# Dynamics of microscopic objects in optical tweezers: experimental determination of underdamped regime and numerical simulation using multiscale analysis

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## Abstract

This article presents new experimental observations and numerical simulations to investigate the dynamic behavior of micro–nano-sized objects under the influence of optical tweezers (OTs). OTs are scientific tools that can apply forces and moments to small particles using a focused laser beam. The motions of three polystyrene microspheres of different diameters, 1,950, 990, and 500 nm, are examined. The results show a transition from the overdamped motion of the largest bead to the underdamped motion of the smallest bead. The experiments are verified using a dynamic model of a microbead under the influence of Gaussian beam OTs that is modeled using ray-optics. The time required to numerically integrate the classic Newton–Euler model is quite long because a picosecond step size must be used. This run time can be reduced using a first-order model, and greatly reduced using a new multiscale model. The difference between these two models is the underdamped behavior predicted by the multiscale model. The experimentally observed underdamped behavior proves that the multiscale model predicts the actual physics of a nano-sized particle moving in a fluid environment characterized by a low Reynolds number.

## Keywords

Multiscale modeling Ray-optics Dynamics Optical tweezers Low Reynolds number Fluid dynamics Brownian motion Method multiple scales## Notes

### Acknowledgments

This study is supported by the National Science Foundation under Grant No. MCB-1148541.

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