Simultaneous Optical and Mechanical Sensing Based on Optomechanical Resonators.

Optical and mechanical resonators have each been abundantly employed in sensing applications, albeit following separate development. Here we show that bringing together optical and mechanical resonances in a unique sensing device significantly improves the sensor performance. To that purpose, we employ nanoscale optomechanical disk resonators that simultaneously support high quality optical and mechanical modes localized in tiny volumes, which provide extraordinary sensitivities. We perform environmental sensing, but the conclusions of our work extend to other sensing applications. First, we determine optical and mechanical responsivities to temperature and relative humidity changes. Second, by characterizing mechanical and optical frequency stabilities, we determine the corresponding limits of detection. Mechanical modes appear more sensitive to relative humidity changes, while optical modes appear more sensitive to temperature ones, reaching, respectively, 0.05% and 0.6 mK of independent resolution. We then prove that simultaneous optical and mechanical monitoring enables disentangling both effects and demonstrates 0.1% and 1 mK resolution, even considering that both parameters may change at the same time. Finally, we highlight the importance of actively tracking the optical mode when optomechanical sensor devices. Not doing so enforces tedious independent calibration, influences the device sensitivity during the experiment, and shortens the sensing range. The present work hence clarifies the requirements for the optimal operation of optomechanical sensors, which will be of importance for chemical and biological sensing.

Nanomechanical Sensing for Mass Flow Control in Nanowire-Based Open Nanofluidic Systems.

Open nanofluidic systems, where liquids flow along the outer surface of nanoscale structures, provide otherwise unfeasible capabilities for extremely miniaturized liquid handling applications. A critical step toward fully functional applications is to obtain quantitative mass flow control. We demonstrate the application of nanomechanical sensing for this purpose by integrating voltage-driven liquid flow along nanowire open channels with mass detection based on flexural resonators. This approach is validated by assembling the nanowires with microcantilever resonators, enabling high-precision control of larger flows, and by using the nanowires as resonators themselves, allowing extremely small liquid volume handling. Both implementations are demonstrated by characterizing voltage-driven flow of ionic liquids along the surface of the nanowires. We find a voltage range where mass flow rate follows a nonlinear monotonic increase, establishing a steady flow regime for which we show mass flow control at rates from below 1 ag/s to above 100 fg/s and precise liquid handling down to the zeptoliter scale. The observed behavior of mass flow rate is consistent with a voltage-induced transition from static wetting to dynamic spreading as the mechanism underlying liquid transport along the nanowires.

Square Membrane Resonators Supporting Degenerate Modes of Vibration for High-Throughput Mass Spectrometry of Single Bacterial Cells.

In nanomechanical mass spectrometry, sensing devices are commonly placed in the vacuum environment and a stream of analytes is directed toward the sensor surface for measurement. Beam structures, such as double-clamped nanobeams and nanocantilevers, are commonly used due to their low inertial mass and the simplicity of the analytical models for mass extraction. The drawback of such structures is their low capture areas, compromising the capture efficiency and throughput of this technique. Bi-axisymmetric resonators, such as ultrathin square or circular membranes, arise as an optimal geometry to maximize capture efficiency while minimizing the device inertial mass. However, these structures present degenerate mechanical modes, whose frequency perturbations upon analyte adsorption are not well described by commonly used models. Furthermore, prior knowledge of the vibration mode shapes of the sensor is crucial for the correct calculation of the analyte's mass, and the mode shape of degenerate modes may change significantly after every adsorption event. In this work, we present an accurate analytical theory to describe the effect of mass adsorption on the degenerate modes of square membrane resonators and propose two different methods based on the new theory to update the vibration mode shapes after every adsorption event. Finally, we illustrate the problem experimentally obtaining the mass and adsorption position of individual Escherichia coli K-12 bacterial cells on commercial square silicon nitride membranes fabricated with very small tolerances.

High-throughput determination of dry mass of single bacterial cells by ultrathin membrane resonators.

