Abstract

Chip-integrated photonic devices have stimulated development in areas ranging from telecommunications to optomechanics. Racetrack resonators have gained popularity for optomechanical transduction due to their high sensitivity and cavity finesse. However, they lack sufficient dynamic range to read out large amplitude mechanical resonators, which are preferred for sensing applications. We present a robust photonic circuit based on a Mach-Zehnder interferometer (MZI) combined with a racetrack resonator that increases linear range without compromising high transduction sensitivity. Optical and mechanical properties of combined MZI-racetrack devices are compared to lone racetracks with the same physical dimensions in the undercoupled, overcoupled and critical coupled regimes. We demonstrate an overall improvement in dynamic range, transduction responsivity, and mass sensitivity of up to 4x, 3x and 2.8x, respectively. Our highly phase sensitive MZI circuit also enables applications such as on-chip optical homodyning.

1. Introduction

In recent years, silicon photonic devices such as modulators and resonators initially designed for telecommunication applications have been repurposed to serve as ultrasensitive optical detectors of mass/temperature [14] and to transduce mechanical motion on-chip [5,6]. Improved access to photonic integrated circuit (PIC) fabrication facilities has made integrated photonics a versatile, low-cost option for engineering highly responsive optomechanical devices. Efforts to develop on-chip optomechanics as a sensing platform have been principally focused on optimizing optical and mechanical quality factor (Q) and decreasing mechanical modal mass [5]. There has been limited focus on the role of optical cavity span (linear range) to mitigate readout nonlinearities in mechanical transduction [7]. Optomechanical crystals, microrings [8,9], and racetrack resonators have been steadfastly explored as high Q sensing elements with substantial cavity finesse, leading to extraordinary displacement sensitivities and signal-to-noise ratios [5,6,10]. However, narrow cavity linewidths inherently prevent linear transduction of high amplitude (high dynamic range) mechanical modes and render the optomechanical system susceptible to environmental perturbations, such as gas adsorption or temperature change, that cause shifts in cavity resonant wavelength [1,2,11]. The resulting change in cavity detuning can induce substantial readout nonlinearities or even loss of mechanical signal [12]. In addition, current approaches to improve nanomechanical sensitivity by decreasing modal mass are facilitated by increasing optomechanical coupling [5]. Stronger coupling and larger amplitudes inevitably give rise to nonlinearities in nanomechanical readout that are detrimental to sensor performance [7,12,13]. In general, large amplitude vibrations with linear readout are desirable to maximize dynamic range in optomechanical sensing [1,1416], especially for mass [1,2,11], temperature [3,4,11] and force [17] sensing in low Q fluidic or atmospheric environments [1,11]. In this work, we present a robust photonic circuit design based on a Mach-Zehnder interferometer (MZI) [4,1820] combined with a racetrack resonator, called a racetrack-loaded MZI, that extends linear range without compromising high optomechanical transduction sensitivity. The devices are fabricated on a standard 220 nm silicon-on-insulator substrate with a 2 micron buried oxide layer. The optical resonance properties of 24 racetrack-loaded MZI devices are compared to 24 lone racetracks with the same physical dimensions in the overcoupled, undercoupled, and critically coupled regimes. The racetrack-loaded MZIs outperform the lone racetracks in terms of optical linear range by a factor of 2-3x when overcoupled, 1.8x near critical coupling, and 3.2x when undercoupled. Furthermore, photonic transduction responsivity is enhanced by 1.7-3.5x when the system is overcoupled, and is comparable to the racetrack architecture in the under- and critically coupled regimes. Improvements over the racetrack design are validated in the readout of the first (1f) and second (2f) harmonics of side-coupled cantilevers [5,6,13]. As indicated by the onset of the 2f signal, racetrack-loaded MZIs exhibit a mechanical linear range improvement of up to 3-4x when under- or critically coupled compared to reference racetracks with matching cantilever dimensions. Linear range increase offered by the MZI enables a mass sensitivity enhancement factor of 2.8x, presenting an improvement route for high dynamic range mass detectors. While cavity transduction of linear mechanical spectra is extended to larger amplitudes, the range of linear proportionality between mechanical amplitude and overall signal power remains similar. Since the MZI circuit is inherently a highly phase sensitive device and converts between phase and amplitude measurements, it may allow for a greater flexibility in applications such as on-chip homodyne detection of mechanical signals [2123].

2. Theory

A racetrack cavity response has both amplitude and phase variation across the cavity detuning. In typical optomechanical transduction, the signal of mechanical motion at a set detuning is reported either directly through power modulation of the optical cavity, or via off-chip phase-sensitive optical homodyning. A simple mechanism that can be applied on-chip to transform the phase signal into an amplitude signal is to couple the racetrack to one arm of an MZI. Direct access to the cavity phase spectrum after output mixing would enable optical homodyning on-chip, while also providing intrinsically broader linewidth than the amplitude spectrum for mechanical transduction. This mechanism should allow for an extension of linear transduction range while maintaining responsivity. We constructed a Mach-Zehnder interferometer (MZI) nanophotonic circuit consisting of a 50:50 input splitter, a reference arm with phase shift θ, and an all-pass racetrack-loaded arm [7,18,19]. Figure 1 shows optical microscope images of an on-chip racetrack-loaded MZI (a) and a lone all-pass racetrack (b) which have matching coupling conditions and device dimensions. For this highly phase sensitive device, transfer functions are used to track the input light amplitude ${s_i}$ as it passes through the reference arm, ${H_{REF}}(\theta )= \left( {1/\sqrt 2 } \right){s_i}{e^{i\theta }}$, and the all-pass racetrack resonator arm, ${H_{RT}}(\phi )$. The racetrack round-trip phase can be approximated as:

$$\phi (x )= \frac{{2\pi ({\lambda - {\lambda_{res}}(x )} )}}{\cal F} = \frac{{2\pi }}{\cal F}\left( {\lambda - \frac{{2\pi c{\lambda_{res}}}}{{2\pi c + Gx{\lambda_{res}}}}} \right)$$
where ${\cal F} = {\lambda ^2}/{L_C}{n_g}$ is the free spectral range, ng is the group index, LC is the cavity length, λ is the measurement wavelength, and λres(x) is the racetrack resonant wavelength. Recombination of the reference and signal fields at the output splitter produces a net amplitude ${s_f}$ given by the sum of the transfer functions. The transmitted field power of the racetrack-loaded MZI and bare racetrack are therefore:
$$\; {T_{RT - MZI}}({\phi ,\; \theta } )= {\left|{\frac{{{s_f}}}{{{s_i}}}} \right|^2} = {\left|{\frac{1}{2}({{H_{RT}}(\phi )+ b{e^{i\theta }}} )} \right|^2}$$
$$\; {T_{RT}}(\phi )= {|{{H_{RT}}(\phi )} |^2} = {\left|{\frac{{\tau - {a_{rt}}{e^{i\phi }}}}{{1 - \tau {a_{rt}}{e^{i\phi }}}}} \right|^2}$$
The resulting ${T_{RT - MZI}}$ is a Fano-shaped optical transmission spectrum [4,1820] as shown in Fig. 2(b). Cavity eigenfrequency change due to near-field mechanical motion: ${\omega _{res}}(x )\approx {\omega _{res}} + Gx$, facilitates mechanical transduction by tuning the round-trip phase, $\; \phi (x )$. Here, $\; G \equiv {\partial _x}{\omega _{res}}$ is the dispersive optomechanical coupling strength and x is the amplitude quadrature. The numerical parameter b accounts for the imperfect split of power to both arms (0 $\le $ b $\le $ 1), which results in non-ideal interference at the output. In this model, b = 1 represents perfect destructive interference. The transmission coefficient τ and coupling coefficient κ of the directional coupler can be tuned during fabrication to achieve maximal linear range. Inherent cavity round-trip loss, art, is determined by the fabrication process. The relative magnitude of the transmission coefficient and round-trip loss establishes the coupling condition of the cavity, and hence the throughput resonance lineshape. Values of τ < art, τ = art, and τ > art define the overcoupled, critically coupled, and undercoupled regimes, respectively. The power coupling $\{{\tau ,{a_{rt}},\kappa } \}$ and energy loss $\{{{\gamma_{ex}},{\gamma_0},\gamma } \}$ formalism parameters are connected as follows [7]: the extrinsic coupling amplitude loss rate, ${\gamma _{ex}}/2\pi = {v_g}({1 - {\tau^2}} )/4\pi {L_C}$, the intrinsic amplitude loss rate ${\gamma _0}/2\pi ={-} {v_g}\ln ({{a_{rt}}} )/2\pi {L_C}$, and the total decay rate, $\gamma = {\gamma _{ex}} + {\gamma _0}$, where ${v_g} = c/{n_g}$ is the group velocity. The transmission function of the all-pass arm TRT can be characterized by either a single Lorentzian optical resonance as in Eq. (3), or by two superimposed resonances (split resonance) manifesting from coherent backscattering in the racetrack cavity [7,11,24,25]. The MZI reference phase: $\theta (\lambda )= 2\pi {L_{arm}}({\lambda \; d{n_{eff}}/d\lambda \; + \; {n_g}} )/\lambda $, where the term in parentheses is the waveguide effective index ${n_{eff}}(\lambda )$, Larm is the reference arm length, and dneff/dλ is the dispersion, which acts to tune θ (hence the MZI on-resonance lineshape) through wavelength space. As θ increases from 0 to π/2, ${T_{RT - MZI}}$ transitions from a typical racetrack Lorentzian to a Fano-lineshape [18], achieving a perfectly antisymmetric Fano exhibiting a theoretically maximum slope and linear range at θ=π/2 (plus any integer multiple of $2\pi $, which enables flexibility in picking ${L_{arm}}$). Examples of the transmission shape ${T_{RT - MZI}}$ versus TRT for a variety of coupling and phase shift θ conditions can be seen in [7].

 figure: Fig. 1.

