Monolithic integration of a nanomechanical resonator to an optical microdisk cavity

We report a Silicon nano-opto-mechanical device in which a nanomechanical doubly-clamped beam resonator is integrated to an optical microdisk cavity. Small flexural oscillations of the beam cause intensity modulations in the circulating optical field in the nearby microdisk cavity. By monitoring the corresponding fluctuations in the cavity transmission via a fiber-taper, one can detect these oscillations with a displacement sensitivity approaching 10 fm·Hz−1/2 at an input power level of 50 μW. Both the in-plane and out-of-plane fundamental flexural resonances of the beam can be read out by this approach — the latter being detectable due to broken planar symmetry in the system. Access to multiple mechanical modes of the same resonator may be useful in some applications and may enable interesting fundamental studies. © 2012 Optical Society of America OCIS codes: (120.4880) Optomechanics; 120.7280 (Vibration analysis); (230.3990) Microoptical devices. References and links 1. K. L. 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Introduction
A nanomechanical resonator [1,2] stores energy in its mechanical oscillations.Small perturbations to the resonator typically result in large changes in the amplitude or frequency of these oscillations.By monitoring these nanomechanical oscillations, one can devise a sensitive probe of both external signals and phenomena intrinsic to the resonator.Detecting the exceedingly small motion of a nanomechanical resonator with high sensitivity, therefore, remains an overarching theme in research involving nanomechanical resonators.
Far field optical techniques provide remarkable sensitivity in displacement (motion) detection [3].Using a typical path-stabilized Michelson interferometer [4][5][6], for instance, one can easily obtain a displacement sensitivity of ∼ 100 fm • Hz −1/2 at 100-μW-level optical powers.However, this sensitivity is degraded as the device size approaches or becomes smaller than the diffraction limited optical probe spot [7].As the moving structure becomes smaller, light is reflected back inefficiently, resulting in a sensitivity loss.Similarly, a Fabry-Perot interferometer can provide very high sensitivity.Impressive displacement sensitivities wellbelow 100 fm • Hz −1/2 have been reported on microelectromechanical systems (MEMS) devices [8][9][10][11][12].However, as above, the moving mirror must be larger than the optical spot size so that one can create a high-finesse cavity.As the device size approaches the wavelength of light, sensitivities of conventional Fabry-Perot interferometers decrease dramatically -due to diffraction and optical losses.A good example to the point is the Fabry-Perot cavity created between the top surface of a nanomechanical beam and a substrate underneath [13].While this provides a usable cavity for nanomechanical displacement detection, the low cavity finesse [14] results in degraded displacement sensitivity.
Near-field (evanescent) optical interactions offer viable approaches for sensitive motion de- (C) 2012 OSA tection beyond the diffraction limit with less stringent coherence and stability requirements.
In this manuscript, we report the design, fabrication and operation of a novel nano-optomechanical device, in which a nanomechanical doubly-clamped beam resonator is integrated to an optical microdisk cavity.This device obviates the need for alignment of the mechanical resonator to the optical cavity.Furthermore, broken planar symmetry of the system during the fabrication process enables us to observe the out-of-plane flexural motion of the mechanical resonator -in addition to the expected in-plane motion.In section 2, we discuss the novel aspects of the device along with a brief description of the fabrication.The experimental set up and the results from measurements are discussed in sections 3 and 4, respectively.Finally, conclusions are presented in the last section.