How bacteria are able to maintain their size remains an open question. Techniques that can measure the biomass (dry mass) of single cells with high precision and high-throughput are demanded to elucidate this question. Here, we present a technological approach that combines the transport, guiding and focusing of individual bacteria from solution to the surface of an ultrathin silicon nitride membrane resonator in vacuum. The resonance frequencies of the membrane undergo abrupt variations at the instants where single cells land on the membrane surface. The resonator design displays a quasi-symmetric rectangular shape with an extraordinary capture area of 0.14 mm2, while maintaining a high mass resolution of 0.7 fg (1 fg = 10-15 g) to precisely resolve the dry mass of single cells. The small rectangularity of the membrane provides unprecedented frequency density of vibration modes that enables to retrieve the mass of individual cells with high accuracy by specially developed inverse problem theory. We apply this approach for profiling the dry mass distribution in Staphylococcus epidermidis and Escherichia coli cells. The technique allows the determination of the dry mass of single bacterial cells with an accuracy of about 1% at an unparalleled throughput of 20 cells/min. Finally, we revisit Koch & Schaechter model developed during 60 s to assess the intrinsic sources of stochasticity that originate cell size heterogeneity in steady-state populations. The results reveal the importance of mass resolution to correctly describe these mechanisms.

Micro-Kelvin Resolution at Room Temperature Using Nanomechanical Thermometry.

Ultrahigh sensitivity temperature measurement is becoming increasingly relevant for different scientific and technological fields from fundamental physics to high-precision engineering applications. Here, we demonstrate the use of a nanomechanical resonator-free standing silicon nitride membranes with thicknesses in the nanoscale-for room temperature thermometry reaching an unprecedented resolution of 15 µK. These devices were characterized by using an interferometric system at high vacuum, where there are only two possible mechanisms for heat transfer: thermal conductivity and radiation. While the expected behavior should be to decrease the frequency of the mechanical resonance due to the thermoelastic effect, we observe that the nanomechanical response can be both positive and negative depending on the thermal flux: a heat point source always shifts the mechanical resonance to lower frequencies, while a distributed heat source shifts the resonance to higher frequencies.

High Dynamic Range Nanowire Resonators.

Dynamic range quantifies the linear operation regime available in nanomechanical resonators. Nonlinearities dominate the response of flexural beams in the limit of very high aspect ratio and very small diameter, which leads to expectation of low dynamic range for nanowire resonators in general. However, the highest achievable dynamic range for nanowire resonators with practical dimensions remains to be determined. We report dynamic range measurements on singly clamped silicon nanowire resonators reaching remarkably high values of up to 90 dB obtained with a simple harmonic actuation scheme. We explain these measurements by a comprehensive theoretical examination of dynamic range in singly clamped flexural beams including the effect of tapering, a usual feature of semiconductor nanowires. Our analysis reveals the nanowire characteristics required for broad linear operation, and given the relationship between dynamic range and mass sensing performance, it also enables analytical determination of mass detection limits, reaching atomic-scale resolution for feasible nanowires.

Publisher Correction: Optomechanical detection of vibration modes of a single bacterium.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Optomechanical detection of vibration modes of a single bacterium.

Low-frequency vibration modes of biological particles, such as proteins, viruses and bacteria, involve coherent collective vibrations at frequencies in the terahertz and gigahertz domains. These vibration modes carry information on their structure and mechanical properties, which are good indicators of their biological state. In this work, we harnessed a particular regime in the physics of coupled mechanical resonators to directly measure these low-frequency mechanical resonances of a single bacterium. We deposit the bacterium on the surface of an ultrahigh frequency optomechanical disk resonator in ambient conditions. The vibration modes of the disk and bacterium hybridize when their associated frequencies are similar. We developed a general theoretical framework to describe this coupling, which allows us to retrieve the eigenfrequencies and mechanical loss of the bacterium low-frequency vibration modes (quality factor). Additionally, we analysed the effect of hydration on these vibrational modes. This work demonstrates that ultrahigh frequency optomechanical resonators can be used for vibrational spectrometry with the unique capability to obtain information on single biological entities.

Optical Transduction for Vertical Nanowire Resonators.