Fig. 1. Optical microscope images of (a) a racetrack-loaded MZI and (b) a bare racetrack resonator both with 5 µm radii, 10 µm straight sections, and 5 µm long side-coupled cantilevers. The transfer functions HREF and HRT are depicted on-plot together with the transmission coefficient, τ, coupling coefficient, κ, and the phase shift, θ, of the 33 µm reference arm (Larm) to illustrate the phase tracking process. The input light field si is split 50:50 to each arm and is recombined at a second 50:50 combiner to produce the output signal sf. The dark square visible next to the racetrack in both images was an etch window used to release the narrow clamped cantilever that is adjacent and parallel to the racetrack. Only the cantilever support anchor is resolved as a light square. (c) is a scanning electron microscope image of a focused ion beam cut cross-section showing a 210 nm wide nanomechanical cantilever coupled to a 500 nm wide racetrack waveguide with a resolved 160 nm gap spacing and a 220 nm device layer thickness. An in-plane schematic of the racetrack-cantilever optomechanical system is shown in (d).

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 figure: Fig. 2.

Fig. 2. Racetrack and MZI racetrack transmission spectra T (mV) are depicted vs. wavelength λ (nm) as black and blue circles in (a) and (b), respectively. The spectra are theoretically fit via Eqs. (2) and (3) (shown in orange) to yield transmission coefficients of 0.974 and 0.976, respectively. First order point derivatives of both spectra dT/dλ (mV/nm) are plotted in red to illustrate optical linear ranges of 0.06 nm and 0.13 nm for the racetrack and the MZI resonances, respectively, by our definition (marked with vertical dashed lines on-plot). The grating coupler envelope is subtracted from the baseline transmission in (a) and (b).

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3. Experimental details and results

Racetrack-loaded MZIs and lone (reference) racetrack resonator circuits with the same coupling conditions were fabricated on-chip by the AMF (previously IME) foundry in Singapore. To tune linear range and cavity slope, four coupling conditions were employed with average τ values of 0.923, 0.975, 0.986, and 0.994, corresponding to optical racetrack quality factors ranging from 3000 - 45000. Side-coupled nanomechanical cantilevers were embedded near the straight racetrack section of each circuit. The cantilever lengths were 2 µm, 3.5 µm, and 5 µm with widths of 200 nm, 180 nm, and 180 nm, respectively, and cantilever-racetrack gaps of 160 nm and 200 nm, for a total of 24 racetracks and 24 racetrack-MZI devices. To characterize our circuits both optically and mechanically, we employed the confocal nanophotonic pump-probe measurement scheme described in [5,7,26].

3.1 Optical characterization

The optical transmission spectra of the 24 racetrack-loaded MZIs and 24 racetracks were acquired using a Santec TSL-510 tunable diode probe laser swept from 1520 -1580 nm with 15.4 $\mu $W input at the on-chip grating couplers (after accounting for a 1.54% coupling efficiency). A typical optical racetrack transmission spectrum is plotted in Fig. 2(a) as black circles with a Lorentzian fit (Eq. (3)) in orange. Fitting yielded τ, art, λres, and ${\cal F}$ values of 0.974, 0.994, 1547.79 nm and 14.03 nm, respectively. The point derivative dT/dλ shown in red directly reveals a maximum slope of −450.84 mV/nm and a 0.06 nm linear range (indicated by vertical dashed lines on-plot). Similarly, in Fig. 2(b) the optical resonance of a MZI racetrack device is depicted as blue circles with a theoretical fit to Eq. (2) in orange, yielding b, dneff/dλ, λres, Larm, ng, τ, and art values of 0.966, −1.96 × 10−5 nm−1, 1535.26 nm, 33.039 µm, 3.444, 0.976, and 0.996, respectively. The point derivative of the spectrum dT/d$\lambda $ shown in red indicates a maximum slope of −508.88 mV/nm and a 0.13 nm linear range. Both devices in Fig. 2 were designed to have identical coupling conditions. A comparison of the two devices quickly shows the main feature of the ring-loaded MZI, that is, a doubling of the linear range while maintaining the same maximum cavity slope. Theoretically fitting each of the 24 racetrack-loaded MZI and reference racetrack spectra yielded expectedly similar transmission coefficients, with a maximum discrepancy of 1.3%. The fitted art and τ values for each device are available in [7]. The maximum slope point on the resonance determines the sensitivity limit of the photonic circuit to nanomechanical vibration [5] and is hence the optimal detection laser setpoint. When optomechanical coupling, G=∂xωres, is sufficiently high, shifts in cavity resonant frequency ωres (due to large amplitude vibration in x) relative to the detection laser setpoint ωl, cause the setpoint to transiently change position on the transmission spectrum [7,11,12]. If the cavity slope at the setpoint changes sign over the course of the oscillation, the mechanical response becomes highly nonlinear. Therefore, we define an empirical linear range that is twice the wavelength span from the cavity minimum (the point of zero slope) to the maximum slope point, and centered at the maximum slope point, as shown by dashed lines in Fig. 2(a). Similarly, the Fano linear range is twice the span between zero and maximum slope points as illustrated in Fig. 2(b). We principally aimed to increase the linear transduction range of the cavity, not the range of linear proportionality between mechanical amplitude and overall signal power. Amplitude-to-power conversion is determined by cavity slope and measurement gain. The linear range and maximum slope for the 48 devices are shown in Fig. 3, with racetrack devices as red stars and MZI-racetrack devices as blue dots. As indicated by the average values of slope and linear range (depicted via box plots), the MZI devices show a linear range enhancement of 2-3x when overcoupled, 1.8x near critical coupling, and 3.2x when undercoupled. Further, MZI racetrack photonic transduction responsivity (slope) is superior by factors ranging from 1.7x to 3.5x in the overcoupled regime and is comparable to the racetrack in the under- and critically coupled regimes.

 figure: Fig. 3.

Fig. 3. The logscale (a) linear range (nm) and (b) slope (1/nm) are shown for racetrack resonators (red stars) and racetrack-loaded Mach-Zehnder interferometers (blue circles) as a function of the average fitted transmission coefficient τ (0.923, 0.975, 0.986, and 0.994). The average linear range (a) and slope (b) for each coupling condition and circuit architecture is depicted as box plots with standard deviation bars.

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3.2 Mechanical characterization

Improvements in linear transduction offered by the MZI circuit were verified by assessing mechanical linear range in the readout of side-coupled flexural mode cantilevers [6]. We employed racetrack-loaded MZIs and reference racetracks with 3.5 µm long cantilevers having fundamental eigenfrequencies of ∼23.5 MHz, modal masses of 80.4 fg, quality factors of ∼5000 (at 10−4 Torr and 298 K), and 160 nm cantilever-racetrack gaps (G ${\approx} $ 0.6 rad GHz/nm) [7]. The probe laser at the input grating was tuned to the maximum transduction point (peak slope) of the previously characterized optical resonance of each device. Cantilever thermomechanical (TM) noise was acquired while under vacuum (∼10−4 Torr) using a Zurich Instruments ultrahigh frequency (UHF) lock-in amplifier (LIA) via LabONE software as described in [7] to calibrate mechanical amplitude. By Lorentzian fitting the TM power spectral density we determined transduction responsivity ${\cal R}$ (V/m) as in [27]. A direct quantification of mechanical linear range can be done by determining the fundamental (1f) cantilever amplitude that corresponds to the onset of the second (2f) harmonic signal [13]. Appearance of a higher harmonic is taken as a proxy for the onset of nonlinearity. The 1f harmonic signal arises from the slope of the optical transmission curve sampled during the oscillation cycle while the 2f harmonic identifies non-zero curvature in the optical transmission curve. We measured the 1f and 2f signals with rising levels of actuation to find the critical amplitude. For driving we employed a 1.0 mW Photonetics TUNICS-BT pump laser (coupling efficiency 1.54%) tuned to the optical resonant wavelength where maximum driven mechanical signal power was observed. Setting the pump position on-resonance at the point of steepest slope on the racetrack-MZI Fano response and the minimum of the racetrack Lorentzian also avoids accidental self-oscillation (optomechanical damping rate [11], ${\Gamma _{opt}} \approx 0$) while facilitating maximum resonant power enhancement for actuation [7]. The maximum optical damping rate associated the 15.4 $\mu $W probe light in the bus of our Doppler regime device was $|{{\Gamma _{opt}}} |\approx $1 Hz. The pump was positioned on an optical resonance not under test by the probe laser such that a fibre-coupled optical band-pass filter (with bandwidth ∼0.25 nm) at output could selectively pass only probe light to the photodiode. Laser power was channeled through a Lucent Electro-Optic Modulator (EOM) prior to chip-coupling to provide an AC voltage modulation for in-phase mechanical actuation. Voltage amplitudes were output from the LIA to the EOM. Driven 1f and 2f signals of each device were empirically fit to a Lorentzian to extract the peak amplitude (in volts) as a function of AC drive voltage. Driven 1f amplitudes were converted to metres via ${\cal R}$ (V/m) [27] to account for slight differences in drive power for direct comparison between devices. Figures 4(a) and 4(b) depict the 2f signal versus fundamental amplitude for the racetrack resonators (red stars) and the MZI racetracks (blue circles) in the (a) critically coupled (τ = 0.986) and (b) undercoupled (τ = 0.994) regimes. The critically coupled racetrack device exhibited a 2f signal at a 1f amplitude of 0.3 nm, whereas the MZI racetrack had a 2f signal onset at a 1f amplitude of 0.8 nm, indicating minimum linear range improvement of 2.7x. Furthermore, the MZI racetrack 2f signal doesn’t reach the ∼9 µV 2f amplitude of the bare racetrack device until the 1f amplitude was 1.2 nm, which implies a linear range improvement closer to 4x. In the undercoupled case (4b), the racetrack and MZI racetrack 2f onset occurred at 1f amplitudes of 0.15 nm and 0.45 nm, respectively, reflecting an approximate 3x linear range improvement. In both coupling regimes, the MZI racetrack allows for a larger 1f amplitude to be reached before the 2f component appears and hence achieves a higher dynamic range.

