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On October 13, 2019 is the ninetieth birthday of the renowned physicist Professor Valerian I. Tatarskii. He is one of the founders of the international journal Waves in Random and Complex Media and its Associate Editor from 1991 to 1998. Outstanding seminal works of Professor V. I. Tatarskii made a global impact on physical science. The article describes main milestones of his life in science and his achievements in the theory of wave propagation in random media. [ABSTRACT FROM AUTHOR]

In a previous study [J. Opt.19, 0905603 (2017)JOOPDB0150-536X10.1088/2040-8986/aa7cac], we revealed that the complete second-order statistics of narrowband polarized waves are characterized by 13 parameters, in contrast to the four parameters of the traditional Stokes vector description of the statistics of partially polarized light. In this study, we analyzed the second-order statistics of the field of a randomly rotating source of electromagnetic radiation and showed that it includes covariance of the right- and left-circular polarizations that are not captured by the Stokes vector formalism. We illustrate this finding using simple examples of rotating quadrupoles and dipole pairs.

We propose a concept of devising the authentic cross spectral densities (CSDs) of partially coherent beam waves by averaging the second moment of a coherent field over a certain number of random parameters. Several CSD examples created by randomization are presented. We discuss application of randomization to generation of twisted Gaussian Schell model beams and show that compound randomization leads to a new, more general class of twisted beams. We revisit the necessary nonnegative definiteness condition of Opt. Lett.34, 1399 (2009)OPLEDP0146-959210.1364/OL.34.001399 and show that the two-dimensional space of parameters is necessary.

Point spread function (PSF) for imaging through inhomogeneous refractive medium, such as atmospheric turbulence, is bounded by three constraints [Opt. Eng.52, 046001 (2013)OPEGAR0091-328610.1117/1.OE.52.4.046001]. PSF is non-negative, band-limited, and the third constraint, related to the energy conservation principle, warrants the absence of fluctuations in the image of a uniformly bright object. We develop a version of the common warp and blur model for the anisoplanatic image distortions by turbulence that satisfies these three constraints. In order to comply with the third constraint, our model supplements warp and blur by a random PSF power, which was found to be related to the Jacobian of the warp field. We illustrate statistics of the warp and blur using a simple example of anisoplanatic phase screen.

Comprehensive analysis of non-diffracting optical waves with two-point binomial coherence function (BCF) is presented. This coherence function consists of two terms, each depending on either separation of points or the central point. We establish the necessary and sufficient conditions for nonnegative definiteness of the BCFs. Spectral analysis, including calculations of the eigenvalues and eigenfunctions, for the general BCF case is presented. We consider two simple BCF examples of and analyzed the conditions leading to the maximum irradiance contrast.

We show that the Green's function proposed in a recent paper by M. Fu and Y. Zhao [Opt. Express29(4), 6257 (2021)10.1364/OE.418065] does not satisfy Helmholtz equation and thus cannot be used to describe monochromatic light propagation from a spherical surface.

We show that the "intensity bump" cross-spectral density used in Opt. Lett.45, 698 (2020)OPLEDP0146-959210.1364/OL.385246 does not satisfy the non-negative definiteness requirement and cannot be used as a cross-spectral density model.

In the study, we introduce a new technique, sparse spectrum with uniform wave vectors (SU), for generation of phase screen samples. In a manner similar to the known sparse spectrum (SS) technique, it uses a trigonometric series with random discrete spectral support. However, in contrast to the SS technique, random wave vectors are uniformly distributed on individual segments of the wave vector plane partition in the SU technique. We compare the accuracy and computational effectiveness of the SU technique with the subharmonics complemented discrete Fourier transform (DFT) technique, SS technique, and randomized DFT technique [ J. Opt. Soc. Am. B36, 3249 (2019)JOBPDE0740-322410.1364/JOSAB.36.003249]. The SU and SS techniques generate unbiased samples and indicate superior computational effectiveness for 1 MP and larger screens.

Following the development of the companion paper [J. Opt. Soc. Am.36, 1433 (2019)JOAOD60740-323210.1364/JOSAA.36.00XXXX], additional models for the coherence of quasi-monochromatic light are constructed by placing incoherent monopole and dipole sources inside a spherical ball and on a circular plane disk. The paraxial approximation, which is valid for sunlight, reduces the number of different models from eight to three. Based on the solar images corresponding to these three models, the ball model is considered the most appropriate. The ball model can be modified to match the limb-darkening observations.

Models for the coherence of quasi-monochromatic light from spherical incoherent sources are constructed by placing incoherent monopole and dipole sources on the surface of a sphere. All models allow for relatively simple numerical calculations of coherence functions for arbitrary source sizes and positions of observation points. We show analytically and confirm numerically that the far-field regime for transverse coherence is formed at distances larger than the source size, regardless of the wavelength.

