Pseudo-nondiffracting beams generated by radial harmonic functions

A pseudo-nondiffracting beam (PNDB) is characterized by an almost constant intensity along a finite propagation distance and a beamlike shape in its transverse dimensions. In other words, the intensity distribution is distributed as a sword of light. There are several methods for achieving a PNDB. From the viewpoint of geometrical optics, a sword beam has been demonstrated by axicon.1 With diffraction theory, it has been shown that the Bessel beam2 and a beam diffracted from the holographic axilens3 behave as PNDB’s. Other kinds of PNDB have been obtained by numerical iterative methods.4,5 Multiplexing a few PNDB’s has been achieved also by numerical iterative methods,6 and one-dimensional PNDB’s have been found analytically7 and numerically.8 In this paper we propose a new PNDB that is general in the sense that in the limit, when its parameters go to infinity, it converges to the Bessel beam. It consists of four independent parameters, each affecting the beam’s transverse width, sidelobe height, and longitudinal interval length. The proposed PNDB’s are created by radial harmonic functions (RHF’s) coded on Fourier holograms. The RHF can be used as a phase-only pupil filter for increasing the depth of focus of imaging systems, as demonstrated in Section 5. The relations between the hologram and the resulting beam are analyzed in Section 3. Knowing the mutual dependence between the holograms and the PNDB’s enables us to shift and rotate the beams in space, as well as change their scale, by changing a few parameters of the holograms’ distribution. These effects are also demonstrated in Section 5.