 figure: Fig. 4.

Fig. 4. The 2f harmonic signal (µV) is plotted vs. the fundamental (1f) mechanical amplitude (nm) for the racetrack resonators (red stars) and the MZI racetracks (blue circles). Results are depicted for devices that are (a) critically coupled, τ = 0.986, and (b) undercoupled, τ = 0.994.

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3.3 Optical actuation and mass sensitivity

Linear range generally increases as the devices become more overcoupled at the expense of transduction sensitivity and optical power enhancement. The latter is largest close to critical coupling [7]. Limitations in pump power can be compensated for by increasing EOM driven amplitude or optomechanical coupling, which lead to transduction nonlinearities if not accompanied by increases in cavity linewidth and overall dynamic range as offered by our MZI racetrack architecture. As shown in Figs. 2 and 3, balance between linear range and transduction sensitivity is achieved by our MZI device with τ = 0.976, which also offers more ideal power enhancement for optical pumping [7]. The racetrack-loaded MZI architecture is also superior to the lone racetrack design for mass sensing applications. Mass sensitivity is proportional to the mechanical eigenfrequency shift $\delta {\Omega _0}$/${\Omega _0} \propto {a_{noise}}/{a_{driven}} = 1/SNR$ due to loading [1], where SNR is the signal-to-noise ratio, ${a_{driven}}$ is the amplitude of the 1f signal before the onset of the 2f readout nonlinearity, and ${a_{noise}}$ is the TM noise peak height. In the case where the coupling coefficient τ = 0.986, for instance, the MZI racetrack device has ${a_{driven}}$ = 0.61 nm and ${a_{noise}}$ = 87.4 pm/Hz1/2 while the racetrack exhibits an ${a_{driven}}$ = 0.22 nm and ${a_{noise}}$ = 87.6 pm/Hz1/2. The 1 Hz bandwidth SNRs for the racetrack-loaded MZI and the lone racetrack are hence 698 and 251, respectively, which demonstrates an improvement in the frequency shift sensitivity $\delta {\Omega _0}$ /${\Omega _0}$ by a factor of 2.8x in favor of the racetrack-loaded MZI.

4. Conclusion

To reduce the readout nonlinearities observed in racetrack resonator coupled optomechanical systems, we have designed, fabricated, and tested silicon-on-insulator nanophotonic racetrack-loaded Mach Zehnder interferometers (MZIs) and compared them against lone racetrack resonators with the same physical dimensions. An all-pass racetrack resonator is coupled to one arm of an MZI, while the reference arm has a phase shift set to π/2 at a wavelength of 1550 nm. Improvements in optical linear range offered by the racetrack-loaded MZI were demonstrated via optical spectra and by transducing the harmonics of racetrack-coupled nanomechanical cantilevers. Optical measurements of the racetrack-loaded MZI Fano resonance versus the racetrack Lorentzian response indicate linear range enhancement factors of 2-3x when overcoupled, 1.8x near critical coupling, and 3.2x when undercoupled in favor of the racetrack-loaded MZI. Further, transduction sensitivity is enhanced by a factor of 1.7x – 3.5x when overcoupled and is comparable to the lone racetrack in the under- and critically coupled regimes. By measuring the amplitude of the first two cantilever harmonics with ramping cantilever actuation, the racetrack-loaded MZIs are shown to have a mechanical linear range of up to 3-4x greater than the equivalent racetrack architecture in the under- or critically coupled regimes. Enhancements in linear range for all coupling conditions imply that mechanical readout nonlinearities may be circumvented when photonically transducing high dynamic range nanomechanical devices such as cantilevers, improving their performance as mass, temperature, and biochemical sensors. A direct consequence of the linear range improvement is a frequency-shift sensitivity enhancement by a factor of ∼2.8x. Large amplitudes of vibration in nano-optomechanical systems may also be of interest in signal processing or mechanical computing [28]. Our highly phase-sensitive circuit may enable on-chip homodyne measurements, whereby an input laser field is split to form a local oscillator and a detection signal then recombined at the output combiner where differences in phase are detected. Homodyne approaches are generally implemented using optical fibers and discrete external components and traditionally involve intricate setups with many components such as fibre stretchers [23]. Careful pre-polarization and near-perfect mode overlap are also required to achieve acceptable signal-to-noise ratios. In our on-chip implementation, polarization sensitive grating couplers automatically admit only TE or TM polarization, and the interfering optical modes are pre-aligned by the integrated photonics. In this work we demonstrated 50:50 splitting of the optical power into the two arms of the MZI. In future work, for example for the situation where power in the signal arm is constrained by backaction or other reasons, power sent to the local oscillator (reference arm) could be increased by modifying the input splitter ratio (e.g. from 50:50 to 90:10) thereby increasing the photocurrent associated with the beating of the local oscillator and the small detection signal [29]. In addition, balanced homodyne detection could be easily incorporated by modifying the MZI output coupler to be a 2 × 2 coupler instead of 2 × 1.

Funding

Natural Sciences and Engineering Research Council of Canada (356093-2013, RGPIN-2019-06400, USRA Program); Vanier Canada Graduate Scholarship Program; Alberta Innovates.

Acknowledgments

This work was supported by the National Research Council’s Nanotechnology Research Center (NANO) and its fabrication, microscopy, and characterization facilities; and by the Natural Sciences and Engineering Research Council Canada. Device fabrication was facilitated through the Canadian Microelectronics Corporation (CMC) and the AMF (previously IME) foundry in Singapore. The authors would like to thank Doug Vick for focused ion beam characterization.

Disclosures

The authors declare no conflicts of interest.

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24. J. N. Westwood-Bachman, Z. Diao, V. T. K. Sauer, D. Bachman, and W. K. Hiebert, “Even nanomechanical modes transduced by integrated photonics,” Appl. Phys. Lett. 108(6), 061103 (2016). [CrossRef]  

25. V. Van, Optical Microring Resonators: Theory, Techniques, and Applications (CRC, 2016).

26. V. T. K. Sauer, Z. Diao, and M. R. Freeman, “Confocal Scanner for Highly Sensitive Photonic Transduction of Nanomechanical Resonators,” Appl. Phys. Express 6(6), 065202 (2013). [CrossRef]  

27. M. Li, H. X. Tang, and M. L. Roukes, “Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications,” Nat. Nanotechnol. 2(2), 114–120 (2007). [CrossRef]  

28. M. Bagheri, M. Poot, M. Li, W. P. H. Pernice, and H. X. Tang, “Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical memory operation,” Nat. Nanotechnol. 6(11), 726–732 (2011). [CrossRef]  

29. A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4(5), 415–419 (2008). [CrossRef]  

References

  • View by:

  1. S. K. Roy, V. T. K. Sauer, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, “Improving mechanical sensor performance through larger damping,” Science 360(6394), eaar5220 (2018).
    [Crossref]
  2. A. Venkatasubramanian, V. T. K. Sauer, S. K. Roy, M. Xia, D. S. Wishart, and W. K. Hiebert, “Nano-Optomechanical Systems for Gas Chromatography,” Nano Lett. 16(11), 6975–6981 (2016).
    [Crossref]
  3. T. P. Purdy, K. E. Grutter, K. Srinivasan, and J. M. Taylor, “Quantum correlations from a room-temperature optomechanical cavity,” Science 356(6344), 1265–1268 (2017).
    [Crossref]
  4. C. Yu, Y. Zhang, X. Zhang, K. Wang, C. Yao, P. Yuan, and Y. Guan, “Nested fiber ring resonator enhanced Mach-Zehnder interferometer for temperature sensing,” Appl. Opt. 51(36), 8873–8876 (2012).
    [Crossref]
  5. V. T. K. Sauer, Z. Diao, M. R. Freeman, and W. K. Hiebert, “Optical racetrack resonator transduction of nanomechanical cantilevers,” Nanotechnology 25(5), 055202 (2014).
    [Crossref]
  6. V. T. K. Sauer, Z. Diao, M. R. Freeman, and W. K. Hiebert, “Nanophotonic detection of side-coupled nanomechanical cantilevers,” Appl. Phys. Lett. 100(26), 261102 (2012).
    [Crossref]
  7. J. Bachman, “Improving the performance of nano-optomechanical systems for use as mass sensors,” Ph. D. Thesis, University of Alberta, (2019).
  8. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Compact silicon microring resonators with ultra-low propagation loss in the C band,” Opt. Express 15(22), 14467–14475 (2007).
    [Crossref]
  9. D. P. Cai, J. H. Lu, C. C. Chen, C. C. Lee, C. E. Lin, and T. J. Yen, “High Q-factor microring resonator wrapped by the curved waveguide,” Sci. Rep. 5(1), 10078 (2015).
    [Crossref]
  10. E. Gavartin, P. Verlot, and T. J. Kippenberg, “Stabilization of a linear nanomechanical oscillator to its thermodynamic limit,” Nat. Commun. 4(1), 2860 (2013).
    [Crossref]
  11. M. P. Maksymowych, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, “Optomechanical spring enhanced mass sensing,” Appl. Phys. Lett. 115(10), 101103 (2019).
    [Crossref]
  12. M. Poot, K. Y. Fong, M. Bagheri, W. H. P. Pernice, and H. X. Tang, “Backaction limits on self-sustained optomechanical oscillations,” Phys. Rev. A: At., Mol., Opt. Phys. 86(5), 053826 (2012).
    [Crossref]
  13. H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13(14), 5293–5301 (2005).
    [Crossref]
  14. J. Lee, Z. Wang, K. He, R. Yang, J. Shan, and P. X. L. Feng, “Electrically tunable single- and few-layer MoS2 nanoelectromechanical systems with broad dynamic range,” Sci. Adv. 4(3), eaao6653 (2018).
    [Crossref]
  15. N. Kacem, J. Arcamone, F. Perez-Murano, and S. Hentz, “Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications,” J. Micromech. Microeng. 20(4), 045023 (2010).
    [Crossref]
  16. L. G. Villanueva, E. Kenig, R. B. Karabalin, M. H. Matheny, R. Lifshitz, M. C. Cross, and M. L. Roukes, “Surpassing fundamental limits of oscillators using nonlinear resonators,” Phys. Rev. Lett. 110(17), 177208 (2013).
    [Crossref]
  17. J. Melcher, J. Stirling, F. G. Cervantes, J. R. Pratt, and G. A. Shaw, “A self-calibrating optomechanical force sensor with femtonewton resolution,” Appl. Phys. Lett. 105(23), 233109 (2014).
    [Crossref]
  18. Y. Lu, J. Yao, X. Li, and P. Wang, “Tunable asymmetrical Fano resonance bistability in a microcavity-resonator-coupled Mach Zehnder interferometer,” Opt. Lett. 30(22), 3069–3071 (2005).
    [Crossref]
  19. V. Van, W. N. Herman, and P. T. Ho, “Linearized microring-loaded Mach-Zehnder modulator with RF gain,” J. Lightwave Technol. 24(4), 1850–1854 (2006).
    [Crossref]
  20. S. Darmawan, Y. M. Landobasa, P. Dumon, R. Baets, and M. K. Chin, “Nested-Ring Mach – Zehnder Interferometer in Silicon-on-Insulator,” IEEE Photon. Technol. Lett. 20(1), 9–11 (2008).
    [Crossref]
  21. J. A. Cox, A. L. Lentine, D. C. Trotter, and A. L. Starbuck, “Control of integrated micro-resonator wavelength via balanced homodyne locking,” Opt. Express 22(9), 11279–11289 (2014).
    [Crossref]
  22. F. Raffaelli, G. Ferranti, D. H. Mahler, P. Sibson, J. E. Kennard, A. Santamato, G. Sinclair, D. Bonneau, M. G. Thompson, and J. C. F. Matthews, “A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers,” Quantum Sci. Technol. 3(2), 025003 (2018).
    [Crossref]
  23. A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
    [Crossref]
  24. J. N. Westwood-Bachman, Z. Diao, V. T. K. Sauer, D. Bachman, and W. K. Hiebert, “Even nanomechanical modes transduced by integrated photonics,” Appl. Phys. Lett. 108(6), 061103 (2016).
    [Crossref]
  25. V. Van, Optical Microring Resonators: Theory, Techniques, and Applications (CRC, 2016).
  26. V. T. K. Sauer, Z. Diao, and M. R. Freeman, “Confocal Scanner for Highly Sensitive Photonic Transduction of Nanomechanical Resonators,” Appl. Phys. Express 6(6), 065202 (2013).
    [Crossref]
  27. M. Li, H. X. Tang, and M. L. Roukes, “Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications,” Nat. Nanotechnol. 2(2), 114–120 (2007).
    [Crossref]
  28. M. Bagheri, M. Poot, M. Li, W. P. H. Pernice, and H. X. Tang, “Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical memory operation,” Nat. Nanotechnol. 6(11), 726–732 (2011).
    [Crossref]
  29. A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4(5), 415–419 (2008).
    [Crossref]

2019 (1)

M. P. Maksymowych, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, “Optomechanical spring enhanced mass sensing,” Appl. Phys. Lett. 115(10), 101103 (2019).
[Crossref]

2018 (3)

J. Lee, Z. Wang, K. He, R. Yang, J. Shan, and P. X. L. Feng, “Electrically tunable single- and few-layer MoS2 nanoelectromechanical systems with broad dynamic range,” Sci. Adv. 4(3), eaao6653 (2018).
[Crossref]

S. K. Roy, V. T. K. Sauer, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, “Improving mechanical sensor performance through larger damping,” Science 360(6394), eaar5220 (2018).
[Crossref]

F. Raffaelli, G. Ferranti, D. H. Mahler, P. Sibson, J. E. Kennard, A. Santamato, G. Sinclair, D. Bonneau, M. G. Thompson, and J. C. F. Matthews, “A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers,” Quantum Sci. Technol. 3(2), 025003 (2018).
[Crossref]

2017 (1)

T. P. Purdy, K. E. Grutter, K. Srinivasan, and J. M. Taylor, “Quantum correlations from a room-temperature optomechanical cavity,” Science 356(6344), 1265–1268 (2017).
[Crossref]

2016 (2)

A. Venkatasubramanian, V. T. K. Sauer, S. K. Roy, M. Xia, D. S. Wishart, and W. K. Hiebert, “Nano-Optomechanical Systems for Gas Chromatography,” Nano Lett. 16(11), 6975–6981 (2016).
[Crossref]

J. N. Westwood-Bachman, Z. Diao, V. T. K. Sauer, D. Bachman, and W. K. Hiebert, “Even nanomechanical modes transduced by integrated photonics,” Appl. Phys. Lett. 108(6), 061103 (2016).
[Crossref]

2015 (1)

D. P. Cai, J. H. Lu, C. C. Chen, C. C. Lee, C. E. Lin, and T. J. Yen, “High Q-factor microring resonator wrapped by the curved waveguide,” Sci. Rep. 5(1), 10078 (2015).
[Crossref]

2014 (3)

V. T. K. Sauer, Z. Diao, M. R. Freeman, and W. K. Hiebert, “Optical racetrack resonator transduction of nanomechanical cantilevers,” Nanotechnology 25(5), 055202 (2014).
[Crossref]

J. Melcher, J. Stirling, F. G. Cervantes, J. R. Pratt, and G. A. Shaw, “A self-calibrating optomechanical force sensor with femtonewton resolution,” Appl. Phys. Lett. 105(23), 233109 (2014).
[Crossref]

J. A. Cox, A. L. Lentine, D. C. Trotter, and A. L. Starbuck, “Control of integrated micro-resonator wavelength via balanced homodyne locking,” Opt. Express 22(9), 11279–11289 (2014).
[Crossref]

2013 (4)

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
[Crossref]

V. T. K. Sauer, Z. Diao, and M. R. Freeman, “Confocal Scanner for Highly Sensitive Photonic Transduction of Nanomechanical Resonators,” Appl. Phys. Express 6(6), 065202 (2013).
[Crossref]

L. G. Villanueva, E. Kenig, R. B. Karabalin, M. H. Matheny, R. Lifshitz, M. C. Cross, and M. L. Roukes, “Surpassing fundamental limits of oscillators using nonlinear resonators,” Phys. Rev. Lett. 110(17), 177208 (2013).
[Crossref]

E. Gavartin, P. Verlot, and T. J. Kippenberg, “Stabilization of a linear nanomechanical oscillator to its thermodynamic limit,” Nat. Commun. 4(1), 2860 (2013).
[Crossref]

2012 (3)

