High- photonic microcavity sensors have enabled the label-free measurement of nanoparticles, such as single viruses and large molecules, close to the fundamental limits of detection. However, key scientific challenges persist: (1) photons do not directly couple to mechanical parameters such as mass density, compressibility, or viscoelasticity, and (2) current techniques cannot measure all particles in a fluid sample due to the reliance on random diffusion to bring analytes to the sensing region. Here, we present a new, label-free microfluidic optomechanical sensor that addresses both challenges, enabling, for the first time, the rapid photonic sensing of the mechanical properties of freely flowing particles in a fluid. Sensing is enabled by optomechanical coupling of photons to long-range phonons that cast a near-perfect net deep inside the device. Our opto-mechano-fluidic approach enables the measurement of particle mass density, mechanical compressibility, and viscoelasticity at rates potentially exceeding 10,000 particles/second. Uniquely, we show that the sensitivity of this high- microcavity sensor is highest when the analytes are located furthest from the optical mode, at the center of the device, where the flow is fastest. Our results enable till-date inaccessible mechanical analysis of flowing particles at speeds comparable to commercial flow cytometry.
© 2016 Optical Society of America
The sensitivity of resonant optical sensors to nanoparticles can be improved by either reducing the mode volume [1,2] or by increasing the light-particle interaction time. The latter method often employs high- whispering-gallery resonators (WGRs) [3–5], like those shown in Fig. 1(a), with which even single viruses [6,7] and single molecules have been measured [8–10]. While extremely capable, such submerged-WGR methods [10,11] cannot provide 100% detection efficiency since they rely on random diffusion processes to bring particles to the sensor. Additionally, the randomized particle arrival location only enables statistical or binary measurements, and computation-intensive techniques  must be invoked for more information. Further, the need for particle adsorption and frequent rinsing are prohibitive for the analysis of large numbers of particles. Optofluidic ring resonators (OFRRs) [13–15] improve on this significantly by confining the analyte within an internal microfluidic channel that ensures thorough analysis. However, analytes are still undetectable deep in the core of OFRRs since the resonant optical field only has short range of 1–2 μm in the proximity of the resonator shell. In contrast, commercial flow cytometers, which are non-resonant labeled optical sensors, deliver near-perfect capture efficiency on very large populations of bio-particles with impressive speeds of particles/second , but they cannot reach sensitivity comparable to WGRs.
An orthogonal sensing problem is the fast non-contact measurement of particle mechanical properties such as mass density, elastic moduli, and viscoelastic dissipation. Microelectromechanical (MEMS) techniques [17–20] have shown impressive mass-measurement capabilities with very good temporal resolution using kilohertz-megahertz vibrational modes. On the other hand, since the mass density and compressibility of particles do not couple directly to optical fields, it becomes necessary for optical techniques to invoke photon-phonon interactions that are sensitive to such properties. These optomechanical couplings [21,22] also uniquely offer access to gigahertz-frequency vibrational modes that can help increase temporal resolution far beyond the capabilities offered by MEMS. Till date, all optomechanical particle and protein sensors [23,24] have required the adsorption of the analytes in order to perform detection [Fig. 1(a)], and no system has demonstrated sensitivity to compressibility. Further, existing optomechanical systems are still handicapped by random diffusion, and it has proven impractical to decouple the optical mode perturbation from the mechanical effect . Thus, a fundamental scientific and technological gap persists in performing such mechanical measurements optically on micro/nano-particulate solutions with extremely high throughput and near-perfect capture efficiency.
