Calculations for experiments with vortex beams at the Novosibirsk free electron laser facility
Beams of photons with an orbital angular momentum (or vortex beams) are of interest both for fundamental physics and for various applications. In the visible range, there are many ways to generate such beams, for example, using spatial light modulators (SPM). In the terahertz frequency range, for which SPM has not yet been developed, diffractive optical elements (DOEs) remain one of the most effective devices for generating vortex beams. For example, in the case of a high-power terahertz radiation source, such as the Novosibirsk free-electron laser, radiation-resistant silicon phase DOEs are used to transform a Gaussian beam into beams with a specified mode composition. To support the experiments, a program in Matlab environment with an easy-to-use interface has been written to simulate radiation transmission through optical systems consisting of a sequence of amplitude-phase elements. The calculations were performed within the framework of the scalar theory of diffraction. The software calculates the Rayleigh-Sommerfeld integral in the Fresnel approximation using combination of two approaches of the impulse response method and the transfer function method that ensures the solution correctness in the entire Fresnel diffraction region. In this paper we describe the program and present the results of calculations of the formation of vortex beams by binary phase axicons and their transformation after transmission through two-dimensional periodic gratings of round holes. It is found that behind the lattice in the planes corresponding to the planes of self-images of the classical Talbot effect, a lattice of vortex ring beams appears, the topological charge of which corresponds to the charge of the incident beam. The approaches to the analytical solution of this problem are studied.