V. T. K. Sauer, Z. Diao, M. R. Freeman, and W. K. Hiebert, “Nanophotonic detection of side-coupled nanomechanical cantilevers,” Appl. Phys. Lett. 100(26), 261102 (2012).
[Crossref]

C. Yu, Y. Zhang, X. Zhang, K. Wang, C. Yao, P. Yuan, and Y. Guan, “Nested fiber ring resonator enhanced Mach-Zehnder interferometer for temperature sensing,” Appl. Opt. 51(36), 8873–8876 (2012).
[Crossref]

M. Poot, K. Y. Fong, M. Bagheri, W. H. P. Pernice, and H. X. Tang, “Backaction limits on self-sustained optomechanical oscillations,” Phys. Rev. A: At., Mol., Opt. Phys. 86(5), 053826 (2012).
[Crossref]

2011 (1)

M. Bagheri, M. Poot, M. Li, W. P. H. Pernice, and H. X. Tang, “Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical memory operation,” Nat. Nanotechnol. 6(11), 726–732 (2011).
[Crossref]

2010 (1)

N. Kacem, J. Arcamone, F. Perez-Murano, and S. Hentz, “Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications,” J. Micromech. Microeng. 20(4), 045023 (2010).
[Crossref]

2008 (2)

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4(5), 415–419 (2008).
[Crossref]

S. Darmawan, Y. M. Landobasa, P. Dumon, R. Baets, and M. K. Chin, “Nested-Ring Mach – Zehnder Interferometer in Silicon-on-Insulator,” IEEE Photon. Technol. Lett. 20(1), 9–11 (2008).
[Crossref]

2007 (2)

M. Li, H. X. Tang, and M. L. Roukes, “Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications,” Nat. Nanotechnol. 2(2), 114–120 (2007).
[Crossref]

S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Compact silicon microring resonators with ultra-low propagation loss in the C band,” Opt. Express 15(22), 14467–14475 (2007).
[Crossref]

2006 (1)

2005 (2)

Anetsberger, G.

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4(5), 415–419 (2008).
[Crossref]

Arcamone, J.

N. Kacem, J. Arcamone, F. Perez-Murano, and S. Hentz, “Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications,” J. Micromech. Microeng. 20(4), 045023 (2010).
[Crossref]

Arcizet, O.

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4(5), 415–419 (2008).
[Crossref]

Aspelmeyer, M.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
[Crossref]

Bachman, D.

J. N. Westwood-Bachman, Z. Diao, V. T. K. Sauer, D. Bachman, and W. K. Hiebert, “Even nanomechanical modes transduced by integrated photonics,” Appl. Phys. Lett. 108(6), 061103 (2016).
[Crossref]

Bachman, J.

J. Bachman, “Improving the performance of nano-optomechanical systems for use as mass sensors,” Ph. D. Thesis, University of Alberta, (2019).

Baets, R.

S. Darmawan, Y. M. Landobasa, P. Dumon, R. Baets, and M. K. Chin, “Nested-Ring Mach – Zehnder Interferometer in Silicon-on-Insulator,” IEEE Photon. Technol. Lett. 20(1), 9–11 (2008).
[Crossref]

Bagheri, M.

M. Poot, K. Y. Fong, M. Bagheri, W. H. P. Pernice, and H. X. Tang, “Backaction limits on self-sustained optomechanical oscillations,” Phys. Rev. A: At., Mol., Opt. Phys. 86(5), 053826 (2012).
[Crossref]

M. Bagheri, M. Poot, M. Li, W. P. H. Pernice, and H. X. Tang, “Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical memory operation,” Nat. Nanotechnol. 6(11), 726–732 (2011).
[Crossref]

Bonneau, D.

F. Raffaelli, G. Ferranti, D. H. Mahler, P. Sibson, J. E. Kennard, A. Santamato, G. Sinclair, D. Bonneau, M. G. Thompson, and J. C. F. Matthews, “A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers,” Quantum Sci. Technol. 3(2), 025003 (2018).
[Crossref]

Cai, D. P.

D. P. Cai, J. H. Lu, C. C. Chen, C. C. Lee, C. E. Lin, and T. J. Yen, “High Q-factor microring resonator wrapped by the curved waveguide,” Sci. Rep. 5(1), 10078 (2015).
[Crossref]

Carmon, T.

Cervantes, F. G.

J. Melcher, J. Stirling, F. G. Cervantes, J. R. Pratt, and G. A. Shaw, “A self-calibrating optomechanical force sensor with femtonewton resolution,” Appl. Phys. Lett. 105(23), 233109 (2014).
[Crossref]

Chan, J.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
[Crossref]

Chen, C. C.

D. P. Cai, J. H. Lu, C. C. Chen, C. C. Lee, C. E. Lin, and T. J. Yen, “High Q-factor microring resonator wrapped by the curved waveguide,” Sci. Rep. 5(1), 10078 (2015).
[Crossref]

Chin, M. K.

S. Darmawan, Y. M. Landobasa, P. Dumon, R. Baets, and M. K. Chin, “Nested-Ring Mach – Zehnder Interferometer in Silicon-on-Insulator,” IEEE Photon. Technol. Lett. 20(1), 9–11 (2008).
[Crossref]

Cox, J. A.

Cross, M. C.

L. G. Villanueva, E. Kenig, R. B. Karabalin, M. H. Matheny, R. Lifshitz, M. C. Cross, and M. L. Roukes, “Surpassing fundamental limits of oscillators using nonlinear resonators,” Phys. Rev. Lett. 110(17), 177208 (2013).
[Crossref]

Darmawan, S.

S. Darmawan, Y. M. Landobasa, P. Dumon, R. Baets, and M. K. Chin, “Nested-Ring Mach – Zehnder Interferometer in Silicon-on-Insulator,” IEEE Photon. Technol. Lett. 20(1), 9–11 (2008).
[Crossref]

Diao, Z.

J. N. Westwood-Bachman, Z. Diao, V. T. K. Sauer, D. Bachman, and W. K. Hiebert, “Even nanomechanical modes transduced by integrated photonics,” Appl. Phys. Lett. 108(6), 061103 (2016).
[Crossref]

V. T. K. Sauer, Z. Diao, M. R. Freeman, and W. K. Hiebert, “Optical racetrack resonator transduction of nanomechanical cantilevers,” Nanotechnology 25(5), 055202 (2014).
[Crossref]

V. T. K. Sauer, Z. Diao, and M. R. Freeman, “Confocal Scanner for Highly Sensitive Photonic Transduction of Nanomechanical Resonators,” Appl. Phys. Express 6(6), 065202 (2013).
[Crossref]

V. T. K. Sauer, Z. Diao, M. R. Freeman, and W. K. Hiebert, “Nanophotonic detection of side-coupled nanomechanical cantilevers,” Appl. Phys. Lett. 100(26), 261102 (2012).
[Crossref]

Dumon, P.

S. Darmawan, Y. M. Landobasa, P. Dumon, R. Baets, and M. K. Chin, “Nested-Ring Mach – Zehnder Interferometer in Silicon-on-Insulator,” IEEE Photon. Technol. Lett. 20(1), 9–11 (2008).
[Crossref]

Feng, P. X. L.

J. Lee, Z. Wang, K. He, R. Yang, J. Shan, and P. X. L. Feng, “Electrically tunable single- and few-layer MoS2 nanoelectromechanical systems with broad dynamic range,” Sci. Adv. 4(3), eaao6653 (2018).
[Crossref]

Ferranti, G.

F. Raffaelli, G. Ferranti, D. H. Mahler, P. Sibson, J. E. Kennard, A. Santamato, G. Sinclair, D. Bonneau, M. G. Thompson, and J. C. F. Matthews, “A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers,” Quantum Sci. Technol. 3(2), 025003 (2018).
[Crossref]

Fong, K. Y.

M. Poot, K. Y. Fong, M. Bagheri, W. H. P. Pernice, and H. X. Tang, “Backaction limits on self-sustained optomechanical oscillations,” Phys. Rev. A: At., Mol., Opt. Phys. 86(5), 053826 (2012).
[Crossref]

Freeman, M. R.

V. T. K. Sauer, Z. Diao, M. R. Freeman, and W. K. Hiebert, “Optical racetrack resonator transduction of nanomechanical cantilevers,” Nanotechnology 25(5), 055202 (2014).
[Crossref]

V. T. K. Sauer, Z. Diao, and M. R. Freeman, “Confocal Scanner for Highly Sensitive Photonic Transduction of Nanomechanical Resonators,” Appl. Phys. Express 6(6), 065202 (2013).
[Crossref]

V. T. K. Sauer, Z. Diao, M. R. Freeman, and W. K. Hiebert, “Nanophotonic detection of side-coupled nanomechanical cantilevers,” Appl. Phys. Lett. 100(26), 261102 (2012).
[Crossref]

Gavartin, E.

E. Gavartin, P. Verlot, and T. J. Kippenberg, “Stabilization of a linear nanomechanical oscillator to its thermodynamic limit,” Nat. Commun. 4(1), 2860 (2013).
[Crossref]

Gröblacher, S.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
[Crossref]

Grutter, K. E.

T. P. Purdy, K. E. Grutter, K. Srinivasan, and J. M. Taylor, “Quantum correlations from a room-temperature optomechanical cavity,” Science 356(6344), 1265–1268 (2017).
[Crossref]

Guan, Y.

