Facile Measurement of the Rotation of a Single Optically Trapped Nanoparticle Using the Diagonal Ratio of a Quadrant Photodiode
Optical tweezers are a powerful tool for exploring physical properties of particles in various environments through analysis of their dynamics in a trapping potential. Analysis of the trapped particle's position is often done using interferometric back-focal-plane detection microscopy in which interference between the trapping laser and the light interacting with the trapped particle is projected on a quadrant photo-diode (QPD). The QPD measurements are almost universally the voltage ratios between the transverse components of the detector (left/right; up/down) that are calibrated to ascertain particle positions and orientations (i.e., rotation). In this paper, we demonstrate how measuring the diagonal ratio of the QPD allows tracking the spinning and orbital motion of optically trapped objects with enhanced sensitivity compared to the conventional transverse ratio and reveals additional information about particle dynamics. The diagonal ratio "balances" the signal from opposite sides of the QPD, allowing common mode noise reduction and increased measurement sensitivity of the rotating nanospheres at frequencies from below 200 Hz to above 15 kHz. We show that the variability in particle rotation rates is due to slight differences in the aspect ratio of the nanoparticles. We also measure in situ a gradual acceleration in the spinning frequency of trapped nanoparticles due to photothermal shedding of surface ligands and the resulting decrease of rotational friction in solution. The accelerating particles spin at rates exceeding 30 kHz and are eventually "optically printed" onto the glass coverslip on top of the liquid cell enclosure. The diagonal ratio is a simple, readily available, and powerful enabler for measuring rotational dynamics with a 5-fold sensitivity increase over conventional QPD measurements. This affords opportunities for controlling the orientational dynamics of trapped nanoparticles, which is crucial for various applications, including nanoscale mechanical motors.