Device design and fabrication
A scanning electron microscope (SEM) image of one of our devices is shown in Fig. 1(a).Here, a nanomechanical doubly-clamped beam is co-fabricated on a chip with a microdisk structure.The illustration in Fig. 1(b) displays the cross-sectional view of the device at the x 1 − x 3 plane at the center of the beam.All the microdisks in this study have the same diameter of 40 μm.The thickness t of the beam and the microdisk are determined by the thickness of the Silicon layer and t = 230 nm.The width w of the beam and the gap values x e 1 between the beam and the microdisk are set in the fabrication process.In equilibrium, there is a small bending in the beam, which breaks the symmetry by offsetting the center of the beam in the x 3 direction to an equilibrium position x e 3 (see below for a detailed discussion of x e 3 ).In this study, we have kept the beam width at w = 250 nm and varied the gap as x e 1 =150, 250 and 350 nm.We have also varied the beam lengths l as l =7, 10, 12 and 15 μm.Given the three different x e 1 and four different l values, we have collected data on a total of 12 different resonators.The optical coupling to the device is accomplished by bringing a separate fiber-taper into the vicinity of the cavity as described below.
Two devices that are quite similar to our device in design have recently been reported.We now compare our device to these and describe the differences where appropriate.The first device that appears to be similar to ours is described in [22].There, a nanomechanical beam resonator, which serves both as the mechanical element and the input-output coupler to a microdisk resonator, is fabricated next to the microdisk structure.The optical coupling to the nanomechanical waveguide is accomplished by two grating couplers with 10% efficiency each.In our design, the nanomechanical beam is independent from the rest of the elements on the chip, and the light is coupled into and out of the microdisk through a fiber-taper waveguide.The fibertaper obviates the need for the inefficient grating couplers.The fact that the nanomechanical beam need not have traveling optical modes in our design allows us to change the linear dimensions of the nanomechanical beam arbitrarily.A second similar device is described in [24].Here, the mechanical resonator has a curved geometry while the optical coupling method is identical to ours.The curved geometry, while interesting, comes with some complexities.For instance, the geometry sets some hard limits on the resonator dimensions and hence its mechanical parameters.Scaling this device down in size and up in frequency appears challenging because the mechanical element must be wrapped around the disk.In contrast, in our simple linear geometry, one can simply reduce the length of the beam or make the beam wider.To fabricate our devices, we use a Silicon-on-Insulator (SOI) wafer, which has a 500 nm Si device layer on top of a 3 μm SiO 2 layer.As a first step, a thermal oxide is grown in the Silicon layer in order to reduce the thickness of the Silicon layer by a wet etch.Next, electron beam lithography is performed to define a metal mask.The mask pattern is transferred into the Silicon by an anisotropic dry etch in a reactive ion etcher (RIE).The metal mask is then removed.Normally, at this step one can release the beams and complete the fabrication process.However, in our case, we define mesa structures in order to isolate the devices from the rest of the chip for efficient optical coupling using a fiber-taper.For the purpose of fabricating the mesa structures, we perform a photolithography step followed by deep-RIE.The final step is the release of the suspended structures in an HF vapor etcher.

Experimental set up
A schematic of our measurement setup is superimposed on the SEM image of a device in Fig. 1(a).A fiber-taper is used for coupling light into and out of the microdisk resonator.The tapered region has a diameter of d ≈ 1 μm.The device chip is mounted onto a piezostage (for positioning with respect to the tapered waveguide) in a vacuum chamber with a base pressure of 2×10 −2 Pa.A tunable diode laser operating in the telecom band is used for probing the devices.The light coming from the laser passes through the fiber-taper, interacts with the microdisk and is directed onto a high-speed photodetector.A fiber polarization controller is used for selectively exciting transverse electric (TE) and transverse magnetic (TM) whispering gallery mode (WGM) resonances of the microdisk.The transmission profile is monitored with a multimeter; a radio-frequency (rf) spectrum analyzer is used for mechanical measurements.
When the microdisk is driven close to one of its WGM resonances, the mechanical oscillations of the doubly-clamped beam induce modulations in the optical field circulating around the microdisk through local optical index changes.Thus, the mechanical signals are embedded in the cavity transmission T and can be detected by monitoring the rf spectrum of T .For small oscillations of the nanomechanical resonator at the limit κ Ω m (κ is the cavity linewidth and Ω m is the mechanical resonance frequency), the optical power P out incident on the photodetector can be expressed as [23] P out (t) In this expression, P in is the incident power on the waveguide; the transmission T and the derivative |∂ T /∂ ω| are evaluated at the optical detection frequency ω d ; δ x i (t) is the small time-dependent oscillation amplitude of the mechanical resonator in the i direction (i = 1, 3).g i = ∂ ω o /∂ x i is the optomechanical coupling coefficient, where ω o is the optical resonance frequency and x i is the time-dependent position of the mechanical device.Q o ≈ 35, 000 is shown in Fig. 1(d).The lower effective index of TM modes increases the mode matching between the waveguide and the microdisk, thus offering better coupling.

