Real-time sensing of flowing nanoparticles with electro-opto-mechanics

High-Q optical resonators allow label-free detection of individual nanoparticles through perturbation of optical signatures but have practical limitations due to reliance on random diffusion to deliver particles to the sensing region. We have recently developed microfluidic optomechanical resonators that allow detection of free-flowing particles in fluid media with near perfect detection efficiency, without requiring labeling, binding, or direct access to the optical mode. Rapid detection of single particles is achieved through a long-range optomechanical interaction that influences the scattered light spectra from the resonator, which can be quantified with post-processing. Here, we present a hybrid electromechanical-optomechanical technique for substantially increasing the bandwidth of these optomechanofluidic sensors, enabling real-time operation. The presented system demonstrates temporal resolution of better than 20~\us (50,000 events/second) with particle sensing resolution down to 490 nm, operating in the air without any stabilization or environmental control. Our technique significantly enhances the sensing capabilities of high-Q optical resonators into the mechanics domain, and allows extremely high-throughput analysis of large nanoparticle populations.

ously used to develop sensors for the density 19 and viscosity 16 of bulk fluid samples. Recently, we have demonstrated that the vibrational modes existing in OMFRs cast a nearly perfect 'phonon net' that may also be used to quantify the mechanical properties of individual particles that rapidly flow through the OMFR microchannel, without requiring adsorption 21 .
In this work, we introduce a new experimental method for significantly improving the detection speed and signal-to-noise ratio of these particles measurements through the use of electro-opto-mechanical transduction.
Our preliminary work 21 demonstrated that the center frequency and linewidth of the OMFR vibrational modes are sensitive to the mechanical parameters of flowing particles. These measurements were performed by optically extracting the spectrum of the thermalmechanical fluctuations of the vibrational mode. However, since this vibrational noise signal is close to the noise floor of the measurement apparatus, the measurements require spectral analysis, averaging, and curve fitting of the optical and electronic signals. The instrumentation limit of these measurements is ultimately set by the capabilities of the hardware with which spectra can be evaluated. In the present work, we demonstrate that processingintensive extraction of the entire vibrational spectrum is not necessary and that it is instead sufficient to quantify the mechanical transfer function at a single frequency. Optical detection of this mechanical response to an applied force is shown to enable real-time measurements of the vibrational mode frequency fluctuations during particle transit events. Our experiments showcase a system operating in the air without any environmental controls, that has a measurement noise floor of 490 nm (particle diameter) and can sample transits as fast as 20 μs . Our experiments are a major step towards practical real-time flow cytometry analysis of the mechanical properties of individual particles.
The fabrication of OMFRs has previously been reported in 18,22 . Briefly, these microcapillary resonators are fabricated from fused silica capillaries (Polymicro Technologies TSP-700850) of 850 μm outer diameter that are adiabatically drawn under laser heating used for softening the material. The diameter of an OMFR can be locally varied by modulating the laser power during the drawing process. Microcapillaries having microbottle geometry with 60-70 μm outer diameter can be easily produced by this method, and support simultaneous confinement of optical and mechanical modes in the regions of the highest diameter. One end of the device is connected to a syringe pump, using which analyte solutions can be flowed through at the desired rate. The OMFRs are vertically oriented during experiments to prevent particles from settling due to gravity. In Fig. 3(a), we show that frequency shifts of the vibrational mode associated with in-  average. The shaded box in each data set represents the mean and ± one standard deviation.
dividual particle transits can be clearly observed above the background noise fluctuation in real-time, without needing any post processing. Fig. 3(b) shows a sampling of individual particle transits at flow rates of 10 μl/min , 15 μl/min , and 50 μl/min ; zoomed in to show detail and the extremely high rate of measurement. These observations are made using the same OMFR and the same vibrational mode, allowing an estimation of transit speed and the frequency perturbation caused by each individual particle. The frequency shift associated with each transit is different even though the particles are nominally monodisperse. This variation is well known from our previous work 21 and occurs as a function of the local properties of the phonon mode where the transit occurs. Additionally, background noise levels between all the presented transits in Fig. 3(b) are similar, and only appear different due to the different vertical scaling of each figure. Using this technique, we are able to detect particle transits with timescales as short as 490 μs , which is presently only limited by the achieved syringe pump flow rate. This timescale corresponds to a measurement throughput exceeding 1000 particles/second, which is 40x faster than our previous result 21 . As anticipated, the particle transit times decrease ( Fig. 4(a)) as the nominal flow rate at the syringe pump is increased.
We gathered observations of 41 transits of the analyte particles at flow rates of 10, 15, and 50 μl/min as shown in Fig. 4(b). The vibrational mode frequency shift associated with these transits shows clustering around 0.5-0.75 kHz with significant variation beyond this range.
This spread is not explained by the 5% diameter variation in particles that the manufacturer has characterized. The large variations in sensitivity are thus most likely caused because of inadequate control over particle trajectory through the OMFR, i.e. particles follow different streamlines in the liquid flow. The sensitivity of the system with respect to particle location has been previously discussed in 21 . It is thus imperative for future experiments to implement hydrodynamic focusing (i.e. sheath and core flow) which is a standard technique used in flow cytometry. This will also help make the possible consistent measurement of particle populations and comparisons between individual particle groups in mixed analytes.
The limit of measurement achieved by this system is set by both random and systematic In Fig. 5 we present Allan deviation measurements of the mechanical frequency of the OMFR mode, without any particles present in the flowing carrier liquid (water). These measurements are taken without environmental protection or feedback stabilization, indicating the potential for further improvement. We see that the uncertainty is minimized for averaging time around 120 ms, with long-term drift affecting the measurement for longer averaging times. However, since we aim to measure particle transits times at or below than 400 μs , the system cannot afford time-averaging of the frequency data to this extent. At fast timescales, a minimum Allan deviation of 8 Hz is measured when using nearly the full bandwidth of this system (τ = 20 μs , equaling 50,000 events/second). This Allan deviation quantification allows us to estimate the detection limit of the OMFR sensor, by comparison of the noise floor with calibration particle measurements. We first assume that hydrodynamic focusing will ultimately reliably allow us to access the highest sensitivity region of the vibrational mode. Presently, the greatest experimentally observed vibrational frequency We indicate the frequency Allan deviation for a few key averaging times that represent important timescales in this system (see text).
shift for the 3.6 μm particle population is ∆f max = 3.13 kHz, which is likely obtained by particles transiting a high-sensitivity region of the vibrational mode. However, since higher sensitivity particle trajectories may exist, we may only use this 3.13 kHz detection as a lower-bound estimate of the highest achievable sensitivity. Using the measured 8 Hz Allan deviation for averaging time of 20 μs , a volume ratio analysis obtains the particle size noise floor as 490 nm. The current OMFR system is thus very close to the regime where single viruses (typically 100 nm) may be detectable.
Presently, our real-time system for detecting free-flowing nanoparticles in solution operates at a single frequency and cannot characterize the complete mechanical spectrum. Even so, the particle density and compressibility properties can be derived from these simple measurements 21 . Ultimately, it is trivial to extend this system for performing multifrequency measurements of the optomechanical response. In the near future, the uncertainties arising from vibration, temperature, pressure 27,28 may also be mitigated through such multi-frequency measurements performed on several mechanical modes simultaneously. Finally, positive feedback could be used to dynamically boost the sensitivity of the system 24 but with a sacrifice of measurement bandwidth. Chap. 14.