Nano-Optomechanical Resonators in Microfluidics - Nano Letters

Page 1 of 15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Nano-optomechanical resonators in microfluidics King Yan Fong, Menno Poot, and Hong X. Tang∗ Department of Electrical Engineering, Yale University, New Haven, CT 06511, USA E-mail: [email protected]

Abstract Operation of nanomechanical devices in liquid has been challenging due to the strong viscous damping that greatly impedes the mechanical motion. Here we demonstrate an optomechanical micro-wheel resonator integrated in microfluidic system that supports low-loss optical resonances at near-visible wavelength with quality factor up to 1.5 million, which allows the observation of the thermal Brownian motion of the mechanical mode in both air and water environment with high signal-to-background ratio. A numerical model is developed to calculate the hydrodynamic effect on the device due to the surrounding water, which agrees well with the experimental results. With its very high resonance frequency (170 MHz) and small loaded mass (75 pg), the present device has an estimated mass sensitivity at the attogram level in water.

Micro- and nano-scale mechanical resonators have been developed as important tools in both fundamental studies and technological applications. Because of their very small spring constant and mass, even tiny forces acting on the resonator or masses adhering on its surface can greatly alter its dynamics, which can be detected with extremely high precision. SubattoNewton (< 10−18 N) force sensitivity has been demonstrated, 1 which allows detection of the force from a single electron spin. 2 As the dimensions of the mechanical devices continue ∗

To whom correspondence should be addressed

1 ACS Paragon Plus Environment

Nano Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

to be scaled down, the mass sensitivity has reached attogram (10−21 kg), 3,4 zeptogram (10−24 kg), 5 yoctogram (10−27 kg) 6 level, and down to the mass of a single proton 7 in the past few years. A recent demonstration showed that this nanomechanical technology holds a promise to perform mass spectrometry on a single molecule with extremely high resolution. 8 However, so far most nanomechanical sensors operate in vacuum or air; very few operate in liquid since the enormous fluidic damping rapidly deteriorates the device performance. The mechanical quality factor (QM ) is dramatically lowered and the displaced fluid effectively adds mass. Both effects make operation in liquids extremely challenging. For example, AFM cantilevers in liquid have very low quality factors: QM < 5. 9,10 Moreover, as the resonator dimension is scaled down, the Reynold’s number is reduced and thus the fluidic viscous damping becomes more significant.. One approach to circumvent these problems is to use a hollow resonator structure through which the fluids and analytes flow. 11,12 With this approach attogram sensing has been achieved. 13 Nevertheless, more general operation of nanomechanical systems in liquid remains an important goal since only then the sensing can take place in environments where many biological and chemical samples naturally reside in. 14 Efforts towards this direction include development of schemes that can efficiently actuate and detect the motion of the resonator in the highly dissipative liquid environments, such as thermo-optical excitation, 15,16 magnetomotive drive and detection, 17 and piezoelectric actuation. 18 Efficient transduction of nanomechanical resonators in fluids also benefits the study of fluid dynamics in new parameter regimes 19–21 and the stochastic dynamics of fluid-structure interaction due to Brownian noise. 22,23 Among all the transduction schemes, cavity-enhanced optical readout has shown superior sensitivity. 24 For photonic cavities in water, however, the optical absorption of water itself can severely degrade the optical Q and cause undesirable thermo-optical effects. It is well known that water is strongly absorptive at telecom wavelengths. The optical extinction coefficient at λ = 1.55 µm is κ = 9.86 × 10−5 , 25 corresponding to a propagation loss of 34


