Spiral Caustics of Vortex Beams

“We discuss the nonparaxial focusing of laser light into a three-dimensional (3D) spiral distribution. For calculating the tangential and normal components of the electromagnetic field on a preset curved surface we propose an asymptotic method, using which we derive equations for calculating stationary points and asymptotic relations for the electromagnetic field components in the form of one-dimensional (1D) integrals over a radial component. The results obtained through the asymptotic approach and the direct calculation of the Kirchhoff integral are identical. For a particular case of focusing into a ring, an analytical relation for stationary points is derived. Based on the electromagnetic theory, we design and numerically model the performance of diffractive optical elements (DOEs) to generate field distributions shaped as two-dimensional (2D) and 3D light spirals with the variable angular momentum. We reveal that under certain conditions, there is an effect of splitting the longitudinal electromagnetic field component. Experimental results obtained with the use of a spatial light modulator are in good agreement with the modeling results.”