Measurements
Thermal-mechanical oscillations of the NEMS resonator can be detected by exciting the cavity at a single wavelength close to its resonance and monitoring the spectrum of T .Figure 2(a) displays the high-frequency spectrum of the transmission, measured using the optical cavity mode shown in Fig. 1(d).For this measurement, the cavity is driven at one of its maximum sensitivity points, λ d ≈ 1577.08 nm, with an input power of P in ≈ 50 μW.Two well-separated thermal peaks are observed at 5.55 MHz and 10.31 MHz, corresponding to the fundamental flexural modes of the mechanical resonator in the x 3 (out-of-plane) and x 1 (in-plane) directions, respectively.Both peaks can be fit by Lorentzians with mechanical quality factors of Q m ≈ 1, 300.Independent measurements on the resonator using a Michelson interferometer  A fully planar device, where the nanomechanical resonator lies on the same plane as the microdisk [x 1 − x 2 plane in Fig. 1(a)], should exhibit strong optomechanical coupling g 1 only in the x 1 direction; the out-of-plane coupling g 3 in the x 3 direction should be zero due to the symmetry if the device is truly planar [25].The modes observed in Fig. 2(a) in the x 1 and x 3 directions with comparable strengths are most likely a consequence of the slight bending of the beams during fabrication, which is also noticeable in high-magnification high-tilt SEM images.This bending breaks the symmetry by offsetting the center of the beam in the x 3 direction to an equilibrium position x e 3 .Hence, the oscillations of the mechanical resonator in the x 3 direction can modulate the local dielectric index of the cavity, giving rise to a non-zero optomechanical coupling in the x 3 direction.We provide a more detailed discussion of this unexpected phenomenon below.
We now describe the displacement calibration.The measured signals can be converted into displacements by considering the rms thermal amplitude of the mode (δ x i ) 2 1/2 at temperature θ [17]: where k B is the Boltzmann constant.The mode stiffnesses k i can be found using device geometry and material properties.For the in-plane mode, k 1 ≈ 5 N•m −1 , and for the out-of-plane mode, k 3 ≈ 2 N•m −1 .With θ = 300 K [19], one obtains rms amplitudes of (δ x 1 ) 2 1/2 ≈ 28 pm and (δ x 3 ) 2 1/2 ≈ 45 pm.Using this calibration, the displacement sensitivities (noise floors) are found to be √ S 1 ≈ 9 fm•Hz −1/2 and √ S 3 ≈ 59 fm•Hz −1/2 .Thermal noise measurements can be used to determine the optomechanical coupling coefficients g i .Returning to Eq. ( 1), we notice that the thermal oscillations of the i th mechanical mode result in a total (integrated) optical noise power 1 and P out 3 for the in-plane (diamonds) and outof-plane (circles) mechanical modes.The dashed lines are best fits using the available P out i , P in , |∂ T /∂ ω| and (δ x i ) 2 1/2 , with the fit parameters being the optomechanical coupling coefficients g i .Thus, g i are found as g 1 /2π ≈ 46 MHz/nm for in-plane motion and g 3 /2π ≈ 10 MHz/nm for out-of-plane motion.Furthermore, we have not observed dissipative coupling and believe that the mechanical resonator couples only dispersively to the microcavity.order to understand the effects of device dimensions on coupling, we have repeated the measurements on with a range of linear dimensions and nominal gap In we have changed both the lengths l of the doubly-clamped beams and the equilibrium gaps x e 1 while the diameter the microdisks fixed at 40 μm.Four length values (l =7, 10, 12 15 μm), three gap values (x e 1 250 and used, resulting in 12 resonators with equal thicknesses (t = 230 nm) and widths (w = 250 nm).In Fig. 3(a) and (b), we respectively display the experimentally obtained g 1 /2π and g 3 /2π for each beam as a function of x e 1 .Both g 1 and g 3 tend to increase as x e 1 gets smaller due to stronger field gradients in the vicinity of the microdisk.For the in-plane mode, the shorter the beam, the larger the g 1 at any given x e 1 .However, the situation changes for the out-of-plane coupling: longer beams exhibit larger g 3 .For the shortest beam (l = 7 μm), g 3 ≈ 0.
As noted above, the out-of-plane coupling can be explained by a small bending in the beams, which displaces their centers in the out-of-plane direction, resulting in symmetry breaking.This small equilibrium displacement in the out-of-plane direction is shown as x e shorter beams are not expected to undergo significant bending, thus resulting in small g 3 as observed in the experiments.To gain more insight, we can estimate the vertical offset x e 3 for each device using a perturbative method [25].These estimates of x e 3 obtained for each device are shown in Fig. 3(c).These estimates are obtained as follows.The presence of a dielectric mechanical resonator perturbs the energy in the cavity, providing the optomechanical coupling.We first determine g 3 for each device from the experiments as outlined above.Next, we calculate the energy change in the cavity using g 3 along with calculated optical mode volumes, evanescent decay lengths and overlap integrals.Finally, we extract the x e 3 value, which is necessary for such a coupling to occur.The results are consistent with the earlier assumption that longer softer beams have larger offset values x e 3 , whereas x e 3 ≈ 0 for shorter beams.The large error bar for the longest beam (l = 15 μm) may be due to undercuts for the particular device, changing its k 3 from the estimated value and causing excess bending.

