Characterization and tracking of the three-dimensional translational motion and rotation of single nanoparticles using a fiber-based microcavity with high finesse

Abstract

Sophisticated new sensor techniques have to be developed to enable the detection of the temporal dynamics of single nanoparticles and molecules. Some of the new microscopy techniques are based on nanoparticle labeling, achieving high sensitivity on the single nanometer scale, but also changing the nanoparticle's natural behavior. In this work, a fiber-based Fabry-Perot (FP) microcavity with high finesse is presented, which allows the detection of unlabeled nanoparticles. Single nanoparticle resolution is achieved by forcing the light to thousands of round trips between two high-reflective mirrors of micrometer size and consequently enhancing the interaction between light and nanoparticle. So far, fiber-based FP cavities in air, vacuum and liquid helium have been reported in the past. In order to enable single nanoparticle measurements in liquids, two different microfluidic channels are demonstrated. Both channels allow an easy integration of the fiber-based FP cavity, provide a controllable laminar flow, and the measurement of small sample volumes. Furthermore the microfluidic channel and the integrated FP cavity are embedded in a sensing platform, that provides a high passive stability of $\sim1$pm and a low root-mean-square measurement noise of $0.39$pm. Combined with a high Cooperativity of the FP cavity in water of $C\sim Q\lambda_0^3/({n_{\mathrm{m}}^3 V_{\mathrm{m}}})=2.1\cdot10^4$ single SiO$_2$ nanospheres with a hydrodynamic radius down to $11.7$nm can already be detected. In this work, it is shown that the FP cavity allows the detection of hundreds of single SiO$_2$ nanosphere transit events within a few hours. From the derived statistical data, the SiO$_2$ nanosphere's mean polarizability, as well as the mean effective refractive index, are deduced. Here, the first important finding is the detection of the nanosphere's expanded size in pure water originating from a hydrate shell. This allows the estimation of the mean thickness as well as the mean refractive index of the hydrate shell of different SiO$_2$ nanosphere samples. Besides, the effect of salt on the hydrate shell is investigated. Already small salt concentrations presumably lead to a suppression of the formation of the hydrate shell and give indications of the significantly lower polarizability of the bare nanosphere. Furthermore, by improving the measurement time resolution, the polarizability of a single SiO$_2$ nanosphere is determined. In addition, the autocorrelation of the dispersive signal of several SiO$_2$ nanosphere transit events is compared with the theoretical numerical autocorrelation of a punctiform nanosphere and the Monte Carlo simulated autocorrelation of several nanosphere transit events with expanded size. As a result, a purely diffusive motion is identified. Completely new is the detection of the three-dimensional Brownian motion of a single nanosphere with a microcavity. By the simultaneous measurement of the dispersive shifts of the fundamental and two higher-order transverse modes, the three-dimensional coordinate of the nanosphere can be derived with a high spatial resolution of $8$nm and a high temporal resolution of $0.3$ms. This is first analyzed by simulations and then demonstrated with measured signals. From the three-dimensional track, the nanosphere's diffusivity, as well as its hydrodynamic radius, is deduced. The rotational diffusion of single anisotropically shaped nanoparticles is measured by the polarization-split fundamental mode with a high temporal resolution of $0.07$ms. Already nanospheres with a specified roundness of >0.98 can be investigated in their rotational diffusion, showing that this detection method is highly sensitive. The presented FP microcavity already achieves a sensitivity, which allows the detection of different molecules like viruses, ribosomes, and exosomes. Therefore, it is a promising candidate for a future detection of the dynamics of single, unlabeled molecules with a small molecular mass.