Azimuthally Spliced Power-Exponential Phase Modulation for Focal Spot Shaping of Circular Airy Beams

Circular airy beam (CAB) is a kind of new structured light with non-diffracting, self-focusing, and self-healing properties. Due to its wide applications, recently, numerous researchers have used various methods to modulate this kind of beam. We theoretically verify and experimentally demonstrate the azimuthal modulation method to shapes the focal spot of the CAB by modulating the CAB with the azimuthally spliced power-exponential phase. The results show that after modulating by an azimuthally spliced power-exponential phase, multi-focal spots can be generated on the self-focusing focal plane of the modulated CAB, and the number of the focal spots can be precisely controlled by controlling the number of segments of the spliced power-exponential phase. The situations of generating three, four, and five focal spots can be achieved via appropriate azimuthally spliced power-exponential phase modulation. We also calculate the intensity distribution, energy flow density, angular momentum density, and optical force of the modulated beam after tight focusing. The results illustrate the theoretical possibility of stable multiparticle trapping by the modulated beam. Our results pave the way for on-demand shaping of the self-focusing focus of the CAB, which will facilitate related applications, such as CAB based multi-particle trapping.