We describe an optical transduction mechanism to measure the flexural mode vibrations of vertically aligned nanowires on a flat substrate with high sensitivity, linearity, and ease of implementation. We demonstrate that the light reflected from the substrate when a laser beam strikes it parallel to the nanowires is modulated proportionally to their vibration, so that measuring such modulation provides a highly efficient resonance readout. This mechanism is applicable to single nanowires or arrays without specific requirements regarding their geometry or array pattern, and no fabrication process besides the nanowire generation is required. We show how to optimize the performance of this mechanism by characterizing the split flexural modes of vertical silicon nanowires in their full dynamic range and up to the fifth mode order. The presented transduction approach is relevant for any application of nanowire resonators, particularly for integrating nanomechanical sensing in functional substrates based on vertical nanowires for biological applications.

Mechano-Optical Analysis of Single Cells with Transparent Microcapillary Resonators.

The study of biophysical properties of single cells is becoming increasingly relevant in cell biology and pathology. The measurement and tracking of magnitudes such as cell stiffness, morphology, and mass or refractive index have brought otherwise inaccessible knowledge about cell physiology, as well as innovative methods for high-throughput label-free cell classification. In this work, we present hollow resonator devices based on suspended glass microcapillaries for the simultaneous measurement of single-cell buoyant mass and reflectivity with a throughput of 300 cells/minute. In the experimental methodology presented here, both magnitudes are extracted from the devices' response to a single probe, a focused laser beam that enables simultaneous readout of changes in resonance frequency and reflected optical power of the devices as cells flow within them. Through its application to MCF-7 human breast adenocarcinoma cells and MCF-10A nontumorigenic cells, we demonstrate that this mechano-optical technique can successfully discriminate pathological from healthy cells of the same tissue type.

Author Correction: Scalable high-precision tuning of photonic resonators by resonant cavity-enhanced photoelectrochemical etching.

The original version of this Article omitted the fourth author, Sara Ducci from Matériaux et Phénomènes Quantiques, Université Paris Diderot, CNRS UMR 7162, Sorbonne Paris-Cité, 10 rue Alice Domon et Léonie Duquet, Paris 75013, France. This mistake has been corrected in both the HTML and PDF versions of the Article.

Scalable high-precision tuning of photonic resonators by resonant cavity-enhanced photoelectrochemical etching.

Photonic lattices of mutually interacting indistinguishable cavities represent a cornerstone of collective phenomena in optics and could become important in advanced sensing or communication devices. The disorder induced by fabrication technologies has so far hindered the development of such resonant cavity architectures, while post-fabrication tuning methods have been limited by complexity and poor scalability. Here we present a new simple and scalable tuning method for ensembles of microphotonic and nanophotonic resonators, which enables their permanent collective spectral alignment. The method introduces an approach of cavity-enhanced photoelectrochemical etching in a fluid, a resonant process triggered by sub-bandgap light that allows for high selectivity and precision. The technique is presented on a gallium arsenide nanophotonic platform and illustrated by finely tuning one, two and up to five resonators. It opens the way to applications requiring large networks of identical resonators and their spectral referencing to external etalons.

Silicon nanowires: where mechanics and optics meet at the nanoscale.

Mechanical transducers based on nanowires promise revolutionary advances in biological sensing and force microscopy/spectroscopy. A crucial step is the development of simple and non-invasive techniques able to detect displacements with subpicometer sensitivity per unit bandwidth. Here, we design suspended tapered silicon nanowires supporting a range of optical resonances that confine and efficiently scatter light in the visible range. Then, we develop an optical method for efficiently coupling the evanescent field to the regular interference pattern generated by an incoming laser beam and the reflected beam from the substrate underneath the nanowire. This optomechanical coupling is here applied to measure the displacement of 50 nm wide nanowires with sensitivity on the verge of 1 fm/Hz(1/2) at room temperature with a simple laser interferometry set-up. This method opens the door to the measurement of the Brownian motion of ultrashort nanowires for the detection of single biomolecular recognition events in liquids, and single molecule spectroscopy in vacuum.

Optomechanics with silicon nanowires by harnessing confined electromagnetic modes.

