Sharp focusing of linearly polarized asymmetric Bessel beam

We conduct the numerical and experimental study of sharp focusing of a linearly polarized asymmetric Bessel beam with topological charge $n=3$ and a crescent-shaped transverse intensity pattern. Using the Debye integral, we show that in the focal plane of a high NA aplanatic lens ($\mathrm{NA}=0.9$–$0.95$) the intensity distribution is also crescent-shaped. Using the FDTD method it is shown that a binary zone plate with $\mathrm{NA}=0.995$ also forms a crescent-shaped focal spot that is rotated around the optical axis. An asymmetric Bessel beam was generated using a spatial light modulator (SLM) and focused using an immersion objective with $\mathrm{NA}=1.25$. A crescent-shaped intensity pattern formed in the focal plane was rotated by $90$ degrees relative to the SLM-aided crescent.