Objective The circular Airy beam (CAB) has received significant attention because of its peculiar "abruptly autofocusing effect". The "abruptly autofocusing effect" has shown significant advantages in biomedical treatment, laser cutting, and other applications because the CAB can be applied solely to the target without damaging other areas. Various schemes have been designed to improve the "abruptly autofocusing effect". For example, direct blocking of the first few rings of the CAB and modulation of the CAB's angular spectrum can significantly enhance its "abruptly autofocusing effect". On the other hand, the propagation of light beams in anisotropic media has always been of interest. In 2001, Ciattoni A discovered that when a circularly polarized (CP) beam propagates along the optical axis of a uniaxial crystal, a portion of the light beam acquires a topological charge vortex phase of +/- 2 due to spin reversal. In 2020, Ling X H et al. found that the conversion efficiency of spin angular momentum (SAM) to orbital angular momentum (OAM) is related to the anisotropy of the crystal and shape of the beam. To improve the "abruptly autofocusing effect" of the CAB and improve the conversion efficiency of SAM to OAM, this study investigates the propagation characteristics of a modified CAB (MCAB) propagating along the optical axis of a uniaxial crystal. Methods The method proposed by Ciattoni A is adopted to deal with the propagation of light beams along the optical axis of a uniaxial crystal. According to the results of Ciattoni A, a light field propagating along the optical axis of a uniaxial crystal can be treated as a linear superposition of ordinary and extraordinary components. Based on the angular spectrum theory, the propagation dynamics of these two components can be obtained by the Fourier transform of the MCAB's angular spectrum. A closed -form approximation of the CAB's angular spectrum with a suitable plane wave angular spectrum representation has been reported by Chremmos I et al. A modulation function is introduced to modulate the CAB's angular spectrum. The "abruptly autofocusing effect" of the MCAB is superior to that of the ordinary CAB. Following the approach proposed by Ciattoni A, the propagation characteristics of the MCAB in a uniaxial crystal can be obtained.Results adn Discussions In our numerical study, the incident light is a left-hand CP (LHCP) MCAB without a vortex. During the propagation, a right-hand CP (RHCP) component is generated. First, we investigate the intensity, phase, and polarization distributions of the MCAB at z=100 mm. Due to the "abruptly autofocusing effect," the radii of the first rings for the LHCP and RHCP components become smaller [Figs. 2(c), (d)]. The phase distribution shows that the LHCP component has no vortex, whereas the RHCP component has a vortex phase with a topological charge number of 2 [Figs. 2(e), (f)]. This is the singularity of the central phase that causes the RHCP component to be a hollow beam throughout the propagation. The polarization distribution shows that the beam is no longer a uniformly CP beam (Fig. 3). Due to the anisotropy of a uniaxial crystal, the abruptly autofocusing positions of the two components differ. The "abruptly autofocusing effect" of the MCAB is approximately 3. 4 times as strong as that of an ordinary CAB (Fig. 4). Furthermore, we investigate the propagation dynamics of the two components. The results show that both the LHCP and RHCP components exhibit an "abruptly autofocusing effect". The LHCP component without a vortex forms a solid beam at the focus, whereas the RHCP with a vortex forms a hollow beam at the focus (Fig. 5). For a 10 cm long crystal, the efficiency of conversion from the LHCP component to the RHCP component with a vortex can reach 43. 28%, which is approximately 10% higher than that of an ordinary CAB (Fig. 6). Conclusions Similar to other ordinary beams, when an LHCP MCAB propagates along the optical axis in a uniaxial crystal, an RHCP vortex MCAB with a topological charge number of 2 is generated. With a proper modulation function, the "abruptly autofocusing effect" of the MCAB is much stronger than that of an ordinary CAB, and the efficiency of conversion from the LHCP component to the RHCP component with a vortex is also improved.
