Peculiarities of focusing circularly and radially polarized super-Gaussian beams using ring gratings with varying relief height

The focusing features of a super-Gaussian beam, as well as Laguerre-super-Gaussian $(1,0)$ modes with radial and circular polarizations on ring gratings (direct and inverse) with a variable height of individual relief rings were investigated in this paper. The change in the height of the relief from the maximum height in the center to the minimum at the edges of the element (direct ring grating) is considered and the reverse case, when the maximum height of the relief was at the edges and the minimum in the center (reverse ring grating). The comparison was carried out with the action of a diffractive axicon with a comparable grating period. Numerical simulation was carried out by the finite differences in the time domain method. It was shown that the direction of change in the height of the relief rings of elements significantly affects the diffraction pattern in the near zone. In particular, for a super-Gaussian beam, the use of a direct ring grating made it possible to reduce the size of the focal spot by $18.7\%$ for radial polarization ($\sigma=5~\mu$m), the use of a reverse ring grating led to a decrease in the focal spot by $36.9\%$ ($\sigma=12.25~\mu$m) in comparison with the action of a diffractive axicon. It was also shown in the paper that when the reverse ring grating is illuminated by the Laguerre-superGauss $(1,0)$ mode with circular polarization, the formation of a narrow and extended region of reduced intensity on the optical axis (optical trap) is observed.