Discussion and conclusions
Our device design, which allows the measurement of both in-plane and out-of-plane mechanical oscillations of a doubly-clamped nanomechanical beam with high displacement sensitivity, could provide a unique platform for sensing applications and fundamental studies.From a fundamental physics point of view, one could investigate the intermodal coupling between the in-plane and out-of-plane modes.By increasing the circulating light intensity in the cavity, it might be possible to observe a strong coupling between these two mechanical modes.In that case, one further tune the individual resonance frequencies by changing the intensity of the incident light.As a result, one could observe a power transfer and accomplish adiabatic and diabatic transition process between these modes based on optical forces.In mass sensing applications, the straightforward access to the two mechanical modes in a device such as ours might allow accurate mass and position measurements for the attached mass.Other sensing application including force sensing could also benefit from similar approaches.
The device here could be improved by using smaller diameter cavities, which would allow for a stronger optomechanical coupling due to the reduced optical mode volume.Microdisk cavities could be deformed into racetrack resonators with the nanomechanical beam residing along the linear side, resulting in an enhanced coupling.The stability of this design further increased by anchoring the fiber-taper onto fixed supports.By simply an additional modulated laser in a pump-probe scheme, one could excite mechanical modes via optical gradient forces and attain large amplitude responses.

Figure 1 (
Figure 1(c) shows the normalized transmission spectrum of a 40-μm-diameter microdisk coupled to a doubly-clamped beam (l × w × t =12 μm × 250 nm × 230 nm) as a function of detection wavelength.The beam and microdisk are separated by a nominal equilibrium gap fabricated to be x e 1 ≈ 250 nm.The optical transmission spectrum is optimized in the x 1 − x 3 plane for TM polarization in the under-coupled regime by changing the position of the fibertaper with respect to the microdisk.Several dips corresponding to optical modes with different radial and azimuthal numbers can be observed.Each displays a Lorentzian lineshape.A representative mode with optical resonance at a wavelength of 1577.1 nm and optical quality factor

Fig. 1 .
Fig. 1.(a) Schematic of the experimental setup superimposed on the SEM image of a doubly-clamped beam resonator coupled to a microdisk.The linear dimensions of the beam are l × w × t = 15 μm × 250 nm × 230 nm and the disk diameter is 20 μm.Light from a diode laser is directed into the fiber-taper waveguide and then sent sent onto a high-speed photodetector (PD).A fiber polarization controller (FPC) is used in order to selectively excite optical modes and a spectrum analyzer (SA) is used for noise measurements.(b) Cross-sectional view of the device through the center of the beam in the x 1 − x 3 plane.The optical mode is localized near the microdisk perimeter as shown in the simulation.Note the small offset x e 3 in the x 3 direction.(c) Normalized optical transmission T optimized for TM polarization of a 40-μm-diameter microdisk coupled to a (l × w × t = 12 μm × 250 nm × 230 nm) doubly clamped beam.(d) Zoomed-in spectrum of a TM mode with a quality factor of Q o ≈ 35, 000.

Fig. 2 .
Fig. 2. (a) Thermal noise peaks of a doubly-clamped beam resonator (l × w × t = 12 μm × 250 nm × 230 nm) measured in vacuum with a probe power of P in ≈ 50 μW.The low frequency peak is the out-of-plane mode and the high frequency peak is the in-plane mode.(b) Integrated optical noise powers of the in-plane (diamonds) and out-of-plane (circles) mode as a function of the probe wavelength.

Fig. 3 .
Fig. 3. (a) g 1 /2π and (b) g 3 /2π as a function of x e 1 for beams having different lengths.(c) Calculated x e 3 as a function of length Each data is obtained from an average over four devices with the same l different x 1 values.