Valerii P. Aksenov

Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor

Reconstruction the phase front of a vortex laser beam is conducted by use of a Hartmann-Shack wavefront sensor. The vortex beam in the form of the Laguerre-Gaussian LG(0)(1) mode is generated with the help of a spiral phase plate. The new reconstruction technique based on measured wavefront gradients allows one to restore the singular phase surface with good accuracy, whereas the conventional least-squares approach fails.

Fluctuations of retroreflected laser radiation in a turbulent atmosphere

The problem of fluctuations of the laser radiation field retroreflected from a target in a turbulent atmosphere is formulated based on the equations of statistical moments of the location Green function. The asymptotic methods for solving the above equations were used to investigate spatial coherence, mean value, and normalized variance and covariance of retroreflected radiation intensity in the case of weak and strong turbulence. The reflections of plane and spherical waves from a mirror and a diffuse target were considered. It is ascertained that, in some cases, the scales of the mutual coherence function of the retroreflected field were statistically inhomogeneous. The effect of amplification of fluctuation intensity is the strongest for a point reflector. The level of the residual covariance strongly depends on the field at the transmitting aperture, the type of the target, and its dimensions.

The influence of the vortex phase on the random wandering of a Laguerre?Gaussian beam propagating in a turbulent atmosphere: a numerical experiment

A numerical experiment is used to study the variance of the wandering of a Laguerre–Gaussian laser beam propagating in a turbulent atmosphere. It is shown that a laser beam with an initial intensity distribution coinciding with that of the Laguerre–Gaussian beam but not having a vortex phase distribution is less resistant to the action of atmospheric turbulence than the Laguerre–Gaussian beam except in the near diffraction zone. The regularities of the beam wandering associated with the values of the azimuth and radial indices of the beam as well as with the intensity and the outer scale of the turbulence are determined.

Increase in laser beam resistance to random inhomogeneities of atmospheric permittivity with an optical vortex included in the beam structure

The role of the vortical phase in the initial structure of the wave field of a laser beam propagating in the turbulent atmosphere in statistical regularities of beam wandering is studied. It is found that in the near diffraction zone the variances of wandering of the vortical beam and the fundamental Gaussian beam turns out to be identical, if the initial radius of the Gaussian beam is equal to the radius of the ring intensity distribution of the vortical beam. In the far diffraction zone, the vortical beam wanders more slightly than the Gaussian beam with the same effective radius of the initial intensity distribution does. It is also shown that laser beams with the initial ring intensity distribution similar to the intensity distribution of a vortical beam, but not having the vortical phase distribution, are less resistant to the atmospheric turbulence than the vortical beam.

Correction of vortex laser beam in a closed-loop adaptive system with bimorph mirror

The phase correction of a vortex laser beam is undertaken in the closed-loop adaptive system including a Hartmann-Shack wavefront sensor with singular reconstruction technique and a bimorph piezoceramic mirror. After correction the vortex doughnutlike beam is focused into a beam with bright axial spot that considerably increases the Strehl ratio and optical system resolution. Since the phase break cannot be exactly reproduced on the flexible mirror surface, off-axis vortices appear in the far field at the beam periphery.

Theory of singular-phase reconstruction for an optical speckle field in the turbulent atmosphere

Analytical expressions are derived and computational algorithms are constructed for retrieving optical-field phase distribution under strong scintillation. The input data for the phase reconstruction are the wave-front slopes registered by a Hartmann sensor or shearing interferometer. The theory is based on representing the slope-vector field as the sum of its potential and solenoid components; it introduces the concept of phase-source and phase-vortex density and uses strict integral expressions relating these quantities to the wave-front slopes. To overcome the difficulties arising from the singular character of phase distribution, use is made of regularization of the wave-front slopes. The slopes can be measured with an ideal point wave-front sensor. It is shown that the slopes measured at the output of a nonideal sensor can be treated as regularized values of these slopes. Numerical simulation of phase unwrapping from the reference values of the wave-front slopes has shown that the algorithm designed for visualization of local phase singularities and those for phase reconstruction are very helpful in eliminating the measurement noise.

Potential and vortex features of optical speckle fields and visualization of wave-front singularities

The feasibility of noninterferometric methods to measure phase distribution in a laser beam cross section for visualization of the vortex dislocations of an optical speckle-field wave front is analyzed. Peculiarities of the phase retrieved from the measured intensity distribution (the phase problem in optics) and from the wave-front slopes measured by a Hartmann sensor are discussed. A concept of the vortex and the potential parts of the phase is introduced. An analytic formula to retrieve the potential phase from the measured intensity has been obtained. We show that the considered means of measurements allow the positions of the dislocation centers to be sensed and the spatial configuration of the intensity zero lines to be reconstructed.

Random wandering of laser beams with orbital angular momentum during propagation through atmospheric turbulence

The propagation of laser beams having orbital angular momenta (OAM) in the turbulent atmosphere is studied numerically. The variance of random wandering of these beams is investigated with the use of the Monte Carlo technique. It is found that, among various types of vortex laser beams, such as the Laguerre-Gaussian (LG) beam, modified Bessel-Gaussian beam, and hypergeometric Gaussian beam, having identical initial effective radii and OAM, the LG beam occupying the largest effective volume in space is the most stable one.

Fluctuations of orbital angular momentum of vortex laser-beam in turbulent atmosphere

This paper studies the effect of turbulence on the orbital angular momentum (OAM) of the Laguerre-Gaussian beam propagating through the atmosphere. An integral representation of laser beam OAM through the beam intensity distribution and the gradient of the medium permittivity is derived. The equations are obtained for the first OAM statistical moments: the mean and the mean square. It is shown that the OAM value, averaged over medium realizations, coincides with the OAM value in a homogeneous medium. Asymptotic equations are derived, which allow OAM fluctuations to be estimated under the extreme conditions of weak and strong turbulence, depending on the diffraction parameters of the beam. It is found that the rate of growth of OAM fluctuations increases, as the propagating beam passes from the conditions of weak turbulence to the conditions of strong turbulence.

The effect of optical vortex on random Laguerre-Gauss shifts of a laser beam propagating in a turbulent atmosphere

The work is devoted to studying the random walk of the center of mass of a vortex laser beam propagating in a medium with inhomogeneities in the dielectric permittivity. The beam is the circular mode of the Laguerre-Gauss beam LG0l. We have obtained estimates of the effect of turbulent propagation conditions, diffraction parameters, and azimuthal index (topological charge) of the beam on the magnitude of the variance of its center of mass displacements. We detected the “gyroscope effect” in which random displacements of the center of mass of the vortex of the laser beam turn out to be as small as the topological charge of the optical vortex included in the beam is large.