We investigated the propagation dynamics of the Circular Airy Beams (CAB) with optical vortices (OVs) by numerical calculation. Comparing to the common CAB, the maximum intensity of CAB with vortices can be increased greatly at the focal plane and its focal intensity profile is doughnut-shaped when an on-axis vortex is imposed. The case for an off-axis OV and multiple OVs have been investigated as well. We demonstrate that two opposite OVs will annihilate exactly at the focal plane, with the focal intensity is highly increased.

The radiation force of circular Airy beams (CAB) on a dielectric Rayleigh particle is investigated in this paper. Our results show that the CAB can be used to trap the particle whose refractive index is larger than the ambient at different positions along the beam axis. Comparing with the Gaussian beam under the same conditions, the longitudinal and the transverse gradient force of CAB on the Rayleigh particle are increased, and the particle can be trapped more stable. Our analyses also demonstrate that the trapping properties of CAB can be modulated by controlling corresponding parameters of CAB.

We theoretically and experimentally study the propagation characteristics of the circular Airy beam (CAB) when its first few light rings are blocked. It is shown that the focus position of the blocked CAB will remain the same, and its abruptly autofocusing property will be enhanced. Since the maximum focal intensity almost remains the same when the first ring is blocked, a better result of abruptly autofocusing property can be obtained when only the first ring is eliminated. Compared with the common CAB with a same hollow region, the intensity of the blocked CAB will focus at a different position and the intensity will be increased much larger than the common CAB.

The radiation force of highly focused Lorentz-Gauss beams (LG beam) on a dielectric sphere in the Rayleigh scattering regime is theoretically studied. The numerical results show that the Lorentz-Gauss beam can be used to trap particles with the refractive index larger than that of the ambient. The radiation force distribution has been studied under different beam widths of the Lorentz part. The trapping stability under different conditions is also analyzed.

We found a new type of noncircular symmetrical Airy beam called an elliptical Airy beam (EAB). Using a simple single-pixel checkerboard hologram method, we achieved the EAB in an experiment. We observed its unique property of double focusing and the ability of the energy to flow towards the endpoints of the long axis during propagation. These particular properties will have some potential applications.

In this work, the radiation force on a Rayleigh dielectric particle induced by the partially coherent circular Airy beam (PCCAB) is investigated. Our numerical results show that the PCCAB can be used to trap and manipulate particles. The radiation force distribution and trapping stability have been analyzed under different coherent lengths. It is found that, with the increase of the spatial coherent length, the radiation force is increased and the particle can be stably trapped at more points. Therefore, the radiation force as well as the depth of potential well can be effectively modulated by controlling the spatial coherent length in optical micromanipulation. The trapping properties of PCCAB have also been studied under other different parameters, including the scale factor and initial radius.