The optomechanical coupling that emerges in an optical cavity in which one of the mirrors is a mechanical resonator has allowed sub-Kelvin cooling with the prospect of observing quantum phenomena and self-sustained oscillators with very high spectral purity. Both applications clearly benefit from the use of the smallest possible mechanical resonator. Unfortunately, the optomechanical coupling largely decays when the size of the mechanical system is below the light wavelength. Here, we propose to exploit the optical resonances associated to the light confinement in subwavelength structures to circumvent this limitation, efficiently extending optomechanics to nanoscale objects. We demonstrate this mechanism with suspended silicon nanowires. We are able to optically cool the mechanical vibration of the nanowires from room temperature to 30-40 K or to obtain regenerative mechanical oscillation with a frequency stability of about one part per million. The reported optomechanical phenomena can be exploited for developing cost-optimized mass sensors with sensitivities in the zeptogram range.

Shedding light on axial stress effect on resonance frequencies of nanocantilevers.

The detection back-action phenomenon has received little attention in physical, chemical, and biological sensors based on nanomechanical systems. We show that this effect is very significant in ultrathin bimetallic cantilevers, in which the laser beam that probes the picometer scale vibration largely modifies the resonant frequencies of the system. The light back-action effect is nonlinear, and some resonant frequencies can even be reduced to a half with laser power intensities of 2 mW. We demonstrate that this effect arises from the stress and strain generated by the laser heating. The experiments are explained by two-dimensional nonlinear elasticity theory and supported by finite element simulations. The found phenomenology is intimately connected to the old unsolved problem about the effect of surface stress on the resonance frequency of singly clamped beams. The results indicate that to achieve the ultimate detection limits with nanomechanical resonators one must consider the uncertainty due to the detection back-action.

Nanomechanical mass sensing and stiffness spectrometry based on two-dimensional vibrations of resonant nanowires.

One-dimensional nanomechanical resonators based on nanowires and nanotubes have emerged as promising candidates for mass sensors. When the resonator is clamped at one end and the atoms or molecules being measured land on the other end (which is free to vibrate), the resonance frequency of the device decreases by an amount that is proportional to the mass of the atoms or molecules. However, atoms and molecules can land at any position along the resonator, and many biomolecules have sizes that are comparable to the size of the resonator, so the relationship between the added mass and the frequency shift breaks down. Moreover, whereas resonators fabricated by top-down methods tend to vibrate in just one dimension because they are usually shaped like diving boards, perfectly axisymmetric one-dimensional nanoresonators can support flexural vibrations with the same amplitude and frequency in two dimensions. Here, we propose a new approach to mass sensing and stiffness spectroscopy based on the fact that the nanoresonator will enter a superposition state of two orthogonal vibrations with different frequencies when this symmetry is broken. Measuring these frequencies allows the mass, stiffness and azimuthal arrival direction of the adsorbate to be determined.

Mass sensing based on deterministic and stochastic responses of elastically coupled nanocantilevers.

Coupled nanomechanical systems and their entangled eigenstates offer unique opportunities for the detection of ultrasmall masses. In this paper we show theoretically and experimentally that the stochastic and deterministic responses of a pair of coupled nanocantilevers provide different and complementary information about the added mass of an analyte and its location. This method allows the sensitive detection of minute quantities of mass even in the presence of large initial differences in the active masses of the two cantilevers. Finally, we show the fundamental limits in mass detection of this sensing paradigm.

Arrays of dual nanomechanical resonators for selective biological detection.

Arrays of small nanomechanical resonators with dual geometry have been fabricated for sensitive biological detection. The arrays consist of silicon nitride resonating 100 nm thick cantilevers with sensing gold areas alternately placed on the free and fixed cantilever ends. The Au areas act as sensing regions as can be functionalized by means of thiol chemistry. The nanomechanical arrays provide a double flavor of the adsorbed molecules: the added mass reported by the cantilevers with the Au area at the tip and the nanoscale elasticity reported by the cantilevers with the Au area at the clamp. The devices were applied for DNA detection based on Watson-Crick pairing rules. The proposed design for nanomechanical resonators provides higher specificity for DNA sensing in comparison with conventional single cantilevers. The nanoscale elasticity induced by the DNA hybridization arises from the intermolecular interactions between the adsorbates bound to the cantilever and the surface stress.