Letter Cite This: ACS Photonics XXXX, XXX, XXX−XXX
pubs.acs.org/journal/apchd5
Dynamic Phonon Manipulation by Optomechanically Induced Strong Coupling between Two Distinct Mechanical Resonators Jianguo Huang,†,‡,§ Lip Ket Chin,‡ Hong Cai,§ Huan Li,∥ Jiu Hui Wu,† Tianning Chen,† Mo Li,∥ and Ai-Qun Liu*,‡
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†
School of Mechanical Engineering, Xi’an Jiaotong University and State Key Laboratory for Strength and Vibration of Mechanical Structures, 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 Innovis Tower, 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 for optical and quantum computation and communication, which can be implemented with various media including atoms, ions, and phonons. The main challenge lies in implementing a robust control to drastically slow down, store and transport ultrafast optical signals. Cavity optomechanics enable information storage by converting photons into acoustic phonons in mechanical resonators. However, fast and controllable effective coupling between multiple mechanical resonators remains elusive for dynamic phonon manipulation and information transfer. This study considers dynamic phonon manipulation via optomechanically induced strong coupling between two distinct mechanical resonators. When the two resonators within an optical cavity are excited to optomechanical self-oscillation, strong coupling is observed when a parametric pump laser compensates for their mechanical frequency mismatch. The strong and controllable coupling between the mechanical resonators demonstrated on the fully integrated nanoscale optomechanical device is promising for dynamic phonon manipulation and robust optical information storage. KEYWORDS: strong coupling, optomechanics, phonon manipulation, parametric amplification, optical modulation
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Although optical information storage in the form of acoustic phonons has been demonstrated in optomechanical systems,13−15 one of the main challenges remaining is the realization of dynamic phonon manipulation between distinct mechanical resonators in these systems. In practical applications of optical communications and information processing, it is essential to couple distributed mechanical resonators and enable them to communicate with each other and exchange the stored information. One approach aims to couple the distributed mechanical resonators to a common optical field, whereby the former form the local information processing units and the latter plays the role of a communication data bus to transport the phonons.24,25 Strong coupling between mechanical resonators is necessary to overcome leakage during phonon manipulation, and the coupling rate must exceed the damping rate of the mechanical resonators. Although optical cavities have been used to synchronize and hybridize distributed mechanical resonators,26−29 the coupling between two mechanical resonators
ptical information storage is essential for optical and quantum computing,1 optical communications,2 and signal processing,3,4 which requires a robust ability to drastically slow down, store, and transport optical signals.5,6 The fast speed of optical signals poses a challenge for signal delay and storage. Various approaches have been demonstrated to store optical information, such as using electronic resonances in atomic mediums,7,8 cavity resonances in optical systems,9,10 rare earth ion in nanoscale optical resonators11 and acoustic phonons in optical12 and optomechanical devices.13−15 The breakthrough development of cavity optomechanics enables the storage of optical information by converting photons into acoustic phonons using the interaction between the optical cavity and the mechanical resonators. The retarded optical force within an optical cavity is used to drive the mechanical nanostructures, for example, spheres,16 toroids,17 cantilevers,18 and membranes,19 into the excited phonon state. The technology and concept to store optical information into optomechanical devices will enable many promising applications, such as radio frequency optomechanical oscillators,20 nonvolatile optical memory,21 wavelength conversion,22 and tunable wavelength routers.23 © XXXX American Chemical Society
Received: April 26, 2019 Published: July 8, 2019 A
DOI: 10.1021/acsphotonics.9b00618 ACS Photonics XXXX, XXX, XXX−XXX
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Figure 1. Dynamic phonon manipulation by strong coupling between two individual mechanical resonators. (a) Schematic of two mechanical resonators on an optical racetrack resonator. The two mechanical resonators are mechanically isolated and coupled through the optical field in the cavity. (b) SEM of the mechanical resonators (scale bar: 2 μm). (c) Schematic of the coupled mechanical resonators in the optomechanical systems. The drive light with a wavelength λd is coupled into the cavity to excite the mechanical resonators with frequency ω1 and ω2 into selfoscillation, 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.
establish a new dynamic coupling between two mechanical resonators via parametric modulation. Our work focuses on the coherent control of phonon manipulation and presents an important step toward achieving the strong coupling between mechanical resonators in integrated photonic circuits, in which a wealth of fascinating phonon dynamics and practical applications can be explored.
