We introduce a type of Fresnel zone plate (FZP) in which its phase is shifted radially outward. This FZP can easily and precisely turn an incident plane wave into an annular beam at its focal plane. High efficiency and flexibility are the advantages of generating doughnut beams by this method. By performing direct calculations and using Bessel function properties, it is shown that a radially shifted zone plate produces annulus focus. Furthermore, by simulating the modified phase structure, in addition to demonstrating the formation of a ring-shaped focus, we also showed that its radius merely depends on the amount of the shift. We also showed that the width of the annulus is a function of focal length. Simulation results were thoroughly examined by experiments. Finally, it is clearly revealed that at a certain distance from the focal plane along the beam propagation, an annular beam is transformed into a Bessel beam, and a focal line is formed.

We aim here to present two models of spiral zone plate-based diffractive elements. To this end, it is shown that by a given combination of two spiral zone plates (SZPs) with opposite-signed charge strengths some novel elements are born whose phase structures are azimuthally shifted. Therefore, they are named azimuthal phase-shifted zone plates. Generally speaking, it is illustrated that both of the two models have the same diffractive functions in generating a variety of petal-like and optical ring lattice beams. Regarding the topological charge of the superimposed SZPs denoted by $P_1$ and $P_2$, it is also elaborated that when the modulus of $|P_1|-|P_2|$ is of unity, the former beam is generated, while the values greater than unity cause the latter one to be generated. Additionally, the number of petals or lattices is simply manageable and given by $|P_1|+|P_2|$. Furthermore, defocusing surveys manifest preserving the shape of the beams in a rather long focal depth and partial rotation of them around the propagation axis is also evident. Numerical results are verified by experiments.