Optomechanical mass spectrometry

Nanomechanical mass spectrometry has proven to be well suited for the analysis of high mass species such as viruses. Still, the use of one-dimensional devices such as vibrating beams forces a trade-off between analysis time and mass resolution. Complex readout schemes are also required to simultaneously monitor multiple resonance modes, which degrades resolution. These issues restrict nanomechanical MS to specific species. We demonstrate here single-particle mass spectrometry with nano-optomechanical resonators fabricated with a Very Large Scale Integration process. The unique motion sensitivity of optomechanics allows designs that are impervious to particle position, stiffness or shape, opening the way to the analysis of large aspect ratio biological objects of great significance such as viruses with a tail or fibrils. Compared to top-down beam resonators with electrical read-out and state-of-the-art mass resolution, we show a three-fold improvement in capture area with no resolution degradation, despite the use of a single resonance mode.

The laser output power is 0.5 W, and the optical response shows a slight thermo-optic effect, resulting in an asymmetric mode shape. We fit the measurement data using a model which takes into account this effect 1 . We obtain an intrinsic quality factor of i = 5 × 10 4 and an extrinsic quality factor e = 8 × 10 5 (under-coupled regime).
Supplementary Figure 4. Narrow-band optical transmission spectrum of the ring resonator.
Detail of one resonance of the ring resonator measured with 10 mW output laser power, in order to maximize optomechanical signal amplitude. A strong thermo-optic behavior is observed, shifting the resonance to higher wavelengths. The wavelength of operation is chosen within the linear slope in the blue area so the transmission signal is maximized. The wavelength modulation induced by the motion of the nanoresonator remains small compared to the width of the optical response (typically 2 pm), even for large mechanical drive amplitudes ( Figure 2c). The measurements are performed at approximately -3 dB from the onset on non-linearity. The phase response shows a close to rad shift, as expected from a pure harmonic oscillator with no parasitic signals. This is the result of good decoupling between electrical actuation and optical detection.
Supplementary Figure 6. Frequency stability measurement. (a) Schematic of closed loop measurements. A PID is used to lock the driving frequency to the phase of the resonator, in a phase locked loop (PLL) configuration. The drive frequency is changed so that Drive = Resonance . This is done by reading the output phase of the resonator and comparing it to its phase at resonance ∅ Ref to obtain a phase error ∅ Err . The PID modifies the driving frequency to minimize this phase error. In our case, the PLL is embedded in our lock-in. (b) Allan deviation of the nanomechanical resonator in open loop and closed loop configurations. The open loop measurements are performed by driving the resonator at resonance and monitoring its phase fluctuations, which are later converted to resonance frequency fluctuations using the linear phase-to-frequency relationship of the resonator close to resonance ∆ / ≅ 2 / 0 . This frequency trace is then used to compute the Allan deviation. In the case of closed loop measurements, the Allan deviation is directly computed from the drive frequency. Both measurements provide very similar results down to an integration time of 10 −2 seconds, which is the response time of our PLL, confirming correct frequency tracking in closed-loop operation. At lower integration times, the frequency is filtered by the PI corrector and the device's resonance frequency is not tracked correctly. At large integration times (typically a few seconds), a drift in the resonance frequency becomes visible, which we attribute to temperature fluctuations. As discussed in Methods, the integration time is chosen close to the PLL response time (~10ms) in order to avoid multiple event detection. Figure 7. Effect of mass deposition on the optical transmission with and without protection layer. (a) Without protective layer, as tantalum particles are deposited on the waveguide and the ring, their optical properties drift. The resonance shifts towards higher wavelengths and the optical transmission of the waveguide degrades. In particular, the slope decreases, degrading the optomechanical transduction gain. (b) Conversely, when the optical part is covered with an amorphous silicon layer, no clear degradation of the optical readout due to particle deposition is observed. Even after depositing the equivalent of 10% of the nanoresonator's mass (brown: before any deposition, orange: between depositions, green; after depositions), the optical resonance wavelength remained within its bandwidth with no discernible change in the transmission. The whole packaging process is as follows: first, the optomechanical devices are assembled with the fibre-to-waveguide transposer chips. Then the assembly is glued to a PCB, and the wire-bonding of the electrical connections is performed. The PCB has electrical pins at the bottom (not shown in the image), which are plugged to the measurement system. In this example, the two transposer chip extremities are less than 1 mm away from each, and less than 500 µm from the optomechanical resonator.

Supplementary
Supplementary Figure 10. Measurement compared to simulation. Experimental (orange) compared to theoretical (blue) mass measurements for (a) 4.6 MDa and (b) 6.8 MDa particles. The blue spectra are obtained by simulating deposition of monodisperse populations on a nanoresonator using the measured frequency noise fluctuations. The same data processing has been used for the four data sets of the main text. The non-zero width of the blue spectra are due to the nanoresonator's frequency noise. The experimental width being larger than the theoretical one, the measurements reflect the actual distribution of the tantalum population. Optical resonators. The optical resonators are silicon rings supported by four spokes connected to a central disk itself clamped to the substrate by a SiO2 pillar (Fig. 1c of the main text). The thickness of the ring resonators and optical waveguides is 220 nm, in order to limit optical losses in silicon. The rings have a 20 m external diameter and a 0.5 m width. The four spokes are 500 nm wide except at their extremity in contact with the ring where they are ~100 nm wide in order to decrease optical losses.

Supplementary
Estimation of the optomechanical coupling. The optomechanical coupling factor is estimated using the thermomechanical noise of the nanoresonator as calibration 4  calculations, we assumed the optical response to be linear around the light frequency 0 , and that the slope measured during a slow spectrum characterization is representative of that during the nanoresonator's measurements at high frequency. From these measurements we determined = 4.05 × 10 17 −1 (0.405 −1 ).