Theoretical and experimental study of self-reconstruction property of astigmatic Bessel beam

In this paper, the self-reconstruction property of astigmatic Bessel beam is studied experimentally and theoretically. Based on the Fresnel diffraction integral theory and Babinet principle, the general expression of the intensity distribution of astigmatic Bessel beams passing through a circular obstacle is derived. The cross-section light intensity at transmission distance of, 10, 30, and 80 mm after astigmatism of the astigmatic Bessel beam are occluded by circular obstacles. The self-reconstruction process of the light field is observed and verified by using an specially designed experimental setup. In the experiment, we choose He-Ne laser as a light source, collimate and expand the beam through a telescope system, and a zero-order astigmatic Bessel beam is generated by a beam vertically incident on the tilted axicon after the diaphragm. A circular obstacle with a radius of 0.2 mm is placed at a distance of 200 mm behind the axicon. Finally, the cross-section intensities at different distances are observed and recorded by a microscope. The experimental phenomena are in good agreement with the theoretical prediction. The results show that the reconstruction of the zero-order astigmatic Bessel beams will occur after passing through the on-axis and off-axis obstacles. And as the transmission distance increases, the outer contour size of the astigmatic Bessel beam becomes larger, and the number of central spot arrays increases, and the complete beam is gradually reconstructed. Particularly, this feature is different from the behavior of the non-diffracting Bessel beam, which maintains the light field unchanged during transmission and has a single central spot. It is expected to be applied to multi-layer multi-particle control. And a new optical property is discovered in the experiments: the reconstruction speed of the beam in the horizontal and vertical direction are not consistent in the reconstruction process, and there is a certain speed difference. Further, we add a spiral phase plate between the diaphragm and the axicon to produce a high-order astigmatic Bessel beam. And it is verified that the high-order astigmatism Bessel beam has the same self-reconstruction characteristics after being shielded by obstacles. Compared with the zero-order aperture system, the high-order beam can not only expand the operating range, but also use the orbital angular momentum carried by the beam to achieve light rotation, which makes the particle manipulation more flexible. The research proves the self-reconstruction characteristics of astigmatic Bessel beams theoretically and experimentally, and broadens the research range of astigmatic Bessel beams. The research results have practical significance and application value in the field of optical micro-manipulation.