We study theoretically the propagation of vortex laser beams in a random medium. The study is based on the extended Huygens-Fresnel principle with the generation of a random field, using the fast Fourier transform. The simulation shows that the stability of vortex beams to fluctuations of an optical medium falls with rising order of optical vortices. A coherence length (radius) of the random medium is of great importance. The coherence radius extension affects adversely the conservation of a beam structure in the random medium. During further free-space propagation, increasing coherence enables to reduce negative effects of fluctuations for beams with high-value topological charges.
The theoretical analysis of optical signal propagation through two-lens imaging system based on double finite Hankel transform of order m was performed. The computation of eigenfunctions of the system considered. This computation gives an opportunity to analyze distortion of the optical signal transmission based on the approximation by functions of this set.
The eigenfunctions of optical operator describing a finite two-lens imaging system are considered accounting for a radial
symmetry. Obtained functions are analogue of the generalized spheroidal functions, which are eigenfunctions of finite
Hankel transform. A peculiarity of the considered calculations of the bounded lens system is in accounting for the
system’s physical characteristics. A possibility of formation of a radially symmetrical optical signal, which transfers
without distortions as a superposition of eigenfunctions matching the parameters of the optical system, is demonstrated.
Gaussian-beam transfers through the imaging systems with circular and with rectangular apertures are compared.
Prolate angular spheroidal functions of zero order and their properties has been considered. The calculation of spheroidal functions has been produced for different parameters. One- and two-dimensional Gaussian beam decomposition into spheroidal functions provided in the paper allowed to evaluate the distortion of the optical signal passing through the lens system. We demonstrate the possibility of the formation of the optical signal transmitted through a lens system without distortion as a superposition of spheroidal functions consistent with the parameters of the optical system.