This work presents a new approach to perform resonantly enhanced optical sensing of freely flowing particles through the action of long-range phonons that extend between solid and fluid phases of the sensor and sample [Fig. 1(b)]. We demonstrate this new principle by flowing analyte solutions confined within a simple microchannel optomechanical device [25,26], thereby also eliminating reliance on random diffusion processes. Being similar to OFRRs, these opto-mechano-fluidic resonators (OMFRs) simultaneously confine light and sound in high- modes of their “bottle” structure. The vibrational modes extend across both solid (shell) and fluid (core) phases [27,28]. Sensing is thus mediated through photon coupling to these phonon modes that permeate the entire fluid volume [Fig. 1(b)]. This potentially allows the OMFR sensor to cast a perfect net that captures measurements on every particle that is present in the sample. In stark contrast to all previous optical sensors, we show here that OMFRs exhibit the greatest sensitivity when the analytes are located furthest from the optical mode, deep in the core of the device. Light in the whispering-gallery resonances is coupled to the phonon modes through the modulation of the optical path length [Fig. 1(c)]. Although opto-mechanics enables the amplification of these phonon modes through radiation pressure and Brillouin scattering [25,26], here we only perform sub-threshold scattering measurements of the thermally occupied phonon mode [Fig. 1(c)]. Previous experiments by this method have already confirmed that bulk fluid density, speed of sound, and viscosity [25–27] can be sensed. We explore the particle-sensing capabilities of the OMFR using baker’s yeast and two types of microbeads. Multimode-sensing capability is demonstrated, which permits the transit measurement of multiple particles with redundancy and indicates future potential for inertial imaging . The system also detects losses associated with individual particles, likely related to viscoelastic properties of the soft material and boundary loss at the interface of the particle and the liquid. We estimate the fundamental throughput limit of the demonstrated sensor to exceed 10,000 events/second at noise-equivalent particle diameters that can approach 660 nm without any environmental controls or advanced instrumentation.
Our experiments are performed on silica OMFRs with diameters ranging from 40–60 μm, prepared through a linear drawing process (see Methods). The spectrum of the OMFR phonon modes is measured through optomechanical coupling with the light propagating in an adjacent tapered fiber (Fig. 2). The phonon spectrum is tracked in real time (see Visualization 1) and shows perturbations occurring during the particle transits [Fig. 3(a)]. Two microscopes help verify each particle transit and triangulate the radial location within the OMFR (see Methods). For each spectrogram, curve fitting to a Lorentzian function is performed to obtain center-frequency traces, as shown in Fig. 3 (see Methods). It is immediately observed that most transit events modify the phonon mode frequency to higher values. Less frequent events occur that shift the phonon frequency lower, though the magnitude of this shift is much smaller. These observations are consistently made using 6 melamine resin particles [Fig. 3(a)], 11 carboxyl magnetic polystyrene particles [Fig. 3(b)], and even household yeast of diameters ranging between 3–4 μm [Fig. 3(c)]. The experiments shown here were performed using two OMFRs with diameters of 55 μm () and 47 μm ().
Two novel insights are generated from the above experiments. First, the phonon frequency shifts that are generated by heavier-than-water particles do not follow the known mass-loading sensing mechanism used by mechanical  and optomechanical oscillators . Second, the sensing mechanism is entirely due to an interaction with the phonon mode since the optical mode is not perturbed during a particle transit. This conclusion is reached since the signal strength remains unaffected during transits, indicating that there is no dispersive or dissipative modification of the ultrahigh- optical mode.
We employ a multiphysical finite-element model to compute the phonon eigenmodes of the hybrid resonator [27,28] (see Methods). The first-order mode shape cross section for a 55 μm OMFR is visualized in Fig. 4(a), indicating that the observed 30.18 MHz mode is a radial breathing mode. Here, the motion of the capillary wall creates a radially symmetric pressure field in fluid, resulting in the storage of kinetic energy in both the fluid and the shell. A pressure maximum occurs at the center of the OMFR, far away from the WGR optical mode of the shell. There is also a notable pressure node that appears near the shell’s inner wall. Next, we will show an experimental verification of this computed mode shape.
The two camera viewpoints captured during each particle transit of the OMFR sensing region enable the triangulation of the particle radial position to within 5 μm (see Methods and Supplement 1). Figure 4(b) plots the phonon mode frequency shift for both 6 μm melamine resin particles and 11 μm carboxyl magnetic polystyrene particles. It is immediately observed that this perturbation data follows the general shape of the standing pressure wave induced within the resonator with the maximum sensitivity at the center of the OMFR at the greatest distance from the optical mode and a sensing null near the inner OMFR wall.
The interaction between an acoustic resonant cavity and a particle present inside the cavity manifests as a resonance frequency shift and acoustic potential acting on the particle . Such mutual interaction has been used to achieve acoustic levitation for containerless studies and for material processing . Recent studies reveal that such interactions not only depend on the properties of the particle and the fluid (size, density, compressibility) , but also on the phonon mode shape and location of the particle [30,33]. We assume that the introduction of the particle brings only small perturbations such that the perturbed pressure field in fluid, , is approximately equal to the unperturbed pressure field in fluid, i.e., . We can estimate the perturbed phonon frequency through the relation (details presented in Supplement 1 and )Supplement 1, and are respectively proportional to the acoustic potential and kinetic energy evaluated over the particle volume and depend on the local value of the standing wave pressure field .
