Kovalev Alexey Andreevich

Birth date: 08.01.1979.
Postal address: Image Processing Systems Institute of the Russian Academy of Sciences, box 3347, building 151, Molodogvardeyskaya st., Samara, 443001, Russia.

Brief biography:
A.A. Kovalev graduated S.P. Korolyov Samara State Aerospace University (SSAU) in 2002 (01.02.00 – Applied Mathematics, mathematical image processing). In 2002 he became a post-graduate student of SSAU. He received his Candidate in Physics & Maths degree (in optics) in 2005 and Doctor in Physics & Maths degree in 2012. Since 2001 he worked at the Laser Measurements laboratory at the Image Processing Systems Institute of the Russian Academy of Sciences at different positions: technician, junior researcher, researcher, senior researcher. He is a coauthor of 136 publications, including two monographs.

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 off-axis 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 complex-shifted 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 three-dimensional and two-dimensional form-invariant half-Pearcey beams (HP-beams). HP-beams generalize Pearcey beams obtained in Opt. Express, 20, 18955 (2012), since these Pearcey beams can be considered as the sum of two first-order HP-beams. Three-dimensional HP-beams have angular spectrum of plane waves, which is non-zero at a half of parabola. For functions of HP-beams complex amplitudes, the orthogonality properties have been revealed. For two-dimensional HP-beam 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 graded-index 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 semi-axis is in a perpendicular plane to the incident beam polarization plane.

Current scientific interests:

– mathematical theory of diffraction;
– computational electrodynamics;
– optical vortices and orbital angular momentum of light;
– photonic-crystal devices (waveguides, lenses).

Main publications of last three years:

1. A.A. Kovalev, V.V. Kotlyar, "Orbital angular momentum of superposition of identical shifted vortex beams," J. Opt. Soc. Am. A 32 (10), 1805–1810 (2015).
2. A.A. Kovalev, V.V. Kotlyar, A.P. Porfirev, "Shifted nondiffractive Bessel beams," Phys. Rev. A. 91 (5), 053840 (2015).
3. A.A. Kovalev, V.V. Kotlyar, S.G. Zaskanov, A.P. Porfirev, "Half Pearcey laser beams," J. Opt. 17(3), 035604 (7 pp) (2015).
4. V.V. Kotlyar, A.A. Kovalev, "Hermite–Gaussian modal laser beams with orbital angular momentum," J. Opt. Soc. Am. A 31 (2), 274–282 (2014).
5. V.V. Kotlyar, A.A. Kovalev, "Airy beam with a hyperbolic trajectory," Opt. Commun. 313, 290–293 (2014).
6. V.V. Kotlyar, A.A. Kovalev and A.G. Nalimov, "Propagation of hypergeometric laser beams in a medium with a parabolic refractive index," J. Opt. 15(12), 125706 (10 pp) (2013).
7. V.V. Kotlyar, A.A. Kovalev, S.S. Stafeev and A.G. Nalimov, "An asymmetric optical vortex generated by a spiral refractive plate," J. Opt. 15(2), 025712 (8 pp) (2013).
8. V.V. Kotlyar, S.S. Stafeev, Y. Liu, L. O’Faolain, and A.A. Kovalev, "Analysis of the shape of a subwavelength focal spot for the linearly polarized light," Appl. Opt. 52(3), 330–339 (2013).