Caustics of the vortex beams generated by vortex lenses and vortex axicons

In this work, the propagation of vortex beams is treated using a catastrophe theory approach. Analytic expressions are deduced to describe caustic surfaces produced by vortex lenses and vortex axicons. The obtained analytics allow us to explain the formation of the shadow region along the optical axis for vortex beams using geometric optics (previously, the zero axial intensity was explained just by diffraction effects). Thus, the presence of a vortex eikonal leads to a fundamental change in the type of axial caustic. Another important distinction of the caustics produced by vortex beams from those produced by nonvortex radial beams has been shown to consist in wavelength-dependence. The results of numerical simulation show that the propagation operator defined using a geometrical optics approximation agrees well with the numerical simulation results obtained using a nonparaxial diffraction operator based on the conical wave expansion.