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.

Target-in-the-loop wavefront sensing and control with a Collett-Wolf beacon: speckle-average phase conjugation.

Adaptive optical systems for laser beam projection onto an extended target embedded in an optically inhomogeneous medium are considered. A new adaptive optics wavefront control technique--speckle-average (SA) phase conjugation--is introduced. In this technique mitigation of speckle effects related to laser beam scattering off the rough target surface is achieved by measuring the SA wavefront slopes of the target return wave using a conventional Shack-Hartmann wavefront sensor. For statistically representative speckle averaging we consider the generation of an incoherent light source, referred to here as a Collett-Wolf beacon, directly on the target surface using a rapid steering (scanning) auxiliary laser beam. Our numerical simulations and experiment show that control of the outgoing beam phase using SA phase conjugation can lead to efficient compensation of turbulence effects and results in an increase of the projected laser beam power density on a remote extended target. The impact of both target anisoplanatism and the Collett-Wolf beacon size on adaptive system performance is studied.

Adaptive laser beam projection on an extended target: phase- and field-conjugate precompensation.

The problem of adaptive laser beam projection onto an extended object (target) having a randomly rough surface in an optically inhomogeneous medium (atmosphere) is analyzed. Outgoing beam precompensation is considered through conjugation of either the target-return wave phase or the complex field. It is shown that in the presence of "frozen" turbulence, both phase-conjugate (PC) and field-conjugate (FC) precompensation can result in a superfocusing effect, which suggests the possibility of achieving a brighter target hit spot in volume turbulence than in vacuum. This superfocusing effect is significantly more distinct for FC precompensation. In the quasi-stationary case (slowly moving turbulence or target), PC and FC beam control lead to enhanced intensity fluctuations at the target surface associated with intermittent formation and disintegration of bright target hit spots that sporadically attach to the extended target surface. This intensity fluctuation level exceeds intensity fluctuations in the absence of beam control and is higher for FC precompensation. In the nonstationary case, both PC and FC lead to an increase of beam width and centroid wander at the extended target surface compared with conventional projection of a collimated or focused beam.

Speckle-field propagation in 'frozen' turbulence: brightness function approach.

Speckle-field long- and short-exposure spatial correlation characteristics for target-in-the-loop (TIL) laser beam propagation and scattering in atmospheric turbulence are analyzed through the use of two different approaches: the conventional Monte Carlo (MC) technique and the recently developed brightness function (BF) method. Both the MC and the BF methods are applied to analysis of speckle-field characteristics averaged over target surface roughness realizations under conditions of 'frozen' turbulence. This corresponds to TIL applications where speckle-field fluctuations associated with target surface roughness realization updates occur within a time scale that can be significantly shorter than the characteristic atmospheric turbulence time. Computational efficiency and accuracy of both methods are compared on the basis of a known analytical solution for the long-exposure mutual correlation function. It is shown that in the TIL propagation scenarios considered the BF method provides improved accuracy and requires significantly less computational time than the conventional MC technique. For TIL geometry with a Gaussian outgoing beam and Lambertian target surface, both analytical and numerical estimations for the speckle-field long-exposure correlation length are obtained. Short-exposure speckle-field correlation characteristics corresponding to propagation in 'frozen' turbulence are estimated using the BF method. It is shown that atmospheric turbulence-induced static refractive index inhomogeneities do not significantly affect the characteristic correlation length of the speckle field, whereas long-exposure spatial correlation characteristics are strongly dependent on turbulence strength.

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.