Page 2 of 15

Page 3 of 15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 1: Device overview. (a) Normalized displacement profile of the fundamental radial breathing mode. (b) Electric field (radial component) distribution of the first four TE modes (TEi ) in air, where the index i represents the mode orders in the radial direction. (c) Scanning-electron micrograph showing a top view of the device. As indicated, the coupling gap g is the separation between the microwheel and the coupling waveguide. (d) Angled view SEM image showing the device positioned in the middle of a microfluidic channel (highlighted in blue) (e) Optical top view of the chip showing arrays of devices and two microfluidic channels (highlighted in blue). (f) Photo of a fully packaged device aligned to a fiber probe. dB/cm. To achieve high Q optical resonances in water, we developed a photonic resonator that operates at near-visible wavelengths λ = 780 nm where κ = 1.43×10−7 , 25 or equivalently 0.1 dB/cm. This would result in an absorption-limited Q of 10 million. This wavelength also falls within the biological transparency window 26 and is therefore useful in biological and medical applications. The design of the nano-optomechanical resonator in this study is a suspended microwheel structure, 27 which mechanically supports radial breathing modes. Fig. 1(a) shows the displacement profile of the fundamental radial breathing mode of a micro-wheel of 10 um radius simulated using a finite element method (FEM). The mode displacement is normalized with respect to the maximum displacement at the outer rim of the microwheel. This mode has an effective mass of 65 pg and a resonance frequency of 175 MHz in vacuum. The mechanical mode is optomechanically coupled to the optical whispering gallery modes, which thus can be used to readout the mechanical motion. Fig. 1(b) shows a cross-sectional plot of the


Nano Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2: Schematic of the measurement setup. TDL: Tunable diode laser. FPC: Fiber polarization controller. PR: Photoreceiver. DAQ: Data acquisition system. simulated radial electric field distribution of the first four transverse-electric (TE) modes in air. The optical modes are mainly located at the outer rim of the micro-wheel. Therefore scattering loss due to the presence of the anchoring spokes at the inner rim has a negligible effect. For the case when the device is immersed in water, simulations show that the TE4 mode is no longer well confined due to the smaller index contrast. The refractive indices of air, water, and silicon nitride used in the simulation are 1, 1.33, and 2.0 respectively The device is made out of a 200 nm thick Si3 N4 (see Supporting Information for details of the fabrication process). Microfluidic channels are etched into the top SiO2 cladding and are sealed with a thin glass slide. Each device is evanescently coupled via a waveguide, and a pair of gratings is used for coupling light into and out of the waveguides. Fig. 1(c) and (d) show SEM images of a device before the cover glass sealing. The free-standing coupling waveguide is supported by a tapered structure for robustness. In fact, the whole device is sturdy enough for direct wet release without the use of critical point drying. This allows repeatedly switching of the device operation between liquid and gaseous environments. Fig. 1(d) shows a device inside a microfluidic channel. Fig. 1(e) is a top-view of the chip after the glass bonding, and a fully packaged device is shown in Fig. 1(f) where a fiber array probe from the top is aligned to the grating couplers on the chip. This design seamlessly


Page 4 of 15

Page 5 of 15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 3: Characterization of low loss optical resonances. (a) Optical transmission spectra in air and water, with coupling gaps of 100 nm and 310 nm respectively. The device has an outer radius of 10 um and a ring width of 2.5 um. (b) Resonance wavelengths of the devices plotted against coupling gap. Resonances belong to the same radial mode are plotted in the same color. (c) Intrinsic quality factor Qi and coupling quality factor Qc of different radial modes plotted against the coupling gap. integrates the microfluidic and optomechanical components. It provides a viable approach for large scale integration of nanomechanical devices 28 with nanophotonic and microfluidic systems. The device was characterized using the setup shown in Fig. 2. A tunable diode laser (New Focus TLB-6712) with a tuning range of 765 – 781 nm was used to measure the optical transmission. A small portion of the laser output was tapped out and sent to a wavelength meter for wavelength and intensity calibration. A fiber probe was aligned to the top of the grating couplers of the device to couple light between optical fibers and waveguides, and the laser light was adjusted to TE-polarized using a fiber polarization controller for optimal transmission. The transmitted light was collected on a 1 GHz photoreceiver (New Focus 1601). The dc signal was sent to a data acquisition system to measure the transmission 5 ACS Paragon Plus Environment