Equation (1) shows that the perturbed frequency is affected by the density contrast and the compressibility contrast of the particle in relation to the ambient carrier fluid. For heavier-than-water particles, the density contrast is positive, whereas the compressibility contrast is generally negative. Particles at the center of the OMFR where the pressure is maximized create the largest perturbation in , while remains relatively small. This results in a frequency increase when a particle is present. On the other hand, when the particle is placed near a pressure node (a fluid velocity maximum), a decrease in the phonon frequency is expected. Since both and can be obtained through simulation (see Methods and Supplement 1), we can predict the phonon mode frequency shift with respect to the particle position. For the radially symmetric mode we used in this work, Fig. 4(c) shows good agreement of the computation with the experimental data in Fig. 4(b).
Using Eq. (1), the density or the compressibility of the sample particle can be measured if the vibrational mode shape and other properties of the particle material are known. This can be especially useful for determining the material compressibility of particles without contact, since density can generally be acquired through simple weighing. Another interesting observation of the above analysis is that both the compressibility and the density of the particle can be determined independently if the particle is much smaller compared with the acoustic wavelength. For example, vanishes when the particle is at the pressure field maximum, resulting in the frequency perturbation being only sensitive to the density contrast. On the other hand, vanishes when the particle is at the pressure node, allowing the measurement of the compressibility contrast. Ultimately, the sensitivity to particle location can be eliminated by implementing a sheath flow that brings particles through the sensor region via the same streamline. Such techniques are already implemented in flow cytometers.
Figure 5(a) presents our fastest measured single particle transit over a 20 ms timescale. This measurement was limited by the available flow rate and suggests a present maximum throughput of 25 particles/second. However, the instrumentation limit of the present experimental setup is far higher at 1000 particles/second, set by the sampling rate of the real-time spectrum analyzer [easily noted in the large number of individual samples in Fig. 5(a)]. Fundamentally, the time constant associated with the center-frequency shift of the energy stored in response to the mode perturbation is related to the modal quality factor. This response timescale can be inferred by direct measurement of the dissipation rate from the phonon mode spectrum. For the presented 55 μm device, the phonon mode linewidth is roughly 10 kHz. This implies a maximum sensing rate limit for this device of about 30,000 particles/second. This number could be reached in the future if sample flow control and faster signal processing hardware can be implemented. We also note that modes with higher dissipation rates are available and can greatly increase the sensing rate limit since the device resonance frequency typically exceeds 30 MHz.
To further understand the sensitivity limit, we characterized the phonon mode frequency stability of the sensor operating in air without environmental protection or feedback stabilization. The Allan deviation data (shown in Figure S6) indicates a noise-equivalent particle diameter (NEPD) of around 840 nm over an averaging time of 2 seconds. We also note that bringing the device into oscillation mode as shown in Ref.  could lower the NEPD to 660 nm with an averaging time of only 0.2 seconds. Significant improvements are possible through feedback stabilization and environmental control. Smaller-diameter OMFRs will indeed have higher sensitivity and can reach substantially smaller NEPD limits since the oscillation frequency scales as the inverse of particle diameter and the density and compressibility perturbations are more appreciable for a smaller device.
The wide spatial extent of the optical mode in bottle-shaped OMFRs also enables the simultaneous measurement of spatially distinct phonon modes. Figure 5(b) shows an example measurement of two frequency-adjacent modes that react to transiting particles with a time lag. Correlating the two spectra provides information on flow speed and spatial separation, with the additional potential to make two independent measurements of the same particle. Additionally, this also enables multimode sensing  and inertial imaging  capabilities with OMFR devices.
The spectrum of scattered photons also carries information on the phonon dissipation associated with the particle. This can be gleaned from linewidth observations  of the real-time optomechanical spectrum, where a greater linewidth indicates a greater phonon mode dissipation rate. Figures 5(c) and 5(d) present direct evidence of increased phonon dissipation during the transits previously shown in Fig. 3. The 30% increase of the phonon dissipation rate measured during the transit of an 11 μm particle [Fig. 5(c)] is more than an order of magnitude greater than would be estimated from the modification of the stored energy in the resonator by the particle. This implies that the increased dissipation is likely related to the viscoelastic properties of the particle material and boundary loss at the interface of the particle and the liquid.
