The Research On "Nondiffracting" Quality Of Zero-order Bessel Beams And Its Application

Durnin J. advanced a theory that the wave equation in free space has a solution as the form of zero-order Bessel function. The beams that correspond to zero-order Bessel function are called zero-order Bessel beams. Based on the character of zero-order Bessel function, the optical field will distribute in a group of concentric rings with a maximum in center, and it will keep the distribution during the spread progress. It is proved that the central light spot of Bessel beams is certainly"nondiffracting"during the spread progress, so it is also called nondiffracting beams.The light spot of nondiffracting beams is invariable with the change of spread distance, and this speciality can make nondiffracting beams useful in laser processing, laser alignment, optical micromanipulation and atomic optics. Because the light spots of nondoffracting beams are the same in different longitudinal positions, the beams can have orientations along transverse direction with the fact that they can not have orientations along longitudinal direction. In order to solve the problem, a kind of localized hollow beams is generated by the interference of multiple Bessel beams. These beams can also have concentric annular spot at transverse direction, and they can also be used in exact alignment, but the distribution of concentric rings is periodic in different longitudinal directions, so it is possible to offer a method of three-dimensional (3D) space collimation by the analysis of the correlative parameters. In this article, we regard zero-order Bessel beams as research objects, and make main researches as follows:1. A conclusion is educed by strict theoretical research, that is, when plane waves illume an annular slit, the zero-order Bessel beams will be generated beyond the convex mirror.This is a basic for more research.2. The spread characteristic of double Bessel beams is analyzed. When double Bessel beams interference under certain condition, a chain of 3D localized hollow beams can be generated on axis. Dependence of the size, the spatial period and the quality of these localized hollow beams on the parameters of the double zero-order Bessel beams are discussed quantitatively. The condition for zero intensity at the central points of the localized hollow beams is given. We also found that the optimal localized hollow beams can be generated only when the radial ratio of the inner to outer rings is taken as a special value. This research is significant for design of new diffractive optical elements to generate localized hollow beams based on interference of double zero-order Bessel beams.3. The nondiffracting spread characteristic of zero-order Bessel beams is analyzed again according to the diffractive angular spectrum theory. The distribution of three-dimensional (3D) diffractive optical field, generated by the coherent superposition of multiple zero-order Bessel beams, is also theoretically analyzed. The theoretical analysis shows that, when the relative parameters of coherent superposing Bessel beams satisfy some conditions, the diffractive optical field could have a self-imaging effect, that is, the distribution of optical field could have periodicity along the diffraction direction. The result of simulation proves the correction of the theoretical analysis. This simulation by computer further shows that, the coherent superstition of Bessel beams can form an array of localize-hollow beams with high quality.