Nano Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

while the ac part was sent to an electrical spectrum analyzer. All optical fibers in the setup are single mode fibers (SM800, 5.6 um core) for 780 nm. Fig. 3(a) shows the measured optical transmission spectra of a device in air and water. The maximum transmission reaches ∼ 0.3%, corresponding to an insertion loss of −13 dB per grating coupler. This coupling efficiency is limited by the separation between the fiber probe and the grating couplers set by the thickness of the cover glass, which is around 100 um. In the measured spectra, groups of resonances having similar quality factors and extinctions are visible. These correspond to the TE whispering-gallery modes of different radial orders (Fig. 1(b)). Their wavelengths are plotted against the coupling gap g in Fig. 3(b). Four modes can be identified in the spectra taken in air while three modes show up in case of water, which agrees with the simulation that the fourth TE mode in water is not well confined. Different radial modes show distinct behavior in quality factor and extinction ratio. As explained in the Supporting Information, the intrinsic quality factor (Qi ) and coupling quality factor (Qc ) can be extracted from their dependence on the coupling gap. Fig. 3(c) plots the measured Qi , Qc for each mode. The mode classification is identified through the measured free spectral range. The highest measured loaded Q is (1.53 ± 0.04) × 106 in air and (1.50 ± 0.03) × 106 in water, confirming that high-Q resonances can be achieved in water. For an optomechanical device with high optical Q, optomechanical backaction can significantly amplify or dampen the motion depending on the laser detuning. 24 When the laser power is high enough, the amplification can completely overcome the intrinsic mechanical damping and cause the resonator to self-oscillate, 29 which has proven useful in sensing. 30 Because of the very high optical Q, our device can self-oscillate in air with low threshold power. Fig. 4(a) shows the normalized transmission and the RF spectrum when the wavelength is scanned across the resonance at an input power of 45 uW. The transmission has an asymmetric shape due to thermo-optical bistability; 31 The resonance is linear (i.e. Lorentzian) at lower input power (1 uW). Fig. 4(b) shows that when approaching the resonance from shorter wavelength, the thermomechanical noise peak becomes sharper and higher due to optome-


Page 6 of 15

Page 7 of 15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 4: Optomechanical oscillations in air. (a) Normalized transmission across a resonance at different laser power (top). Color plot of the measured RF spectrum versus wavelength for input power of 45 uW (bottom). Cross-sectional plots at different wavelengths (dashed-lines) are shown in the inset. (b) Mechanical frequency and linewidth plotted against detuning from the optical resonance. The self-oscillation region is shaded in grey. The blue dashedline is half an optical linewidth away from the resonance. The black dotted-line shows the level of zero mechanical linewidth. chanical amplification. Assuming that the optical linewidth remains the same throughout the scan, the actual detuning can be inferred from the transmission. The mechanical frequency and linewidth at different detuning is plotted in Fig. 4(b). When the detuning approaches half the linewidth of the cavity (indicated by the blue dashed-line), the mechanical linewidth decreases all the way to zero, and the device undergoes self-sustained oscillations (shaded region). 32 As the detuning is further reduced, the optomechanical effect diminishes and the linewidth approaches its original values while reaching the thermo-optical bistable point.


Nano Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 5: Brownian motion in air and water. (a) Thermomechanical noise spectra in air and water with fittings where the frequency dependence of the optomechanical transduction (See Eq. (2) of Ref. 33) is taken into account. Dashed-lines indicate the noise floors of the measurements. Optical powers of 10 µW and 1 mW are used for the measurement in air and water respectively. (b) Resonance frequency (top) and quality factor (bottom) plotted against the width of the micro-wheel. rout is fixed at 10 um. The symbols (errorbars) are mean values (standard deviations) of four devices. When the device is immersed in water, the viscous damping is so great that the device could not be set self-oscillating. Nevertheless, with the very high optical Q, the highlydamped thermomechanical motion can still be resolved in water. Fig. 5(a) shows the noise spectra for device in air and water. In air the radial breathing mode has a frequency of f0 = 179.9MHz and quality factor of QM = 2160, while in water the frequency is slightly shifted down to fw = 169.4MHz and QM is reduced to 9. For the noise spectrum in water, √ 1/2 a noise floor of Snn = 15 am/ Hz is achieved; in air a lower optical power was used to minimize the effect of the optomechanical backaction resulting in a higher noise floor. The only 5.8% drop of the resonance frequency after immersion in water is very small 8 ACS Paragon Plus Environment

