Analyzing radial and azimuthal Brownian motion in Laguerre-Gaussian optical traps

Optical trapping, orchestrated by intensity-gradient forces and radiation pressure, is a powerful technique in physics and nanotechnology that enables precise control and manipulation of microscopic and nanoscale particles with widespread applications in biotechnology, nanoscience, and fundamental physics research. The annular intensity profile and helical phase structure of Laguerre-Gaussian (LG) beams furnish unparalleled conditions for optical trapping, particularly, in the context of studying rotational motion of particles known as tweezing. Here, we study tweezing of dielectric particles trapped with higher-order LG beams under the strong focusing condition and in the presence of spherical aberrations. We quantify the transverse trap stiffness with the aid of two complementary approaches-Boltzmann statistics and the equipartition theorem-through a comprehensive analysis of the times series of the radial and angular position of a particle. In contrast to the quadrant photodiode (QPD) method, which is faster but has a limited field of view and requires careful calibration, our wide-field imaging-based approach provides direct distance calibration and allows accurate stiffness measurements even when the trapped particle experiences a significant slowdown or the light field distribution lacks perfect axial symmetry. The method offers several attractive advantages: (i) it enables reliable characterization of stiffness anisotropy for LG traps with topological charges up to ℓ =7; (ii) it remains robust in the presence of aberrations that distort the axial symmetry of the beam; and (iii) it provides insight into both radial stability and angular-velocity variations. The proposed approach can enhance the accuracy of optical trapping measurements, improve the design of high-order LG optical traps, and deepen our understanding of particle behavior in complex optical potential landscapes.