Sub-ms translational and orientational dynamics of a freely moving single nanoprobe; theory and experiment*

Observing 3D translational and orientational motion of single particles in solution at high time resolution is an outstanding problem in chemical physics. Orientation, encoded in a particle’s polar (θ) and azimuthal (ϕ) angles, impacts chemical reactivity and provides a sensitive report on the local environment, thus being relevant to chemical, biological, polymer and soft matter physics. One way to access the real-time orientation of a particle is to split the emitted/scattered light into multiple polarizations and to measure the light intensity at these.¹ What previous uses of this experiment lack is 3D translational motion. Most 3D localization methods cannot access a Z range far beyond the Rayleigh length of the illuminating light, limiting depth imaging to ~5 μm. Here, we show an experiment that measures 3D translation with a time and spatial resolution of 10 μs and ~10 nm in XYZ. It provides access to 15 μm of depth information, and measures 3D orientation with a time resolution of 250 μs and precisions of ~6° in ϕ and ~11° in θ.² These are compared with precision limits derived using information theory.³

1. J. T. Fourkas, Opt. Lett. 26, 211 (2001)

2. J. S. Beckwith and H. Yang, J. Phys. Chem B, In Peer Review

3. J. S. Beckwith and H. Yang, J. Chem. Phys. 155, 144110 (2021)