Page 8 of 15

Page 9 of 15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

compared to other systems. For example, AFM cantilevers working at hundreds of kHz displayed resonance frequencies after immersion at 1/2 – 1/5 of their original values. 10 SiN nanostrings resonating at 100 MHz range also showed a > 25% decrease. 15 Another observation is that our quality factor is higher than for cantilever systems, which typically have QM . 5. 9,10,15–17 The smaller frequency shift and higher QM hints that the hydrodynamic mass loading and damping due to the surrounding water is relatively small for the micro-wheel structure. In liquid, the dynamics of a mechanical resonator is strongly affected by the fluidic force Ff acting on it (or against its motion). For small amplitude oscillations, Ff (t) has a linear response to the displacement x(t) and can be expressed (in the frequency domain) as Ff [f ] = me (2πf )2 Γ[f ]x[f ], where me is the effective mass of the resonator in vacuum, and Γ[f ] is the dimensionless “hydrodynamic function”. 34 (The definition adopted here differs from those in Refs. 22,34 by a geometrical factor.) Its real (ΓR ) and imaginary part (ΓI ) renormalize the resonance frequency fw → f0 (1 + ΓR [fw ])−1/2 and quality factor Qw → (1 + ΓR [fw ])/ΓI [fw ] (assuming Qw 1). For a rectangular (cantilever) structure, the hydrodynamic function can be solved numerically as described in Refs. 34–36; for the micro-wheel resonator, we developed a boundary integral method for systems with rotational symmetry and solve the corresponding Green’s equation. The details are discussed in the Supporting Information. Fig. 5(b) plots the resonance frequency and quality factor as function of ring width. The model shows the same width dependence as the experimental data and the calculated QM ∼ 10 agrees fairly well with the measured QM ∼ 9. The total loaded mass of the device including the water entrained to the resonator motion is mw = me (1 + ΓR [fw ]) = 75 pg, which is roughly equal to the sum of the original resonator mass (65 pg) and the mass of water enclosed within the Stokes boundary layer around the device (10 pg; See Supporting Information). The entrained mass of water is thus only 15% of the original mass. This is orders of magnitude smaller than that of cantilevers 10,37 where the water mass can be tens of times of the resonator mass. The small water entrainment


Nano Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 15

of our device is the result of the small resonator dimensions, high resonance frequency and thus small Stokes boundary layer thickness (31 nm), and the in-plane motion of the radial breathing mode. 36 Also, the water flow field is mainly confined at the structure’s surface within a few Stokes lengths, which is much smaller than the separation from the surrounding walls (310 nm to the coupling waveguide and 2-3 um to the walls of the microfluidic channels). Hence, the presence of the surrounding walls is expected to have a negligible effect on the resonator dynamics. This is consistent with the good agreement between the experimental results and the theoretical predictions. It also implies that a microfluidic design with even smaller dimensions can be employed without compromising the device performance as long as the walls do not get too close to the boundary layer. The mass sensitivity of the device is determined by the phase noise of the measurement, which contains both the resonator’s thermal motion (Sxx ) and the measurement imprecision noise (Snn ). The minimum resolvable mass is given by δm =

mw Qw x0

[(Sxx [fw ] + Snn ) ∆f ]1/2

for a measurement bandwidth ∆f fw /Qw . 38 Fig. 5(a) shows that (Sxx [fw ] + Snn )1/2 = √ 42 am/ Hz. Assuming the device can be driven to an amplitude of x0 = 100 pm, the √ mass sensitivity is 3.5 ag/ Hz. This amplitude is well within the linear range of operation as shown by the FEM simulation presented in the Supporting Information. To reach such an amplitude, the device can be driven, for example, by radiation pressure force using a pump-probe scheme. 39 For the present device the estimated required laser power is about 30 mW. With electrodes patterned on the device, electrostatic excitation can also be applied to provide the driving force. So far, attogram sensing in fluid has only been achieved using cantilevers with embedded channels. 13 These results suggest that our optomechanical microwheel resonator is very promising for in-situ attogram sensing in water.

