Velocity property of an optical chain generated by the tightly focused femtosecond radially polarization pulse.

Based on the Richards-Wolf vector diffraction integration, we obtained the expressions of the intensity and velocity of femtosecond radially polarized pulses at the focus near a dielectric interface, and the pulses are modulated by an optical system consisting of diffractive optical elements (DOEs) and a high numerical aperture (NA) lens. The factors that affected the intensity distribution and velocity evolution of the three-dimensional optical capture structural pulse (optical chain) are also analyzed. These factors include the DOE structural parameters (bandwidth, phase difference between the rings), the interception ratio of incident beam, the NA, the central wavelength of pulses, and the refractive index of exiting medium. The results show that the velocity of the optical chain will increase with an increase in the DOE bandwidth or a decrease in the refractive index of the exiting medium, and the maximum of the optical chain velocity will decrease versus the NA. Furthermore, the dependence of the optical chain velocity on its intensity distribution is also revealed. The superluminal and subluminal can also be found during the propagation of the optical chain. The velocity distribution difference between bright and dark areas along the axis is more conducive to distinguishing the trapping of the Rayleigh particles. We believe these interesting results have great potential to improve the space-time resolution to detect particle positions during high-speed optical trapping.