Introduction
1 In the previous two Chapters, we have introduced the a novel class of solid-
liquid hybrid optomechanical resonators that perform phonon-mediated op- tical detection of nanoparticles at extremely high speed and at long range without adsorption. The microcapillary-type resonators support ultrahigh-Q optical modes that are coupled to co-localized mechanical (phonon) modes, while fluid analytes are flowed internally without influencing the optics. Phonons permeate the entire cross-section of the resonator, casting a near- perfect net for measuring particles flowing along the fluid streamlines. All particles in the sample must transit and perturb these phonon modes, in turn perturbing the optical readout due to the strong optomechanical coupling.
We have also shown that the detecting rates are ultimately limited by phonon lifetime, and are potentially exceeding 10,000 particles-per-second. However, since the measurement is done by measuring the thermal-mechanical fluctuation spectrum, the vibrational mode signal is close to the noise floor. Therefore the center-frequency tracking of the vibrational modes relies on curve fitting of the spectrum, which can only be done after experiment in the post-processing. Such post-processing requirement significantly slows down the experiment. This measurement technique thus needs to be improved if we want to implement real-time measurement of particles. In this section, an electro-opto-mechanical driving and lock-in technique, for which the author
1Portion of Section 7.1 is reprinted with permission from Suh, J., Han, K., Peterson,
C. W., and Bahl, G. (2017). “Invited Article: Real-time sensing of flowing nanoparticles with electro-opto-mechanics,” APL Photonics, 2(1), 10801.
has participated in the development, is briefly introduced.
Measurement principle and setup
As discussed in Chapter 5, to track the center frequency of the phonon modes, the phonon spectra with a wide frequency range around the phonon mode center frequency are collected and curve fitting to each of them is done to extract the phonon mode center frequency at each time instance. Both the frequency sweep and the curve fitting take time and slow down the mea- surement. The reason why we have to do the curve fitting to extract the frequency, as opposed to just taking the maximum of the spectrum, is that the phonon mode signal strength is very weak since we are monitoring the thermal-mechanical fluctuations of the vibrational modes. We can improve the signal-to-noise ratio by exciting the radiation-pressure induced oscilla- tion like we did in [92]. To excite the radiation-pressure induced oscillation, the optical power circulating inside the resonator has to be larger than the threshold power. However, this is not easy to achieve due to the high me- chanical energy loss (viscous loss and radiation loss) associated with the fluids [3]. Instead, since silica is an insulator, we make use of electrostatic actuation method to drive the resonator actively. As shown in Figure 7.1, a large single-tone RF stimulus is sent to a pair of wire electrodes near the OMFR, applying electrostatic force to the OMFR at frequency ωRF near
the mechanical resonance frequency. Through optomechanical coupling, the electrostatically excited oscillation can be seen from the spectrum (Figure 7.1) as a sharp peak on top of thermal-mechanical fluctuation spectrum of the phonon mode. Compared with the thermal-mechanical fluctuations, the signal-to-noise ratio of the electrostatically excited oscillation is enhanced by more than 50 dB. The RF frequency is chosen at which the RF amplitude response has the largest slope to maximize the sensitivity. As we have dis- cussed in Chapter 5, a photodetector performs heterodyne measurement of the forward scattered light, which is monitored using both a real-time elec- tronic spectrum analyzer, and a lock-in amplifier (Figure 7.2). Part of the RF stimulus is sent directly to the reference port of the lock-in amplifier such that the transfer function from the RF signal input to the optical modula- tion on the photodetector at frequency ωRF can be monitored in real-time
through an oscilloscope (Figure 7.2). During the particle transits, the fre- quency perturbations of the phonon modes translate into both amplitude and phase perturbations of the transfer function. In this work, we monitor only the amplitude of the transfer function. Changes in amplitude are converted back to the center frequency shift of the phonon mode through a calibration done before the experiment.
Figure 7.1: (Reproduced from [160] with permission) Working principle of the electro-static driven OMFR. The difference between the
working principle of the electro-static driven OMFR with the normal OMFR like we have seen in Chapter 5, is that the resonator is actively driven by a single-tone electrostatic force at ωRF by two 100 μm wire
electrodes. The resulting spectrum is shown on the right. On top of the signal from the thermal-mechanical fluctuation with center frequency ωm, a
sharp signal from the electrostatically driven oscillation at ωRF is shown
with a much higher signal-to-noise ratio. Frequency perturbations of the phonon mode due to particle transits exhibit as amplitude perturbations to signal of the electrostatically driven oscillation.
Results
The OMFR used for this test has a 70 μm outer diameter and a 50 μm inner diameter. The measurement is performed using a 24.26 MHz mechanical mode with monodisperse 3.62 μm silica particles mixed in water. As shown in Figure 7.3(a), the frequency perturbation can be clearly seen above the noise floor, without any post-processing. Two measured frequency perturbations are zoomed in to show the particle transit time (Figure 7.3(b)) with flow rate at 50 µl/min. The shortest transit time achieved is about 490 µs, which is
Figure 7.2: (Reproduced from [160] with permission) Experimental setup. An RF stimulus at ωRF generated from the signal generator (SG) is
split and sent to one of the electrodes and the reference port of the lock-in amplifier (LIA). A DC signal is added to the RF stimulus to the OMFR to enhance the electrostatic drive force. The electrical signal from the
photodetector (PD) is split and sent to the electrical spectrum analyzer (ESA) and the input port of LIA. The output from the LIA are monitored in real-time on a oscilloscope. Both amplifiers are used to increase the signal-to-noise ratio.
corresponding to more than 1000 particles/s, 40x faster than what is shown in Chapter 5. We note that this measurement speed is only limited by the available syringe pump flow rate.
Figure 7.3: (Reproduced from [160] with permission) Experimental results. (a) Phonon frequency trace is recorded during the transit of 3.62 μm silica particles through an OMFR with 70 μm outer diameter and 50 μm inner diameter. (b) Two quick transits are measured at flowrate 50 µl/min. The system exhibits similar sensitivity and ultimate throughput limit like we have shown in Chapter 5. Since the sensitivity to particle relies on the radial location of the particles, we cannot make any measurement of the par- ticle properties, like density and compressibility, unless we know the particle position. We have used cameras to triangulate the particle radial position in Chapter 5. However, for fast transits with a time scale of ms or less, the par- ticle transits are too fast to record even for high-speed camera. Therefore, in the future, it is important for us to implement hydrodynamic focusing (sheath flow) to help confine the particle to a known radial location. It is also possible, since the OMFR is made of transparent silica glass, to tag the flowing particle with fluorescent dyes, in the same way as traditional flow cytometry. When the laser light is focused onto the sample stream, the scattered light due to the particle transits can be measured to provide the particle radial location. Furthermore, the simultaneous extraction of optical and mechanical responses for single bioparticles may provide us previously unavailable information.