Vortex beams with high-order cylindrical polarization: features of focal distributions

A detailed analytical and numerical study of the effect of phase vortex singularity has been carried out when focusing high-order cylindrical polarized fields. The possibility of forming a light spot with reduced side lobes when focusing of ring vortex beams with a high-order cylindrical polarization in the paraxial mode. The formation of a compact focal spot is possible at sharp focusing of the Gaussian beam when the order of polarization and the order of the vortex phase singularity coincide. When the orders of polarization and the vortex phase do not coincide, focused intensity distributions resembling chamomiles and cogwheels. Such distributions can be used in laser printing of plasmonic nanotextures for chemo- and biosensing applications.