He, K.

J. Lee, Z. Wang, K. He, R. Yang, J. Shan, and P. X. L. Feng, “Electrically tunable single- and few-layer MoS2 nanoelectromechanical systems with broad dynamic range,” Sci. Adv. 4(3), eaao6653 (2018).
[Crossref]

Hentz, S.

N. Kacem, J. Arcamone, F. Perez-Murano, and S. Hentz, “Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications,” J. Micromech. Microeng. 20(4), 045023 (2010).
[Crossref]

Herman, W. N.

Hiebert, W. K.

M. P. Maksymowych, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, “Optomechanical spring enhanced mass sensing,” Appl. Phys. Lett. 115(10), 101103 (2019).
[Crossref]

S. K. Roy, V. T. K. Sauer, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, “Improving mechanical sensor performance through larger damping,” Science 360(6394), eaar5220 (2018).
[Crossref]

A. Venkatasubramanian, V. T. K. Sauer, S. K. Roy, M. Xia, D. S. Wishart, and W. K. Hiebert, “Nano-Optomechanical Systems for Gas Chromatography,” Nano Lett. 16(11), 6975–6981 (2016).
[Crossref]

J. N. Westwood-Bachman, Z. Diao, V. T. K. Sauer, D. Bachman, and W. K. Hiebert, “Even nanomechanical modes transduced by integrated photonics,” Appl. Phys. Lett. 108(6), 061103 (2016).
[Crossref]

V. T. K. Sauer, Z. Diao, M. R. Freeman, and W. K. Hiebert, “Optical racetrack resonator transduction of nanomechanical cantilevers,” Nanotechnology 25(5), 055202 (2014).
[Crossref]

V. T. K. Sauer, Z. Diao, M. R. Freeman, and W. K. Hiebert, “Nanophotonic detection of side-coupled nanomechanical cantilevers,” Appl. Phys. Lett. 100(26), 261102 (2012).
[Crossref]

Hill, J. T.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
[Crossref]

Ho, P. T.

Kacem, N.

N. Kacem, J. Arcamone, F. Perez-Murano, and S. Hentz, “Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications,” J. Micromech. Microeng. 20(4), 045023 (2010).
[Crossref]

Karabalin, R. B.

L. G. Villanueva, E. Kenig, R. B. Karabalin, M. H. Matheny, R. Lifshitz, M. C. Cross, and M. L. Roukes, “Surpassing fundamental limits of oscillators using nonlinear resonators,” Phys. Rev. Lett. 110(17), 177208 (2013).
[Crossref]

Kenig, E.

L. G. Villanueva, E. Kenig, R. B. Karabalin, M. H. Matheny, R. Lifshitz, M. C. Cross, and M. L. Roukes, “Surpassing fundamental limits of oscillators using nonlinear resonators,” Phys. Rev. Lett. 110(17), 177208 (2013).
[Crossref]

Kennard, J. E.

F. Raffaelli, G. Ferranti, D. H. Mahler, P. Sibson, J. E. Kennard, A. Santamato, G. Sinclair, D. Bonneau, M. G. Thompson, and J. C. F. Matthews, “A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers,” Quantum Sci. Technol. 3(2), 025003 (2018).
[Crossref]

Khan, M. H.

Kippenberg, T. J.

E. Gavartin, P. Verlot, and T. J. Kippenberg, “Stabilization of a linear nanomechanical oscillator to its thermodynamic limit,” Nat. Commun. 4(1), 2860 (2013).
[Crossref]

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4(5), 415–419 (2008).
[Crossref]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13(14), 5293–5301 (2005).
[Crossref]

Landobasa, Y. M.

S. Darmawan, Y. M. Landobasa, P. Dumon, R. Baets, and M. K. Chin, “Nested-Ring Mach – Zehnder Interferometer in Silicon-on-Insulator,” IEEE Photon. Technol. Lett. 20(1), 9–11 (2008).
[Crossref]

Lee, C. C.

D. P. Cai, J. H. Lu, C. C. Chen, C. C. Lee, C. E. Lin, and T. J. Yen, “High Q-factor microring resonator wrapped by the curved waveguide,” Sci. Rep. 5(1), 10078 (2015).
[Crossref]

Lee, J.

J. Lee, Z. Wang, K. He, R. Yang, J. Shan, and P. X. L. Feng, “Electrically tunable single- and few-layer MoS2 nanoelectromechanical systems with broad dynamic range,” Sci. Adv. 4(3), eaao6653 (2018).
[Crossref]

Lentine, A. L.

Li, M.

M. Bagheri, M. Poot, M. Li, W. P. H. Pernice, and H. X. Tang, “Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical memory operation,” Nat. Nanotechnol. 6(11), 726–732 (2011).
[Crossref]

M. Li, H. X. Tang, and M. L. Roukes, “Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications,” Nat. Nanotechnol. 2(2), 114–120 (2007).
[Crossref]

Li, X.

Lifshitz, R.

L. G. Villanueva, E. Kenig, R. B. Karabalin, M. H. Matheny, R. Lifshitz, M. C. Cross, and M. L. Roukes, “Surpassing fundamental limits of oscillators using nonlinear resonators,” Phys. Rev. Lett. 110(17), 177208 (2013).
[Crossref]

Lin, C. E.

D. P. Cai, J. H. Lu, C. C. Chen, C. C. Lee, C. E. Lin, and T. J. Yen, “High Q-factor microring resonator wrapped by the curved waveguide,” Sci. Rep. 5(1), 10078 (2015).
[Crossref]

Lu, J. H.

D. P. Cai, J. H. Lu, C. C. Chen, C. C. Lee, C. E. Lin, and T. J. Yen, “High Q-factor microring resonator wrapped by the curved waveguide,” Sci. Rep. 5(1), 10078 (2015).
[Crossref]

Lu, Y.

Mahler, D. H.

F. Raffaelli, G. Ferranti, D. H. Mahler, P. Sibson, J. E. Kennard, A. Santamato, G. Sinclair, D. Bonneau, M. G. Thompson, and J. C. F. Matthews, “A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers,” Quantum Sci. Technol. 3(2), 025003 (2018).
[Crossref]

Maksymowych, M. P.

M. P. Maksymowych, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, “Optomechanical spring enhanced mass sensing,” Appl. Phys. Lett. 115(10), 101103 (2019).
[Crossref]

Matheny, M. H.

L. G. Villanueva, E. Kenig, R. B. Karabalin, M. H. Matheny, R. Lifshitz, M. C. Cross, and M. L. Roukes, “Surpassing fundamental limits of oscillators using nonlinear resonators,” Phys. Rev. Lett. 110(17), 177208 (2013).
[Crossref]

Matthews, J. C. F.

F. Raffaelli, G. Ferranti, D. H. Mahler, P. Sibson, J. E. Kennard, A. Santamato, G. Sinclair, D. Bonneau, M. G. Thompson, and J. C. F. Matthews, “A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers,” Quantum Sci. Technol. 3(2), 025003 (2018).
[Crossref]

Melcher, J.

J. Melcher, J. Stirling, F. G. Cervantes, J. R. Pratt, and G. A. Shaw, “A self-calibrating optomechanical force sensor with femtonewton resolution,” Appl. Phys. Lett. 105(23), 233109 (2014).
[Crossref]

Painter, O.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
[Crossref]

Perez-Murano, F.

N. Kacem, J. Arcamone, F. Perez-Murano, and S. Hentz, “Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications,” J. Micromech. Microeng. 20(4), 045023 (2010).
[Crossref]

Pernice, W. H. P.

M. Poot, K. Y. Fong, M. Bagheri, W. H. P. Pernice, and H. X. Tang, “Backaction limits on self-sustained optomechanical oscillations,” Phys. Rev. A: At., Mol., Opt. Phys. 86(5), 053826 (2012).
[Crossref]

Pernice, W. P. H.

M. Bagheri, M. Poot, M. Li, W. P. H. Pernice, and H. X. Tang, “Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical memory operation,” Nat. Nanotechnol. 6(11), 726–732 (2011).
[Crossref]

Poot, M.

M. Poot, K. Y. Fong, M. Bagheri, W. H. P. Pernice, and H. X. Tang, “Backaction limits on self-sustained optomechanical oscillations,” Phys. Rev. A: At., Mol., Opt. Phys. 86(5), 053826 (2012).
[Crossref]

M. Bagheri, M. Poot, M. Li, W. P. H. Pernice, and H. X. Tang, “Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical memory operation,” Nat. Nanotechnol. 6(11), 726–732 (2011).
[Crossref]

Pratt, J. R.

J. Melcher, J. Stirling, F. G. Cervantes, J. R. Pratt, and G. A. Shaw, “A self-calibrating optomechanical force sensor with femtonewton resolution,” Appl. Phys. Lett. 105(23), 233109 (2014).
[Crossref]

Purdy, T. P.

T. P. Purdy, K. E. Grutter, K. Srinivasan, and J. M. Taylor, “Quantum correlations from a room-temperature optomechanical cavity,” Science 356(6344), 1265–1268 (2017).
[Crossref]

Qi, M.