due to the static optical coupling has not been able to dynamically control the mechanical resonators for phonon manipulation, which limits the prospect of practical applications in optical information storage.30−33 Here, we demonstrate dynamic phonon manipulation via optomechanically induced strong coupling between two distinct mechanical resonators in a racetrack optical resonator. A light with a constant power is coupled into the cavity to excite the two mechanical resonators into self-oscillation and build an optical connection between them. When the mechanical frequency mismatch is compensated by another amplitude periodically modulated light, the coupled mechanical resonators reach the strong coupling regime. In contrast with traditional static optical connection via perturbation of the optical cavity through mechanical displacement, we
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RESULTS Optical Racetrack Resonator and Mechanical Resonators. The optical racetrack resonator for dynamic phonon manipulation is shown in Figure 1a. A bus waveguide is designed to couple light into the optical racetrack resonator. Two mechanical resonators are located in the two straight sections of the optical racetrack resonator, which are clamped− B
DOI: 10.1021/acsphotonics.9b00618 ACS Photonics XXXX, XXX, XXX−XXX
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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 function of the wavelength detuning. (c) Experimental results demonstrating the measured power spectral density in the frequency domain when sweeping the wavelength detuning at Pdc = 200 μW. (d) P−λ phase diagram of the self-oscillation regions for the two resonators with the fitting lines. The black pentagram marker corresponds to the strong coupling operating region and blue marker for parametric amplification.
x 2̈ − μ(1 − α2x 22)x 2̇ + ω22x 2 + Λ 2 cos(ωpt )x1 = Fth
clamped beams that are released from the substrate with a 300 nm gap underneath. The two clamped−clamped beams have the same cross-sectional dimension of 0.45 × 0.22 μm, but different lengths (L1 = 15 μm and L2 = 10 μm), such that the two mechanical resonators resonate at different frequencies. In addition, the two mechanical resonators are isolated 30 μm apart, such that only optical connection exists. Figure 1b shows a scanning electron microscope (SEM) image of the actual device. A blue detuned drive light (λd) related to the optical resonance frequency (λod) at constant power Pdc is coupled into the optical racetrack resonator to generate the optical force on the two mechanical resonators. The optical force results in optical spring (k0) and optical damping (c0) effects.34 In this case, the optical spring k0 increases the resonance frequency of the mechanical resonators, while the optical damping c0 decreases the mechanical damping, thus, amplifying the mechanical motions. Above a certain threshold power, the optical damping totally compensates for the mechanical damping, and the two mechanical resonators evolve into selfoscillation with frequencies ω1 and ω2. Subsequently, an amplitude modulated pump light of wavelength λp at power Pac with the modulation frequency ωp is coupled into the optical racetrack resonator to modulate the resonance frequencies of the two mechanical resonators through the optical spring effect, as shown in Figure 1c. The equations of the coupled mechanical resonators can be expressed as x1̈ − μ(1 − α1x12)x1̇ + ω12x1 + Λ1 cos(ωpt )x 2 = Fth
(1b)
where xi (i = 1, 2) is the displacement of mechanical resonators I and II, μ and αi is factor related to the nonlinear damping, ωi is the modified mechanical frequency, Λi are the intermodal coupling factors, and Fth is the thermal force (Supporting Information). The terms containing Λ represent the dynamic phonon transfer between the two mechanical resonators. The parametric modulation of the mechanical spring results in the generation of sidebands ω1 ± ωp and ω2 ± ωp, as shown in Figure 1d. When the modulation frequency ωp ≈ ω2 − ω1 compensates for the frequency mismatch between the two mechanical resonators, the phonons in the mechanical resonator I are transferred to mechanical resonator II through sideband ω1 + ωp. Simultaneously, the phonons in mechanical resonator II are transferred to mechanical resonator I through sideband ω2 − ωp. The interaction energy becomes sufficiently large, such that it is no longer possible to distinguish the energy flow direction between the two mechanical resonators, in which the ω1 + ωp from mechanical resonator I and ω2 − ωp from mechanical resonator II result in the normal mode splitting, which is shown schematically in Figure 1d. Optical Coupling and Phonons Preparation. The racetrack optical resonator and mechanical resonators are first characterized using a low power (10 ± 2 μW) probe light. The transmission spectrum of the racetrack optical resonator exhibits a high quality factor Qopt = 1.10 × 105 with an optical line width κ/2π = 1.72 GHz at a resonance wavelength λod = 1586.54 nm. Two different optical resonance wavelengths of the cavity, λod = 1586.54 nm for the drive light and λop =
(1a) C
DOI: 10.1021/acsphotonics.9b00618 ACS Photonics XXXX, XXX, XXX−XXX
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Figure 3. Mode splitting in the strong coupling regime. (a) Experimental confirmation of the sideband generation ω1 + ωp and ω2 − ωp, labeled as black and blue lines, respectively (logarithmic scale). (b) Normalized mode splitting in mechanical resonator II in the frequency domain when sweeping 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, and 500 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 mode splitting 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 an efficiency of 110 Hz/pm.
