This Letter examines the diffraction of a vortex beam by a high numerical aperture of topological charge ±1 generated by conical diffraction. Our research shows the behavior of the vortex beam is similar to the one already observed for Laguerre-Gauss and Bessel beams. We also highlight a similarity between the phase singularity created by a lens and the one created by conical diffraction through a thin crystal. More precisely, if the input beam is homogeneously polarized, we show the electric field in the image plane of a thin crystal caught between two orthogonal polarizers has the same expression as E(z), the component of the electric field along the propagation axis, in the focal plane of a lens.