Raffaelli, F.

F. Raffaelli, G. Ferranti, D. H. Mahler, P. Sibson, J. E. Kennard, A. Santamato, G. Sinclair, D. Bonneau, M. G. Thompson, and J. C. F. Matthews, “A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers,” Quantum Sci. Technol. 3(2), 025003 (2018).
[Crossref]

Rivière, R.

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4(5), 415–419 (2008).
[Crossref]

Rokhsari, H.

Roukes, M. L.

L. G. Villanueva, E. Kenig, R. B. Karabalin, M. H. Matheny, R. Lifshitz, M. C. Cross, and M. L. Roukes, “Surpassing fundamental limits of oscillators using nonlinear resonators,” Phys. Rev. Lett. 110(17), 177208 (2013).
[Crossref]

M. Li, H. X. Tang, and M. L. Roukes, “Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications,” Nat. Nanotechnol. 2(2), 114–120 (2007).
[Crossref]

Roy, S. K.

S. K. Roy, V. T. K. Sauer, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, “Improving mechanical sensor performance through larger damping,” Science 360(6394), eaar5220 (2018).
[Crossref]

A. Venkatasubramanian, V. T. K. Sauer, S. K. Roy, M. Xia, D. S. Wishart, and W. K. Hiebert, “Nano-Optomechanical Systems for Gas Chromatography,” Nano Lett. 16(11), 6975–6981 (2016).
[Crossref]

Safavi-Naeini, A. H.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
[Crossref]

Santamato, A.

F. Raffaelli, G. Ferranti, D. H. Mahler, P. Sibson, J. E. Kennard, A. Santamato, G. Sinclair, D. Bonneau, M. G. Thompson, and J. C. F. Matthews, “A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers,” Quantum Sci. Technol. 3(2), 025003 (2018).
[Crossref]

Sauer, V. T. K.

S. K. Roy, V. T. K. Sauer, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, “Improving mechanical sensor performance through larger damping,” Science 360(6394), eaar5220 (2018).
[Crossref]

A. Venkatasubramanian, V. T. K. Sauer, S. K. Roy, M. Xia, D. S. Wishart, and W. K. Hiebert, “Nano-Optomechanical Systems for Gas Chromatography,” Nano Lett. 16(11), 6975–6981 (2016).
[Crossref]

J. N. Westwood-Bachman, Z. Diao, V. T. K. Sauer, D. Bachman, and W. K. Hiebert, “Even nanomechanical modes transduced by integrated photonics,” Appl. Phys. Lett. 108(6), 061103 (2016).
[Crossref]

V. T. K. Sauer, Z. Diao, M. R. Freeman, and W. K. Hiebert, “Optical racetrack resonator transduction of nanomechanical cantilevers,” Nanotechnology 25(5), 055202 (2014).
[Crossref]

V. T. K. Sauer, Z. Diao, and M. R. Freeman, “Confocal Scanner for Highly Sensitive Photonic Transduction of Nanomechanical Resonators,” Appl. Phys. Express 6(6), 065202 (2013).
[Crossref]

V. T. K. Sauer, Z. Diao, M. R. Freeman, and W. K. Hiebert, “Nanophotonic detection of side-coupled nanomechanical cantilevers,” Appl. Phys. Lett. 100(26), 261102 (2012).
[Crossref]

Schliesser, A.

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4(5), 415–419 (2008).
[Crossref]

Shan, J.

J. Lee, Z. Wang, K. He, R. Yang, J. Shan, and P. X. L. Feng, “Electrically tunable single- and few-layer MoS2 nanoelectromechanical systems with broad dynamic range,” Sci. Adv. 4(3), eaao6653 (2018).
[Crossref]

Shaw, G. A.

J. Melcher, J. Stirling, F. G. Cervantes, J. R. Pratt, and G. A. Shaw, “A self-calibrating optomechanical force sensor with femtonewton resolution,” Appl. Phys. Lett. 105(23), 233109 (2014).
[Crossref]

Shen, H.

Sibson, P.

F. Raffaelli, G. Ferranti, D. H. Mahler, P. Sibson, J. E. Kennard, A. Santamato, G. Sinclair, D. Bonneau, M. G. Thompson, and J. C. F. Matthews, “A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers,” Quantum Sci. Technol. 3(2), 025003 (2018).
[Crossref]

Sinclair, G.

F. Raffaelli, G. Ferranti, D. H. Mahler, P. Sibson, J. E. Kennard, A. Santamato, G. Sinclair, D. Bonneau, M. G. Thompson, and J. C. F. Matthews, “A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers,” Quantum Sci. Technol. 3(2), 025003 (2018).
[Crossref]

Srinivasan, K.

T. P. Purdy, K. E. Grutter, K. Srinivasan, and J. M. Taylor, “Quantum correlations from a room-temperature optomechanical cavity,” Science 356(6344), 1265–1268 (2017).
[Crossref]

Starbuck, A. L.

Stirling, J.

J. Melcher, J. Stirling, F. G. Cervantes, J. R. Pratt, and G. A. Shaw, “A self-calibrating optomechanical force sensor with femtonewton resolution,” Appl. Phys. Lett. 105(23), 233109 (2014).
[Crossref]

Tang, H. X.

M. Poot, K. Y. Fong, M. Bagheri, W. H. P. Pernice, and H. X. Tang, “Backaction limits on self-sustained optomechanical oscillations,” Phys. Rev. A: At., Mol., Opt. Phys. 86(5), 053826 (2012).
[Crossref]

M. Bagheri, M. Poot, M. Li, W. P. H. Pernice, and H. X. Tang, “Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical memory operation,” Nat. Nanotechnol. 6(11), 726–732 (2011).
[Crossref]

M. Li, H. X. Tang, and M. L. Roukes, “Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications,” Nat. Nanotechnol. 2(2), 114–120 (2007).
[Crossref]

Taylor, J. M.

T. P. Purdy, K. E. Grutter, K. Srinivasan, and J. M. Taylor, “Quantum correlations from a room-temperature optomechanical cavity,” Science 356(6344), 1265–1268 (2017).
[Crossref]

Thompson, M. G.

F. Raffaelli, G. Ferranti, D. H. Mahler, P. Sibson, J. E. Kennard, A. Santamato, G. Sinclair, D. Bonneau, M. G. Thompson, and J. C. F. Matthews, “A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers,” Quantum Sci. Technol. 3(2), 025003 (2018).
[Crossref]

Trotter, D. C.

Vahala, K. J.

Van, V.

Venkatasubramanian, A.

M. P. Maksymowych, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, “Optomechanical spring enhanced mass sensing,” Appl. Phys. Lett. 115(10), 101103 (2019).
[Crossref]

S. K. Roy, V. T. K. Sauer, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, “Improving mechanical sensor performance through larger damping,” Science 360(6394), eaar5220 (2018).
[Crossref]

A. Venkatasubramanian, V. T. K. Sauer, S. K. Roy, M. Xia, D. S. Wishart, and W. K. Hiebert, “Nano-Optomechanical Systems for Gas Chromatography,” Nano Lett. 16(11), 6975–6981 (2016).
[Crossref]

Verlot, P.

E. Gavartin, P. Verlot, and T. J. Kippenberg, “Stabilization of a linear nanomechanical oscillator to its thermodynamic limit,” Nat. Commun. 4(1), 2860 (2013).
[Crossref]

Villanueva, L. G.

L. G. Villanueva, E. Kenig, R. B. Karabalin, M. H. Matheny, R. Lifshitz, M. C. Cross, and M. L. Roukes, “Surpassing fundamental limits of oscillators using nonlinear resonators,” Phys. Rev. Lett. 110(17), 177208 (2013).
[Crossref]

Wang, K.

Wang, P.

Wang, Z.

J. Lee, Z. Wang, K. He, R. Yang, J. Shan, and P. X. L. Feng, “Electrically tunable single- and few-layer MoS2 nanoelectromechanical systems with broad dynamic range,” Sci. Adv. 4(3), eaao6653 (2018).
[Crossref]

Westwood-Bachman, J. N.

M. P. Maksymowych, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, “Optomechanical spring enhanced mass sensing,” Appl. Phys. Lett. 115(10), 101103 (2019).
[Crossref]

S. K. Roy, V. T. K. Sauer, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, “Improving mechanical sensor performance through larger damping,” Science 360(6394), eaar5220 (2018).
[Crossref]

J. N. Westwood-Bachman, Z. Diao, V. T. K. Sauer, D. Bachman, and W. K. Hiebert, “Even nanomechanical modes transduced by integrated photonics,” Appl. Phys. Lett. 108(6), 061103 (2016).
[Crossref]

Wishart, D. S.

A. Venkatasubramanian, V. T. K. Sauer, S. K. Roy, M. Xia, D. S. Wishart, and W. K. Hiebert, “Nano-Optomechanical Systems for Gas Chromatography,” Nano Lett. 16(11), 6975–6981 (2016).
[Crossref]

Xia, M.

A. Venkatasubramanian, V. T. K. Sauer, S. K. Roy, M. Xia, D. S. Wishart, and W. K. Hiebert, “Nano-Optomechanical Systems for Gas Chromatography,” Nano Lett. 16(11), 6975–6981 (2016).
[Crossref]

Xiao, S.