injected into the racetrack optical resonator. Figure 2a shows the mechanical line width of mechanical resonators I and II as a function of the wavelength difference of drive light (Δλd = λd − λ̅od). Due to the thermo-optical effect, the original resonance wavelength of the optical cavity, λod = 1586.54 nm, is redshifted to the final wavelength, λ̅od = 1586.81 nm, as sweeping the wavelength λd from 1586.51 to 1586.81 nm, leading to a wavelength difference Δλd of −300 to 0 pm. Mechanical resonator I steps into self-oscillation in the region from −230 to −100 pm (A + B region), and mechanical resonator II steps into self-oscillation in the region from −170 to −40 pm (B + C region). When the mechanical resonators step into selfoscillation, the mechanical line width is significantly reduced due to the optical damping effect. When sweeping the wavelength λd, the optical spring effect changes the resonant frequencies of the mechanical resonators, as shown in Figure
1595.32 nm for the pump light, are used in the experiment. For the two mechanical resonators, the thermomechanical motion modulates the transmission power of the probe light, which is detected as resonances at the mechanical frequency in the noise power spectrum. Two mechanical resonances are observed at ω1′/2π = 7.66 MHz with a mechanical quality factor Qm1 = 2.55 × 103 and a line width κm1/2π = 3.0 kHz and at ω2′/2π = 8.44 MHz with a mechanical quality factor Qm2 = 2.64 × 103 and a line width κm2/2π = 3.2 kHz, which correspond to the fundamental modes of the two mechanical resonators. In addition, the optomechanical coupling coefficients for mechanical resonators I and II are gom1/2π = 183 MHz/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, a blue detuned drive light (λd) with a constant power Pdc is D
DOI: 10.1021/acsphotonics.9b00618 ACS Photonics XXXX, XXX, XXX−XXX
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sideband ω1 + ωp, while the blue curve represents the mechanical resonance ω2 and sideband ω2 − ωp. Other sidebands, such as ω1 + ωp, ω2 − ωp, and higher harmonics, are not shown in the figure. When the pump light’s modulation frequency reaches the resonance frequency difference between the two mechanical resonators, that is, ωp = ω2 − ω1, the phonon transport between the two mechanical resonators occurs. The phonons in mechanical resonator I, generated by the photons in the optical cavity, are transported to mechanical resonator II via a radio frequency absorption process, that is, ℏω1 + ℏωp → ℏω2. The phonons in mechanical resonator II are simultaneously transported to mechanical resonator I via a radio frequency emission process, that is, ℏω2 − ℏωp → ℏω1. A characteristic feature of the dynamic phonon manipulation system in strong coupling regime is normal mode splitting, which is observed in the experiment. The measured power spectral 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 is observed together with the mechanical resonance peak of mechanical resonator II (ω2/2π = 8.417 MHz). When the sideband approaches ω2 by increasing ωp, mode splitting occurs, 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 two mechanical resonators, the resonance frequency ω2 is restored with a sideband at ω1 + ωp. This shows the strong coupling between the two mechanical resonators. To investigate the strength of the controllable coupling between the two mechanical resonators for dynamic phonon transport, we theoretically and experimentally examine the
2b. The optical spring effect is used to modulate the frequencies of the two mechanical resonators and is essential to reach the strong coupling regime. The discontinuity of the mechanical frequency is attributed to the intrinsic and optomechanically induced mechanical Duffing nonlinearity,19 which becomes more pronounced due to the abrupt changes of the vibration amplitude induced by the self-oscillation. For mechanical resonator I (black curve), the abrupt changes at the left edges of regions A and C are due to the self-oscillation of the systems. As for the mechanical resonator II (red curve), we can also observe the same effect at the right edges of regions A and C, which are both induced by the self-oscillation. When the input wavelength approaches the resonance wavelength of the cavity, the thermo-optical effect becomes stronger and the wavelength of the optical cavity is red-shifted, resulting in different self-oscillating regions for the two mechanical resonators. When the optical power Pdc is