Vladimir P. Lukin

Beam spreading of vortex beams propagating in turbulent atmosphere

We present some results obtained by numerical modeling of the propagation of vortex beams LG(0l) through a randomly inhomogeneous medium. The vortex beams are the lower order Laguerre-Gaussian modes. Such beams, if propagated under conditions of weak turbulence, also experience distortions, like a Gaussian beam. However, the statistically averaged vortex beams (LG(0l)) conserve the central intensity dip with a nonzero intensity on the beam axis. The beam broadening of vortex beams is analyzed. The average vortex beams are found to be broadened less than the Gaussian beam while propagated through a randomly inhomogeneous medium. The higher the topological charge l is, the smaller the beam broadening is.

Dynamic characteristics of optical adaptive systems

The effect of time delay on characteristics of an optical adaptive system is considered. Classification of the optical adaptive systems as dynamic feedback systems has been made. Systems with constant delay, a highspeed adaptive system as well as a new class of systems, i.e., predicting adaptive systems, are investigated.

Adaptive Beaming and Imaging in the Turbulent Atmosphere

Adaptive Beaming and Imaging in the Turbulent Atmosphere (SPIE Press Monograph Vol. PM109) By Vladimir P. Lukin, Boris V. Fortes Due to the wide application of adaptive optical systems, an understanding of optical wave propagation in randomly inhomogeneous media has become essential, and several numerical models of individual AOS components and of efficient correction algorithms have been developed. This monograph contains detailed descriptions of the mathematical experiments that were designed and carried out during more than a decades worth of research.

Phase-correction of turbulent distortions of an optical wave propagating under conditions of strong intensity fluctuations.

Phase correction of a plane wave and a spatiolimited beam propagating through a turbulent layer of atmosphere were considered. The required adaptive corrector element size and the system bandwidth were found by numerical simulation. These requirements were determined to be the same as for a weak-intensity scintillation approximation. The size of the required segmented mirror element was found to be equal to Fried length r0, whereas the tolerable time lag was r0/V, where V is the wind velocity. However, the local slope sensors then became impractical, as did tip-tilt correction over the corrector subapertures.

Optical measurements of the outer scale of the atmospheric turbulence

The atmospheric turbulence spectrum even in the surface layer differ by the larger dynamical range and, in accordance with it, in view of the finite correctness of the optical measurements by themselves, cannot be reconstructed from the measuring of any one of the optical wave parameters. Measurements of the fluctuations of the optical wave phase can be used for investigation of the energy range of the turbulence spectrum.

Modeling of the image observed through a turbulent atmosphere

Computer simulations of a wavefront distorted by atmospheric turbulence are considered focusing on large scale and dynamic simulations. Attention is also given to wavefront sensor and wavefront corrector simulations. Computer modeling of adaptive optical systems takes into account an optical wave field in the plane of receiving aperture, a wavefront distortion sensor, a wavefront distortion corrector, and quantum fluctuation of the optical wave intensity.

Causes of non-Kolmogorov turbulence in the atmosphere.

In the present work, we briefly describe a model for atmospheric turbulence energy on the basis of experimental data obtained in Siberia. A series of new studies is considered and the results of our long-term experimental observations are summarized. The results of these studies form the basis for an explanation of some effects in interactions between optical waves and atmospheric turbulence. Our numerous experimental results point to the possible generation of so-called coherent turbulence in the atmosphere. When analyzing the problem, we proceeded based on our own experimental data and comprehension that the coherent turbulence is a result of the action of self-organizing nonlinear processes, which run in continuous media, including atmospheric air. The experimental data confirmed the effect of attenuation of light fluctuations in coherent turbulence.

Features of optical image jitter in a random medium with a finite outer scale

Features of optical wave fluctuations while propagating through a randomly inhomogeneous turbulent medium with a finite outer scale are considered, including conditions when areas with dominating influence of one large-scale coherent structure are observed in the atmosphere, for which the spectrum of atmospheric turbulence can differ significantly from the Kolmogorov-model spectrum. Using an approximate model of the spectrum for coherent turbulence, described earlier in our works, the variance of jitter of an optical image is calculated (under the applicability condition for the smooth perturbation method). The comparison of these equations with known similar equations for Kolmogorov turbulence has shown that the variance of fluctuations are significantly weaker in coherent turbulence than in the Kolmogorov theory under similar conditions. This means that phase fluctuations of optical radiation decrease significantly in coherent turbulence. The importance of this conclusion is noted for interpretation of the results of optical sounding of atmospheric turbulence.

Phase correction of an image turbulence broadening under conditions of strong intensity fluctuations

Phase correction of a plane wave, propagating through a turbulent layer, is considered. The required adaptive corrector element size and the system bandwidth were found by numerical simulation. These requirements were determined to be the same as for weak intensity scintillation approximation. The size of the required segmented mirror element was found to be equal to Fried length r0 while the tolerable time lag was r0/V, where V is the wind velocity. However, the local slope sensors become therewith impractical as well as the tip-tilt correction over the corrector subapertures.

Comparison of Kolmogorov’s and coherent turbulence

Features of optical wave fluctuations while propagating through a randomly inhomogeneous turbulent medium with a finite outer scale are considered, including conditions when areas with dominating influence of one large-scale coherent structure are observed in the atmosphere, for which the spectrum of atmospheric turbulence can differ significantly from the Kolmogorov model spectrum. Using an approximate model of the spectrum for coherent turbulence, described earlier in our works, the variance of jitter of an optical image is calculated (under the applicability condition for the smooth perturbation method). The comparison of these equations with known similar equations for Kolmogorov turbulence has shown that the variance of fluctuations is significantly weaker in coherent turbulence than in the Kolmogorov theory under similar conditions. This means that phase fluctuations of optical radiation decrease significantly in coherent turbulence. The importance of this conclusion is noted for interpretation of the results of optical sounding of atmospheric turbulence.