Acknowledgement M.P. thanks the Netherlands Organization for Scientific Research (NWO)/Marie Curie Cofund Action for support via a Rubicon fellowship. H.X.T. acknowledges support from a 10 ACS Paragon Plus Environment

Page 11 of 15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Packard Fellowship in Science and Engineering and a career award from National Science Foundation. This work was funded by the DARPA/MTO ORCHID program through a grant from the Air Force Office of Scientific Research (AFOSR) and a STIR grant from Army Research Office (ARO).

Supporting Information Available Details of device fabrication procedures, wavelength calibration, method of extraction of intrinsic quality factors, numerical model of hydrodynamic loading, FEM simulation of other mechanical modes, and nonlinear behavior of the displacement of microwheel resonators are presented in the Supporting Information.

This material is available free of charge via the

Internet at http://pubs.acs.org/.

References (1) Mamin, H. J.; Rugar, D. Applied Physics Letters 2001, 79, 3358. (2) Rugar, D.; Budakian, R.; Mamin, H. J.; Chui, B. W. Nature 2004, 430, 329–32. (3) Ilic, B.; Craighead, H. G.; Krylov, S.; Senaratne, W.; Ober, C.; Neuzil, P. Journal of Applied Physics 2004, 95, 3694. (4) Li, M.; Tang, H. X.; Roukes, M. L. Nature nanotechnology 2007, 2, 114–20. (5) Yang, Y. T.; Callegari, C.; Feng, X. L.; Ekinci, K. L.; Roukes, M. L. Nano letters 2006, 6, 583–6. (6) Jensen, K.; Kim, K.; Zettl, A. Nature nanotechnology 2008, 3, 533–7. (7) Chaste, J.; Eichler, A.; Moser, J.; Ceballos, G.; Rurali, R.; Bachtold, A. Nature nanotechnology 2012, 7, 301–4.


Nano Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(8) Naik, A. K.; Hanay, M. S.; Hiebert, W. K.; Feng, X. L.; Roukes, M. L. Nature nanotechnology 2009, 4, 445–50. (9) Hansma, P. K.; Cleveland, J. P.; Radmacher, M.; Walters, D. A.; Hillner, P. E.; Bezanilla, M.; Fritz, M.; Vie, D.; Hansma, H. G.; Prater, C. B.; Massie, J.; Fukunaga, L.; Gurley, J.; Elings, V. Applied Physics Letters 1994, 64, 1738. (10) Walters, D. A.; Cleveland, J. P.; Thomson, N. H.; Hansma, P. K.; Wendman, M. A.; Gurley, G.; Elings, V. Review of Scientific Instruments 1996, 67, 3583. (11) Burg, T. P.; Godin, M.; Knudsen, S. M.; Shen, W.; Carlson, G.; Foster, J. S.; Babcock, K.; Manalis, S. R. Nature 2007, 446, 1066–9. (12) Hyun Kim, K.; Bahl, G.; Lee, W.; Liu, J.; Tomes, M.; Fan, X.; Carmon, T. Light: Science & Applications 2013, 2, e110. (13) Olcum, S.; Cermak, N.; Wasserman, S. C.; Christine, K. S.; Atsumi, H.; Payer, K. R.; Shen, W.; Lee, J.; Belcher, A. M.; Bhatia, S. N.; Manalis, S. R. Proceedings of the National Academy of Sciences of the United States of America 2014, 111, 1310–5. (14) Arlett, J. L.; Paul, M. R.; Solomon, J. E.; Cross, M. C.; Fraser, S. E.; Roukes, M. L. In Controlled Nanoscale Motion, Nobel Symposium 131 ; Linke, H., M˚ a nsson, A., Eds.; Lecture Notes in Physics; Springer Berlin Heidelberg: Berlin, Heidelberg, 2007; Vol. 711; pp 241–270. (15) Verbridge, S. S.; Bellan, L. M.; Parpia, J. M.; Craighead, H. G. Nano letters 2006, 6, 2109–14. (16) Ramos, D.; Tamayo, J.; Mertens, J.; Calleja, M. Journal of Applied Physics 2006, 99, 124904. (17) Venstra, W. J.; Westra, H. J. R.; Gavan, K. B.; van der Zant, H. S. J. Applied Physics Letters 2009, 95, 263103. 12 ACS Paragon Plus Environment