maintained at 200 ± 2 μW, the power spectral density in the frequency domain is measured by changing the wavelength difference from −250 to −20 ± 5 pm, as shown in Figure 2c. With a wavelength difference of −250 pm (i), neither mechanical resonator steps into self-oscillation. When the wavelength difference is decreased to −195 pm (ii), only mechanical resonator I steps into self-oscillation. When the wavelength difference is further reduced to −130 pm (iii), both mechanical resonators step into self-oscillation. Subsequently, only mechanical resonator II steps into self-oscillation when the wavelength difference is reduced to −80 pm (iv), and neither mechanical resonator steps into self-oscillation with a wavelength difference of −20 pm (v). Because the self-oscillation is dependent on the power and wavelength detuning of the drive light, the region of self-oscillation as a function of the power P and wavelength difference (λd − λ̅od) is illustrated in the P−λ phase diagram, as shown in Figure 2d, with conditions (i)−(v) highlighted. Mechanical resonator I steps into self-oscillation with any combination of optical power Pdc and wavelength differences in regions A and B. Furthermore, mechanical resonator II steps into self-oscillation in regions B and C only. The black triangles (red dots) correspond to the combination of power and wavelength detuning, which are required for the mechanical resonator I (II) to step into self-oscillation. The threshold power required for mechanical resonators I and II to step into self-oscillation is experimentally determined as Pth1 = 103 μW and Pth2 = 171 μW, respectively. As a result, by selecting the power and wavelength of the blue detuned drive light, the preparation of the coupled mechanical resonators with high phonon occupation in region B will provide sufficient phonons for dynamic phonon manipulation between the two mechanical resonators. Controllable Dynamic Phonon Manipulation. The dynamic phonon manipulation is realized by applying amplitude modulated pump light (λp = 1595.30 nm) with peak-to-peak amplitude in power Pac = 500 ± 2 μW (mean power is 250 μW) into the racetrack optical resonator. With a drive light (the wavelength detuning is −200 pm) at power Pdc = 500 ± 2 μW, the mechanical resonance frequencies for mechanical resonators I and II are ω1/2π = 7.643 MHz and ω2/2π = 8.417 MHz, respectively. When the pump light modulated at frequency ωp/2π = 0.70 MHz is applied, sidebands are observed in the noise power spectrum, as shown in Figure 3a. The red curve is the noise of background. The black curve represents the mechanical resonance ω1 and
coupling rate. The coupling rate is described by g ≈
Λ1Λ 2 13 ω1ω2
,
where ω1 and ω2 are the renormalized frequencies of mechanical resonators I and II, respectively (Supporting Information). Different from the conventional power-dependent coupling rate, Λ can also be tuned by the wavelength difference of pump light Δλp = λp − λ̅op, which provides another degree of freedom to control the coupling between the two mechanical resonators. The coupling rate is first characterized by varying the power of the modulated pump light (Pac). The coupling rate g can be determined based on the separation 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 = 0.774 MHz. We observe a threshold behavior in the mode splitting because the coupling rate must exceed the line width of two mechanical resonators before it can be observed. When Pac = 300 μW, mode splitting is observed, indicating the occurrence of dynamic phonon manipulation between the two mechanical resonators. The coupling rate increases approximately linearly in relation to Pac, as shown in Figure 3d, because the coefficient of Λ1Λ 2 is proportional to Pac. The coupling rate reaches 2π × 11.5 kHz when Pac is 500 μW. The mode splitting increases linearly with the input power above 300 μW and is generated at an efficiency of 22.8 Hz μW1−. Subsequently, the coupling rate or mode splitting is controlled by the wavelength difference Δλp = λp − λ̅op. It should be noted that the original resonance wavelength of the optical cavity λop = 1595.32 nm is E
DOI: 10.1021/acsphotonics.9b00618 ACS Photonics XXXX, XXX, XXX−XXX
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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 mechanical resonator 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 amplitude and mechanical line width as functions of the pump power due to the parametric amplification.