Device fabrication and setup: the OMFRs are fabricated  from fused-silica capillaries (Polymicro Technologies TSP-700850) by linear drawing under localized heating from 10.6 μm lasers. The diameter of an OMFR can be varied along its length by modulating the laser power during the linear drawing process. This enables the fabrication of localized microbottle resonators with diameters spanning 40–60 μm in the widest region, where the optical and mechanical energy can be simultaneously confined . One end of the centimeter-length device is connected to a fluid reservoir and syringe pump for particle infusion, while the other end is left open as the outlet. The OMFR is vertically oriented so even when the pumping is stopped, particles with a density larger than that of the fluid media continue to flow under the influence of gravity. In this manner, spurious effects due to applied internal pressure  can be minimized.
Optomechanical measurement of phonon modes: a continuous-wave fiber-coupled external cavity diode laser (ECDL) at 1550 nm is used to provide the pump light to the OMFR resonant system. This light is coupled into high- optical whispering-gallery modes of the OMFR via a tapered optical fiber. The thermal-mechanical fluctuations of the device modify the optical path length of the WGR modes at frequencies around 30–50 MHz, depending on the device size. The resulting modulation of light in the fiber waveguide generates optical sidebands to the pump. The spectrum of the phonon mode can then be resolved via temporal interference with the pump and these sidebands on a photodetector and can be measured by a real-time electronic spectrum analyzer (RSA; Tektronix model RSA6120A). By tracking this vibrational power spectrum in real time using the RSA, perturbations of the vibrational phonon mode frequency and linewidth due to the particle can be observed. The obtained spectra are then fitted to a Lorentzian lineshape to find the spectral parameters during particle transits.
Verification of particle transits: two digital microscopes are used to simultaneously monitor the apparent position of each particle during transits from distinct points of view at the same height (see Supplement 1, section 1). The videos captured by the cameras can be used to determine the central axis (symmetry axis) of the OMFR and triangulate the true radial position of each transiting particle. This takes into account the refractive index of the fluid media. The calculation of the particle position is subject to error in determining the central axis of the OMFR. In this work, there is roughly 5 μm uncertainty in knowing the central axis (see Figure S3a). The error bar in Fig. 4 shows the full width at half-maximum of the Gaussian fit of the particle grayscale image in the direction (see Figure S3b).
Phonon mode simulations: our vibrational phonon mode simulations are performed using Comsol Multiphysics using a customized solid-fluid interaction model . Coupling between the solid and fluid components is engaged by local pressure in the fluid that exerts force on the shell and by the normal acceleration of the shell, which launches pressure waves in the fluid. The phonon eigenmodes describing the displacement field in the solid domain and the pressure wave field in the fluid domain can thus be determined. This allows the calculation of the kinetic acoustic energy and potential acoustic energy stored in the fluid domain (see Supplement 1).
Broadly speaking, this work presents a new phonon-mediated optical technique for performing high-throughput photonic measurements of mechanical properties of free-flowing particles in fluid. The technique enables resonant measurements without reliance on random diffusion and spatially decouples the optical mode from the sensing volume. Specific to our demonstration of this concept, the “breathing” phonon modes we show have uniquely maximized the sensitivity when the particles are at the center of the OMFR sensor. Indeed, many more vibrational modes spanning the 10 MHz–12 GHz regimes can be accessed in a single OMFR structure  that has different spatial sensitivity functions. A combination of modes can thus be used to ensure perfect capture and inertial imaging of every particle that flows through the device. At the same time, the less-sensitive “Brillouin modes” of the OMFR  may be employed as 11 GHz frequency references that can help cancel out common-mode fluctuations and even enable feedback stabilization toward the substantial improvement of the detection limit.
National Science Foundation (NSF) (ECCS-1408539, ECCS-1509391).
We would like to acknowledge stimulating scientific discussions with Prof. Rashid Bashir and Prof. Lan Yang. We would also like to thank Jeewon Suh and Alan Luo for providing their insight and expertise, which greatly assisted the research.
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