We studied the autofocusing properties of chirp beams whose phase has an arbitrary power-law dependence on the radius. Two types of such beams were considered (theoretically and numerically): two-parameter beams corresponding to a generalized lens, and three-parameter beams corresponding to a displaced generalized lens. On the basis of theoretical analysis, the conditions imposed on the parameters of the beams, under which the off-axis caustic is formed, are revealed and the equation of the caustic line is obtained. It is shown how changing the beam parameters affects the autofocusing properties. The results of numerical simulation are consistent with theoretical calculations. Thus, we can form beams with controlled autofocusing properties, which are in demand in various applications of optics and photonics.
Spherical functions are the angular part of the family of orthogonal solutions of the Laplace equation written in spherical coordinates. They are widely used to study physical phenomena in spatial domains bounded by spherical surfaces and in solving physical problems with spherical symmetry. In this paper, we simulate the formation and propagation of periodical three-dimensional optical fields based on a superposition of spherical functions with specific indices that provide periodic properties of the generated fields. The results showed the dependence of the structure and shape of simple superpositions of optical three-dimensional fields on their indices, in particular on their parity. We show that a superposition of spherical harmonics with indices of equal parity provides explicit periodic properties of the fields along the z axis.
Vortex light beams are used to compact data channels because they have orbital angular moments with an infinite number of possible quantum states. This allows the transmission of optical information in a single physical medium by encoding the data by different optical vortices. The aim of the paper is to modeling and analysis the state of orbital angular momentum of laser beams during propagation through free space and parabolic fiber in the presence of random fluctuations of the optical medium. The modeling results for Laguerre-Gauss beams showed that after the beams distortion by random noise, they self-regenerate with further propagation in an undisturbed medium, and it is possible to determine the initial state of the orbital angular momentum of the beam by means of binarization of the field expansion coefficients in angular harmonics.
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