also red-shifted to the final wavelength λ̅op = 1595.52 nm. Figure 3e presents the measured power spectral densities of mechanical resonator II by changing Δλp from −180 to −160, −140, and −120 pm at a fixed Pac of 400 μW. Decreasing the wavelength detuning increases the coupling rate, as shown in Figure 3f, for the optical spring increases as the wavelength detuning decreases. It is noted that the power and wavelength of the pump light is limited, because an improper pump light will increase the resonance wavelength of the optical cavity due to the thermo-optical effect, resulting in the mechanical oscillators stepping out of the self-oscillation. The strong coupling requires a careful detuning of pump light to maintain the mechanical oscillators in the self-oscillation regime. We further demonstrate the parametric amplification between the two mechanical resonators. In region C described in Figure 2d, the self-sustained mechanical resonator II is regarded as a phonon cavity,35,36 and the parametric coupling induced by the blue-detuned modulated pump light is used to amplify the motion of mechanical resonator I. A drive light (wavelength detuning is −60 ± 5 pm) is used to excite mechanical resonator II into self-oscillation. Figure 4a shows the frequency spectrum of the two mechanical resonators at the pump frequency ωp = ω1 + ω2. The energy transport caused by the parametric excitation of mechanical resonator I can be considered as a generalized parametric amplification of a single resonator. Figure 4b,c shows the measured power spectral densities of mechanical resonator I by changing Pac from 0 to 600 μW in fine and coarse intervals at a fixed wavelength. When the power of the pump light increases, the
amplitude of resonator I is amplified, and the line width decreases because the parametric excitation of the pump light compensates the intrinsic mechanical damping rate of resonator I, as shown in Figure 4d. In particular, the modulated pump light can provide a tunable interaction strength between two mechanical resonators. This provides a new means to manipulate mechanical resonators in optomechanical systems, in which many interesting prospects such as squeezing, state transferring, and information exchange between mechanical resonators arise.37 More importantly, the strong coupling can also be used for optomechanical information processing with photons and phonons.38,39
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DISCUSSION The demonstrated dynamic phonon manipulation via strong coupling between two distinct mechanical resonators in a racetrack optical resonator are mediated only by the optomechanical modulation. It is unique and unprecedented as strong coupling between two mechanical resonators have not been realized in optomechanical systems. The concept of optomechanically induced strong coupling can be extended in many other types of optomechanical configurations such as coupled micro disk and photonic crystal cavities to achieve more 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 has reached the sideband resolved regime, such as optomechanical crystals, dynamic transport of a single phonon between distinct F
DOI: 10.1021/acsphotonics.9b00618 ACS Photonics XXXX, XXX, XXX−XXX
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mechanical resonators are within reach. In such a regime, the quantum computing and information processing can be expected to emerge. Finally, the demonstrated dynamic phonon manipulation, with its characteristic feature of normal mode splitting and parametric amplification between the two mechanical resonators could enables robust optical information storage based on photon−phonon conversion in addition to dynamic phonon manipulation via strong coupling, presenting an important step in integrated photonic circuits, in which a wealth of fascinating phonon dynamics and practical applications can be explored.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Jianguo Huang: 0000-0002-7821-0441 Huan Li: 0000-0002-8749-0385 Mo Li: 0000-0002-5500-0900
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METHODS Materials and Device Fabrication. The device is fabricated on a silicon-on-insulator wafer with a structure layer of 220 nm.40 The waveguide, ring resonator and grating coupler are patterned by deep UV lithography and etched by plasma dry etching. A 70 nm silicon dioxide hard mask is adopted to ensure the waveguide has a good profile and reduces optical loss, improving the mechanical and optical performance. The silicon structure is then covered by a layer of SiO2 cladding (2 μm thick), which is deposited using plasmaenhanced chemical vapor deposition (PECVD). This process is designed to reduce optical loss and protect unreleased structures. Finally, a released window is opened by hydrofluoric acid vapor to form the mechanical resonators.41,42 The desired gap between the silicon beam and substrate can be achieved by precisely controlling the etching time. The etching rate 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 is pumped in the opposite direction to characterize the mechanical resonators in the racetrack optical resonator. This arrangement 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 measure transmission spectrum of racetrack optical resonator. The power and polarization state of the two pump lights and a probe light from a tunable laser (Santec TSL 510) are controlled using the fiber polarization controller and variable optical attenuator. A pump light with 0 dBm modulated by the electrical-optical modulator and frequency controlled by a programmable function generator (PM 5193) is combined with the other drive light with a 50:50 directional fiber coupler. The pump and probe lights are separated by an optical isolator after they are both sent into the device, which is under a high vacuum (2 × 10−6 Pa). To ensure that only the probe light is measured, another tunable bandpass filter (BVF-200CL) is used before the probe light is detected by the photodetector (FPD 510). The converted electrical signal is sent to the oscilloscope (MDO4104B-3) to measure the time and frequency domain response of the coupled resonators. The schematic of the detailed experimental setup is in the Supporting Information.
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Experimental setup for optical measurement, device parameters and measurement, theoretical derivation of coupled mechanical resonators under the drive light, and numerical simulation of coupled mechanical equations (PDF)
Funding
This work was supported by the Singapore National Research Foundation under the Incentive for Research and Innovation Scheme (1102-IRIS-05-01), administered by PUB and under the Competitive Research Program (NRF-CRP13-2014-01). This work was also supported by Centre for Bio Devices and Signal Analysis (VALENS) and Centre for OptoElectronics and Biophotonics (OPTIMUS) of Nanyang Technology University. Notes
The authors declare no competing financial interest.
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REFERENCES
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.9b00618. G
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DOI: 10.1021/acsphotonics.9b00618 ACS Photonics XXXX, XXX, XXX−XXX
