5193) is combinedwith the other drive light with a 50:50 directional fiber coupler.The pump and probe lights are separated by an optical isolatorafter they are both sent into the device, which is under a highvacuum (2 × 10−6 Pa). To ensure that only the probe light ismeasured, another tunable bandpass filter (BVF-200CL) isused before the probe light is detected by the photodetector(FPD 510). The converted electrical signal is sent to theoscilloscope (MDO4104B-3) to measure the time andfrequency domain response of the coupled resonators. Theschematic of the detailed experimental setup is in theSupporting Information.

■ ASSOCIATED CONTENT

*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acsphoto-nics.9b00618.

Experimental setup for optical measurement, deviceparameters and measurement, theoretical derivation ofcoupled mechanical resonators under the drive light, andnumerical simulation of coupled mechanical equations(PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: eaqliu@ntu.edu.sg.ORCIDJianguo Huang: 0000-0002-7821-0441Huan Li: 0000-0002-8749-0385Mo Li: 0000-0002-5500-0900FundingThis work was supported by the Singapore National ResearchFoundation under the Incentive for Research and InnovationScheme (1102-IRIS-05-01), administered by PUB and underthe Competitive Research Program (NRF-CRP13-2014-01).This work was also supported by Centre for Bio Devices andSignal Analysis (VALENS) and Centre for OptoElectronicsand Biophotonics (OPTIMUS) of Nanyang TechnologyUniversity.NotesThe authors declare no competing financial interest.

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