Page 12 of 15

Page 13 of 15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

(18) Zuniga, C.; Rinaldi, M.; Piazza, G. Quality factor of MEMS and NEMS AlN Contour Mode Resonators in liquid media. 2009 IEEE International Ultrasonics Symposium. 2009; pp 2568–2571. (19) Karabacak, D. M.; Yakhot, V.; Ekinci, K. L. Phys. Rev. Lett. 2007, 98, 254505. (20) Svitelskiy, O.; Sauer, V.; Liu, N.; Cheng, K.-M.; Finley, E.; Freeman, M. R.; Hiebert, W. K. Physical Review Letters 2009, 103, 244501. (21) Lissandrello, C.; Yakhot, V.; Ekinci, K. L. Physical Review Letters 2012, 108, 084501. (22) Paul, M.; Cross, M. Physical Review Letters 2004, 92, 235501. (23) Paul, M. R.; Clark, M. T.; Cross, M. C. Nanotechnology 2006, 17, 4502–4513. (24) Kippenberg, T. J.; Vahala, K. J. Optics Express 2007, 15, 17172. (25) Hale, G. M.; Querry, M. R. Applied optics 1973, 12, 555–63. (26) Weissleder, R. Nature biotechnology 2001, 19, 316–7. (27) Sun, X.; Fong, K. Y.; Xiong, C.; Pernice, W. H. P.; Tang, H. X. Optics express 2011, 19, 22316–21. (28) Bargatin, I.; Myers, E. B.; Aldridge, J. S.; Marcoux, C.; Brianceau, P.; Duraffourg, L.; Colinet, E.; Hentz, S.; Andreucci, P.; Roukes, M. L. Nano letters 2012, 12, 1269–74. (29) Bagheri, M.; Poot, M.; Li, M.; Pernice, W. P. H.; Tang, H. X. Nature nanotechnology 2011, 6, 726–32. (30) Liu, F.; Alaie, S.; Leseman, Z. C.; Hossein-Zadeh, M. Optics express 2013, 21, 19555– 67. (31) Almeida, V. R.; Lipson, M. Optics Letters 2004, 29, 2387.


Nano Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(32) Poot, M.; Fong, K. Y.; Bagheri, M.; Pernice, W. H. P.; Tang, H. X. Physical Review A 2012, 86, 053826. (33) Han, X.; Xiong, C.; Fong, K. Y.; Zhang, X.; Tang, H. X. New Journal of Physics 2014, 16, 063060. (34) Sader, J. E. Journal of Applied Physics 1998, 84, 64. (35) Tuck, E. O. Journal of Engineering Mathematics 1969, 3, 29–44. (36) Brumley, D. R.; Willcox, M.; Sader, J. E. Physics of Fluids 2010, 22, 052001. (37) Ghatkesar, M. K.; Braun, T.; Barwich, V.; Ramseyer, J.-P.; Gerber, C.; Hegner, M.; Lang, H. P. Applied Physics Letters 2008, 92, 043106. (38) Ekinci, K. L.; Yang, Y. T.; Roukes, M. L. Journal of Applied Physics 2004, 95, 2682. (39) Li, M.; Pernice, W. H. P.; Xiong, C.; Baehr-Jones, T.; Hochberg, M.; Tang, H. X. Nature 2008, 456, 480–4.


Page 14 of 15

Page 15 of 15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Graphical TOC Entry


Nano-Optomechanical Resonators in Microfluidics - Nano Letters

Recommend Documents