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.
Due to its self-healing property, the Ring Airy Gaussian Vortex Beams (RAiGV) have potential applications in the fields of particle capture and handling, laser medical treatment, and super-resolution imaging. This paper proposes a cotangent phase modulated RAiGV, and carries out a numerical simulation study on its self-healing property. The results show that the beam will split into multiple lobes during the transmission process. Each lobe consists of a main lobe and multiple side lobes, and the lobes shrink, rotate and converge continuously; when one of the lobes is completely blocked or when blocking all the side lobes of the beam, the beam does not have the self-healing ability; when all the main lobes of the beam are blocked, blocking the innermost ring of the beam, or blocking all the outer rings of the beam, the beam has the self-healing ability. After a certain distance of transmission, the beam field is basically the same as the selffocusing beam field.
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