The diffraction of optical vortices with circular polarization by subwavelength optical microelements with a nonlinear dependence of the change in the refractive index of the substrate was investigated in this paper. The relief height of the elements was varied, as well as the direction of change in the refractive index of the substrate. It was shown that it was possible to obtain a focal spot 37.8% smaller than the focal spot formed by a standard diffractive axicon. It is also shown that it was possible to obtain a light segment 29.7% longer than the light segment formed by the diffractive axicon. It was also demonstrated that it was possible to form a series of optical traps for all considered types of substrates using the ring gratings with a relief height h = 4.24λ without central zones.