Yang, R.

J. Lee, Z. Wang, K. He, R. Yang, J. Shan, and P. X. L. Feng, “Electrically tunable single- and few-layer MoS2 nanoelectromechanical systems with broad dynamic range,” Sci. Adv. 4(3), eaao6653 (2018).
[Crossref]

Yao, C.

Yao, J.

Yen, T. J.

D. P. Cai, J. H. Lu, C. C. Chen, C. C. Lee, C. E. Lin, and T. J. Yen, “High Q-factor microring resonator wrapped by the curved waveguide,” Sci. Rep. 5(1), 10078 (2015).
[Crossref]

Yu, C.

Yuan, P.

Zhang, X.

Zhang, Y.

Appl. Opt. (1)

Appl. Phys. Express (1)

V. T. K. Sauer, Z. Diao, and M. R. Freeman, “Confocal Scanner for Highly Sensitive Photonic Transduction of Nanomechanical Resonators,” Appl. Phys. Express 6(6), 065202 (2013).
[Crossref]

Appl. Phys. Lett. (4)

J. Melcher, J. Stirling, F. G. Cervantes, J. R. Pratt, and G. A. Shaw, “A self-calibrating optomechanical force sensor with femtonewton resolution,” Appl. Phys. Lett. 105(23), 233109 (2014).
[Crossref]

J. N. Westwood-Bachman, Z. Diao, V. T. K. Sauer, D. Bachman, and W. K. Hiebert, “Even nanomechanical modes transduced by integrated photonics,” Appl. Phys. Lett. 108(6), 061103 (2016).
[Crossref]

V. T. K. Sauer, Z. Diao, M. R. Freeman, and W. K. Hiebert, “Nanophotonic detection of side-coupled nanomechanical cantilevers,” Appl. Phys. Lett. 100(26), 261102 (2012).
[Crossref]

M. P. Maksymowych, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, “Optomechanical spring enhanced mass sensing,” Appl. Phys. Lett. 115(10), 101103 (2019).
[Crossref]

IEEE Photon. Technol. Lett. (1)

S. Darmawan, Y. M. Landobasa, P. Dumon, R. Baets, and M. K. Chin, “Nested-Ring Mach – Zehnder Interferometer in Silicon-on-Insulator,” IEEE Photon. Technol. Lett. 20(1), 9–11 (2008).
[Crossref]

J. Lightwave Technol. (1)

J. Micromech. Microeng. (1)

N. Kacem, J. Arcamone, F. Perez-Murano, and S. Hentz, “Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications,” J. Micromech. Microeng. 20(4), 045023 (2010).
[Crossref]

Nano Lett. (1)

A. Venkatasubramanian, V. T. K. Sauer, S. K. Roy, M. Xia, D. S. Wishart, and W. K. Hiebert, “Nano-Optomechanical Systems for Gas Chromatography,” Nano Lett. 16(11), 6975–6981 (2016).
[Crossref]

Nanotechnology (1)

V. T. K. Sauer, Z. Diao, M. R. Freeman, and W. K. Hiebert, “Optical racetrack resonator transduction of nanomechanical cantilevers,” Nanotechnology 25(5), 055202 (2014).
[Crossref]

Nat. Commun. (1)

E. Gavartin, P. Verlot, and T. J. Kippenberg, “Stabilization of a linear nanomechanical oscillator to its thermodynamic limit,” Nat. Commun. 4(1), 2860 (2013).
[Crossref]

Nat. Nanotechnol. (2)

M. Li, H. X. Tang, and M. L. Roukes, “Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications,” Nat. Nanotechnol. 2(2), 114–120 (2007).
[Crossref]

M. Bagheri, M. Poot, M. Li, W. P. H. Pernice, and H. X. Tang, “Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical memory operation,” Nat. Nanotechnol. 6(11), 726–732 (2011).
[Crossref]

Nat. Phys. (1)

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4(5), 415–419 (2008).
[Crossref]

Nature (1)

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A: At., Mol., Opt. Phys. (1)

M. Poot, K. Y. Fong, M. Bagheri, W. H. P. Pernice, and H. X. Tang, “Backaction limits on self-sustained optomechanical oscillations,” Phys. Rev. A: At., Mol., Opt. Phys. 86(5), 053826 (2012).
[Crossref]

Phys. Rev. Lett. (1)

L. G. Villanueva, E. Kenig, R. B. Karabalin, M. H. Matheny, R. Lifshitz, M. C. Cross, and M. L. Roukes, “Surpassing fundamental limits of oscillators using nonlinear resonators,” Phys. Rev. Lett. 110(17), 177208 (2013).
[Crossref]

Quantum Sci. Technol. (1)

F. Raffaelli, G. Ferranti, D. H. Mahler, P. Sibson, J. E. Kennard, A. Santamato, G. Sinclair, D. Bonneau, M. G. Thompson, and J. C. F. Matthews, “A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers,” Quantum Sci. Technol. 3(2), 025003 (2018).
[Crossref]

Sci. Adv. (1)

J. Lee, Z. Wang, K. He, R. Yang, J. Shan, and P. X. L. Feng, “Electrically tunable single- and few-layer MoS2 nanoelectromechanical systems with broad dynamic range,” Sci. Adv. 4(3), eaao6653 (2018).
[Crossref]

Sci. Rep. (1)

D. P. Cai, J. H. Lu, C. C. Chen, C. C. Lee, C. E. Lin, and T. J. Yen, “High Q-factor microring resonator wrapped by the curved waveguide,” Sci. Rep. 5(1), 10078 (2015).
[Crossref]

Science (2)

T. P. Purdy, K. E. Grutter, K. Srinivasan, and J. M. Taylor, “Quantum correlations from a room-temperature optomechanical cavity,” Science 356(6344), 1265–1268 (2017).
[Crossref]

S. K. Roy, V. T. K. Sauer, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, “Improving mechanical sensor performance through larger damping,” Science 360(6394), eaar5220 (2018).
[Crossref]

Other (2)

J. Bachman, “Improving the performance of nano-optomechanical systems for use as mass sensors,” Ph. D. Thesis, University of Alberta, (2019).

V. Van, Optical Microring Resonators: Theory, Techniques, and Applications (CRC, 2016).

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Figures (4)

Fig. 1.
Fig. 1. Optical microscope images of (a) a racetrack-loaded MZI and (b) a bare racetrack resonator both with 5 µm radii, 10 µm straight sections, and 5 µm long side-coupled cantilevers. The transfer functions HREF and HRT are depicted on-plot together with the transmission coefficient, τ, coupling coefficient, κ, and the phase shift, θ, of the 33 µm reference arm (Larm) to illustrate the phase tracking process. The input light field si is split 50:50 to each arm and is recombined at a second 50:50 combiner to produce the output signal sf. The dark square visible next to the racetrack in both images was an etch window used to release the narrow clamped cantilever that is adjacent and parallel to the racetrack. Only the cantilever support anchor is resolved as a light square. (c) is a scanning electron microscope image of a focused ion beam cut cross-section showing a 210 nm wide nanomechanical cantilever coupled to a 500 nm wide racetrack waveguide with a resolved 160 nm gap spacing and a 220 nm device layer thickness. An in-plane schematic of the racetrack-cantilever optomechanical system is shown in (d).
Fig. 2.
Fig. 2. Racetrack and MZI racetrack transmission spectra T (mV) are depicted vs. wavelength λ (nm) as black and blue circles in (a) and (b), respectively. The spectra are theoretically fit via Eqs. (2) and (3) (shown in orange) to yield transmission coefficients of 0.974 and 0.976, respectively. First order point derivatives of both spectra dT/dλ (mV/nm) are plotted in red to illustrate optical linear ranges of 0.06 nm and 0.13 nm for the racetrack and the MZI resonances, respectively, by our definition (marked with vertical dashed lines on-plot). The grating coupler envelope is subtracted from the baseline transmission in (a) and (b).
Fig. 3.
Fig. 3. The logscale (a) linear range (nm) and (b) slope (1/nm) are shown for racetrack resonators (red stars) and racetrack-loaded Mach-Zehnder interferometers (blue circles) as a function of the average fitted transmission coefficient τ (0.923, 0.975, 0.986, and 0.994). The average linear range (a) and slope (b) for each coupling condition and circuit architecture is depicted as box plots with standard deviation bars.
Fig. 4.
Fig. 4. The 2f harmonic signal (µV) is plotted vs. the fundamental (1f) mechanical amplitude (nm) for the racetrack resonators (red stars) and the MZI racetracks (blue circles). Results are depicted for devices that are (a) critically coupled, τ = 0.986, and (b) undercoupled, τ = 0.994.

Equations (3)

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ϕ ( x ) = 2 π ( λ λ r e s ( x ) ) F = 2 π F ( λ 2 π c λ r e s 2 π c + G x λ r e s )
T R T M Z I ( ϕ , θ ) = | s f s i | 2 = | 1 2 ( H R T ( ϕ ) + b e i θ ) | 2
T R T ( ϕ ) = | H R T ( ϕ ) | 2 = | τ a r t e i ϕ 1 τ a r t e i ϕ | 2

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