Study on propagation property of self-focusing pin-like beams

Radially symmetric Airy-like beams have the ability to autofocus abruptly, which leads to a wild application, for instance, particle manipulation and light bullets. On the basic of the theory of 1D self-accelerating Airy beam, this thesis starts the research on propagation property of Airy-like self-focusing pin-like beams. Based on the theory of stationary phase calculation, we obtain the trajectory function of Airy-like beams and dynamics of the optical beam before the focus and beyond. With the method of beam split-step Fourier method, we theoretically analyze the transverse and longitude amplitude trending of this optical beam. It turns out that Airy-like beam propose an abruptly autofocusing property like circularly symmetric Airy beam, its propagation follows a parabolic trajectory and tends to focus on the axial; after focusing, the optical beam morphs into a Bessel-like beam, its main lobe size decreases during the propagation and finally becomes pin-like.