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Register a new userPropagation dynamics of abruptly autofocusing circular Airy-Gaussian vortex beams in the fractional Schrodinger equation
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We introduce axisymmetric Airy-Gaussian vortex beams in a model of an optical system based on the (2+1)-dimensional fractional Schrodinger equation, characterized by its Levy index (LI). By means of numerical methods, we explore propagation dynamics of the beams with vorticities from 0 to 4. The propagation leads to abrupt autofocusing, followed by its reversal (rebound from the center). It is shown that LI, the relative width of the Airy and Gaussian factors, and the vorticity determine properties of the autofocusing dynamics, including the focusing distance, radius of the focal light spot, and peak intensity at the focus. A maximum of the peak intensity is attained at intermediate values of LI, close to LI=1.4 . Dynamics of the abrupt autofocusing of Airy-Gaussian beams carrying vortex pairs (split double vortices) is considered too.
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We have investigated the propagation dynamics of the circular Airy Gaussian vortex beams (CAGVBs) in a (2+1)-dimesional optical system discribed by fractional nonlinear Schrodinger equation (FNSE). By combining fractional diffraction with nonlinear effects, the abruptly autofocusing effect becomes weaker, the radius of the focusing beams becomes bigger and the autofocusing length will be shorter with increase of fractional diffraction Levy index. It has been found that the abruptly autofocusing effect becomes weaker and the abruptly autofocusing length becomes longer if distribution factor of CAGVBs increases for fixing the Levy index. The roles of the input power and the topological charge in determining the autofocusing properties are also discussed. Then, we have found the CAGVBs with outward acceleration and shown the autodefocusing properties. Finally, the off-axis CAGVBs with positive vortex pairs in the FNSE optical system have shown interesting features during propagation.
In this letter, we introduce a new class of light beam, the circular symmetric Airy beam (CSAB), which arises from the extensions of the one dimensional (1D) spectrum of Airy beam from rectangular coordinates to cylindrical ones. The CSAB propagates at initial stages with a single central lobe that autofocuses and then defocuses into the multi-rings structure. Then, these multi-rings perform the outward accelerations during the propagation. That means the CSAB has the inverse propagation of the abruptly autofocusing Airy beam. Besides, the propagation features of the circular symmetric Airy vortex beam (CSAVB) also have been investigated in detail. Our results offer a complementary tool with respect to the abruptly autofocusing Airy beam for practical applications.
We analyze the propagation dynamics of radially polarized symmetric Airy beams (R-SABs) in a (2+1)-dimensional optical system with fractional diffraction, modeled by the fractional Schrodinger equation (FSE) characterized by the Levy index. The autofocusing effect featured by such beams becomes stronger, while the focal length becomes shorter, with the increase of . The effect of the intrinsic vorticity on the autofocusing dynamics of the beams is considered too. Then, the ability of R-SABs to capture nano-particles by means of radiation forces is explored, and multiple capture positions emerging in the course of the propagation are identified. Finally, we find that the propagation of the vortical R-SABs with an off-axis shift leads to rupture of the ring-shaped pattern of the power-density distribution.
We study nonparaxial autofocusing beams with pre-engineered trajectories. We consider the case of linearly polarized electric optical beams and examine their focusing properties such as contrast, beam width, and numerical aperture. Such beams are associated with larger intensity contrasts, can focus at smaller distances, and have smaller spot sizes as compared to the paraxial regime.
We investigate numerically the interactions of two in-phase and out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media, in one transverse dimension. We find that bound and unbound soliton pairs, as well as single solitons, can form in such interactions. If the interval between two incident beams is large relative to the width of their first lobes, the generated soliton pairs just propagate individually and do not interact. However, if the interval is comparable to the widths of the maximum lobes, the pairs interact and display varied behavior. In the in-phase case, they attract each other and exhibit stable bound, oscillating, and unbound states, after shedding some radiation initially. In the out-of-phase case, they repel each other and after an initial interaction, fly away as individual solitons. While the incident beams display acceleration, the solitons or soliton pairs generated from those beams do not.
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