Spiral Caustics of Vortex Beams

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