Kovalev Alexey Andreevich Birth date: 08.01.1979. 

Brief biography: Main scientific results obtained during last years 1. An analytical relationship has been derived for calculating the normalized orbital angular momentum (OAM) of the superposition of offaxis Bessel beams characterized by the same topological charge. This relationship enables generating nondiffractive beams with different intensity distributions but identical OAM. As a result of a complex shift of the Bessel beam, the transverse intensity distribution and OAM of the beam are also shown to change. It was shown that in the superposition of two or more complexshifted Bessel beams, the OAM may remain unchanged, while the intensity distribution is changed. 2. Two theorems have been proven about conservation of the orbital angular momentum (OAM) of a superposition of identical optical vortices with an arbitrary radially symmetric shape, integer topological charge of n, and arbitrary shift from the optical axis. The normalized OAM of such superposition for any real weights equals to the OAM of each individual beam contributing to the superposition. If the centers of the beams are located on a straight line passing through the origin, then, even if the superposition weights are complex, the normalized OAM of the whole superposition equals to that of each contributing beam. These theorems allow generation of vortex laser beams with different (not necessarily radially symmetric) intensity distribution, but with the same OAM. 3. A new solution of the paraxial Helmholtz equation has been obtained that describes a family of threedimensional and twodimensional forminvariant halfPearcey beams (HPbeams). HPbeams generalize Pearcey beams obtained in Opt. Express, 20, 18955 (2012), since these Pearcey beams can be considered as the sum of two firstorder HPbeams. Threedimensional HPbeams have angular spectrum of plane waves, which is nonzero at a half of parabola. For functions of HPbeams complex amplitudes, the orthogonality properties have been revealed. For twodimensional HPbeam acceleration and deceleration of trajectory has been shown for areas before and beyond the focal plane respectively. 4. An integral transform has been derived which describes the paraxial propagation of an optical beam in a gradedindex medium with the permittivity linearly varying with the transverse coordinate. The form of the integral transformation suggests that unlike a straight path in a homogeneous space, any paraxial optical beam will travel on a parabola bent toward the denser medium. 5. By decomposing a vector electromagnetic field in terms of plane waves, the linearly polarized incident wave with high NA has been generally shown to generate a focal spot with the transverse intensity distribution in the form of an ellipse or a dumbbell elongated in a plane parallel to the incident light polarization plane. Meanwhile, the power flux distribution has the form of a circle or an ellipse whose major semiaxis is in a perpendicular plane to the incident beam polarization plane. Current scientific interests: – mathematical theory of diffraction; Main publications of last three years:

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