Freeform axicon with azimuthal variation

摘要

An analytical closed-form equation to design a freeform element that replicates an axicon is presented. In this paper, we get the mentioned analytical closed-form equation step by step. The equation comes from applying both the Fermat principle and the Snell's law at the first refractive surface. This Freeform axicon with azimuthal variation can be applied to produce annular conical beams with the possibility to receive wavefronts not necessarily collimated. In the paper, we test the equation in several scenarios to test the design of the Freeform axicon and the results of the performance of the Freeform axicon were as expected.