Metalens for creation of the longitudinally polarized photonic needle

In this work, we develop a mathematical apparatus to describe continuous subwavelength diffraction gratings for creation of cylindrical beams with arbitrary order. We consider special degenerated cases of gratings periods expressions and propose to introduce nonlinearity to avoid these cases. Also, we propose a metalens based on subwavelength relief that is intended to create the longitudinally polarized photonic needle. The element combines two functions: polarization and phase transformation of the incident beam. The element transforms the incident linearly polarized beam into the radially polarized beam. Simultaneously, the incident field is provided with axicon phase. The numerical simulation is provided with Comsol software. The simulation verifies the efficient creation of longitudinally polarized photonics needle.