The use of low-power high-repetition-rate ultrafast pulsed excitation in stable optical trapping of dielectric nanoparticles has been demonstrated in the recent past; the high peak power of each pulse leads to instantaneous trapping of a nanoparticle with fast inertial response and the high repetition-rate ensures repetitive trapping by successive pulses However, with such high peak power pulsed excitation under a tight focusing condition, nonlinear optical effects on trapping efficiency also become significant and cannot be ignored. Thus, in addition to the above mentioned repetitive instantaneous trapping, trapping efficiency under pulsed excitation is also influenced by the optical Kerr effect, which we theoretically investigate here. Using dipole approximation we show that with an increase in laser power the radial component of the trapping potential becomes progressively more stable but the axial component is dramatically modulated due to increased Kerr nonlinearity. We justify that the relevant parameter to quantify the trapping efficiency is not the absolute depth of the highly asymmetric axial trapping potential but the height of the potential barrier along the beam propagation direction. We also discuss the optimal excitation parameters leading to the most stable dipole trap. Our results show excellent agreement with previous experiments.

The 2018 Nobel Prize in Physics was awarded for the invention of optical trapping and generation of ultrashort pulses, which revolutionized many areas of modern science and technology. However, physics of optical trapping under ultra-short pulsed excitation has not been explored much. The nonlinear nature of optical trapping force/potential under ultra-short pulsed excitation was theoretically investigated, however, without any direct experimental demonstration and development of any generalized theory independent of the particle size. In this work, we present a methodology to numerically estimate trapping force/potential including optical as well as thermal nonlinearity under ultra-short pulsed excitation and implement a variety of detection modalities to capture the particle's real-time trajectories. We show how highly asymmetric nonlinear axial potential, created by a femtosecond pulse-train, can be mapped from the dynamics of the trapped particle. Considering fine-tuning of trap-stiffness by changing nonlinearity, we envision far-reaching applications of using ultra-short pulsed excitation in laser trapping and manipulation.

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