Valeriy V. Kolosov

Target-in-the-loop beam control: basic considerations for analysis and wave-front sensing

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related to maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive-index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing coherent outgoing-wave propagation, and the equation describing evolution of the mutual correlation function (MCF) for the backscattered wave (return wave). The resulting evolution equation for the MCF is further simplified by use of the smooth-refractive-index approximation. This approximation permits derivation of the transport equation for the return-wave brightness function, analyzed here by the method of characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wave-front sensors that perform sensing of speckle-averaged characteristics of the wave-front phase (TIL sensors). Analysis of the wave-front phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric-turbulence-related phase aberrations. We also show that wave-front sensing results depend on the extended target shape, surface roughness, and outgoing-beam intensity distribution on the target surface. For targets with smooth surfaces and nonflat shapes, the target-induced phase can contain aberrations. The presence of target-induced aberrations in the conjugated phase may result in a deterioration of adaptive system performance.

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.

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.

Bit error rate in free-space optical communication systems with a partially coherent transmitting beam

The influence of the degree of transmitting beam coherence on the bit error rate in free-space optical communication systems is studied. It is found that there are optimal values of the output power and degree of coherence of a transmitter optical beam, defined by the Fried radius, for all types of propagation paths (horizontal, vertical, or inclined) and different degrees of manifestation of turbulent effects. The optimal degree of coherence can be determined from the calculated BER minimum.

Anisoplanatic turbulence correction in incoherent imaging by using reference sources with different wavelengths

The possibility of the phase compensation of turbulent distortions of incoherent images of an object illuminated by radiation with different wavelengths is investigated. The research is carried out based on the method that is a further improvement of the algorithm for the numerical simulation of incoherent imaging through the atmosphere in conditions of anisoplanatic turbulence developed by the authors [Lachinova S.L., Vorontsov M.A., Dudorov V.V., Kolosov V.V., Valley M.T. // Proc. SPIE. 2007. V. 6708. 67080E]. The dependence of the degree and region of the enhancement of the image on the ratio of the reference wavelength to the image-forming radiation one is shown.

Orbital angular momentum of a laser beam in a turbulent medium: preservation of the average value and variance of fluctuations

The process of the propagation of vortex laser beams in a turbulent atmosphere with recording of the total orbital angular momentum (OAM) and determination of the beams statistical characteristics, such as the average over realizations of the turbulent medium and the variance of fluctuations, has been simulated numerically. The dependences of OAM fluctuations on the turbulence intensity and the initial topological charge of the beam have been obtained. Numerical results are compared with the earlier asymptotic estimates.

Properties of vortex beams formed by an array of fibre lasers and their propagation in a turbulent atmosphere

Using a numerical simulation, we investigate the possibility of synthesising vortex laser beams with a variable orbital angular momentum by a hexagonal array of fibre lasers under a phase control of individual subapertures of the array. We report the requirements to the parameters of the device generating a vortex beam (number and size of subapertures, as well as their mutual arrangement). The propagation dynamics of synthesised vortex beams is compared with that of conventional Laguerre–Gaussian beams in free space and in a turbulent atmosphere. The spectral properties of the synthesised beam, represented as a superposition of different azimuthal modes, are determined during its propagation in free space. The energy and statistical parameters of the synthesised and Laguerre–Gaussian vortex beams are shown to coincide with increasing propagation distance in a turbulent medium.

Anisoplanatic imaging through atmospheric turbulence: brightness function approach

We present the development of a novel technique for numerical simulation and analysis of wide field-of-view (FOV) incoherent and anisoplanatic imaging of an object through volume turbulence. This technique is based on the recently developed brightness function method [J. Opt. Soc. Am. A, v. 22, p. 126 (2005)]. We present computer simulation results demonstrating the anisoplanatic turbulence effects on an object image quality.

Scintillations of optical vortex in randomly inhomogeneous medium

The comparative numerical and analytical analysis of scintillation indices of the vortex Laguerre–Gaussian beam and the nonvortex doughnut hole and Gaussian beams propagating in the randomly inhomogeneous atmosphere has been performed. It has been found that the dependence of the scintillation index at the axis of the optical vortex on the turbulence intensity at the path has the form of a unit step. It has been shown that the behavior of scintillations in the cross sections of vortex and nonvortex beams differs widely. Despite the scintillation index of vortex beams has been calculated only for the simplest LG01 mode, the obtained results are quite general, because they demonstrate the main properties inherent in scintillations of vortex beams of any type.

Accounting for the effect of large-scale atmospheric inhomogeneities in problems of laser radiation propagation along long high-altitude paths

We show that large-scale atmospheric inhomogeneities observed experimentally can significantly affect optical radiation propagation along long paths, and it is impossible to take into account this effect within the classical turbulence model. We suggest a new algorithm for numerical simulation of laser beam propagation along long low-inclined atmospheric paths with large-scale atmospheric inhomogeneities, which allows one to consider beam refraction and focusing at large-scale inhomogeneities along with beam distortions due to small-scale inhomogeneities and regular refraction in a vertical plane.