A complete asymptotic theory for the aperture-averaged orbital angular momentum (OAM) variance is developed for both weak and strong fluctuation conditions, based on the asymptotic expansions of the Feynman path-integral solution for the fourth-order coherence function of a spherical wave propagating through a random inhomogeneous medium. We show that the OAM fluctuation averaging is very different for circular-symmetric and non-circular-symmetric apertures. Aperture averaging of the OAM fluctuations does not obey the standard "square root" law, and the weak/strong fluctuation conditions for the aperture-averaged OAM are not defined solely by the values of the scintillation index of the incident wave.

A parabolic equation for electromagnetic wave propagation in a random medium is extended to include the depolarization effects in the narrow-angle, forward-scattering setting. Closed-form parabolic equations for propagation of the coherence tensor are derived under a Markov approximation model. For a general partially coherent and partially polarized beam wave, this equation can be reduced to a system of ordinary differential equations, allowing a simple numeric solution. An analytical solution exists for statistically homogeneous waves. Estimates based on the perturbation solution support the common knowledge that the depolarization at the optical frequencies is negligible for atmospheric turbulence propagation. These results indicate that the recently published theory [Opt. Lett.40, 3077 (2015)10.1364/OL.40.003077] is not valid for atmospheric turbulence.

A recently introduced [J. Opt. Soc. Am. A30, 479 (2013)10.1364/JOSAA.30.000479JOAOD61084-7529] sparse spectrum (SS) model of statistically homogeneous random fields makes it possible to generate 3D samples of refractive-index fluctuations with prescribed spectral density at a very reasonable computational cost. The SS technique can be used in the framework of the split-step Fourier method for numerical simulation of wave propagation in turbulence. It allows generation of the phase screen samples that are free from the limitations of the Markov approximation, which is commonly used for theoretical description and numerical modeling of optical waves propagation through turbulence. We investigate statistics of these phase screens and present a numerical algorithm for their generation.

Beam spread and beam wandering are the most perceptible effects of atmospheric turbulence on propagating laser beams. The width of the mean irradiance profile is typically used to characterize the beam spread. This so-called long-term (LT) statistic allows for a relatively simple theoretical description. However, the LT beam size is not a very practical measure of the beam spread because its measurements are sensitive to the movements of the source and detector, and to the large-scale variations of the refractive index that are not associated with turbulence. The short-term (ST) beam spread is measured relative to the instantaneous position of the beam center and is free of these drawbacks, but has not been studied as thoroughly as the LT spread. We present a theoretical model for the ST beam irradiance that is based on the parabolic equation for the beam wave propagation in random media, and the Markov approximation for calculation of the statistics of the optical field, and discuss an approximation that allows introduction of the isoplanatic ST point spread function (PSF). Unlike the LT PSF, the ST PSF depends on the overall beam geometry. This allows optimization of the initial beam field in terms of minimizing the ST beam size at the observation plane. Calculations supporting this conjecture are presented for the simple case of the coherent Gaussian beam, and Kolmogorov turbulence.

Extended Huygens-Fresnel principle (EHF) currently is the most common technique used in theoretical studies of the optical propagation in turbulence. A recent review paper [J. Opt. Soc. Am. A31, 2038 (2014)JOAOD60740-323210.1364/JOSAA.31.002038] cites several dozens of papers that are exclusively based on the EHF principle. We revisit the foundations of the EHF, and show that it is burdened by very restrictive assumptions that make it valid only under weak scintillation conditions. We compare the EHF to the less-restrictive Markov approximation and show that both theories deliver identical results for the second moment of the field, rendering the EHF essentially worthless. For the fourth moment of the field, the EHF principle is accurate under weak scintillation conditions, but is known to provide erroneous results for strong scintillation conditions. In addition, since the EHF does not obey the energy conservation principle, its results cannot be accurate for scintillations of partially coherent beam waves.

Recent calculations [J. Opt. Soc. Am. A31, 1963 (2014)JOAOD60740-323210.1364/JOSAA.31.001963] of the scintillation index of focused beams did not take into account the second order of the perturbation theory, and therefore led the author to erroneous conclusions regarding dependence of the scintillation index for the focused beams on the aperture size. The log-normal intensity probability distribution used for the Bit Error Rate calculations in [J. Opt. Soc. Am. A31, 1963 (2014)JOAOD60740-323210.1364/JOSAA.31.001963] is also invalid for the wide focused beams. As a result, most of the conclusions of [J. Opt. Soc. Am. A31, 1963 (2014)JOAOD60740-323210.1364/JOSAA.31.001963] are incorrect.

A recently published sparse spectrum (SS) model of the phase front perturbations by atmospheric turbulence [J. Opt. Soc. Am. A 30, 479 (2013)] is based on the trigonometric series with discrete random support. The SS model enables fewer computational efforts, while preserving the wide range of scales typically associated with turbulence perturbations. We present an improved version of the SS model that accurately reproduces the power-law spectral density of the phase fluctuations in the arbitrary wide spectral band. We examine the higher-order statistics of the SS phase samples for four versions of the SS model. We also present the calculations of the long-exposure Strehl numbers and scintillation index for the different versions of the SS model. A nonoverlapping SS model with a log-uniform partition emerges as the most appropriate for the atmospheric turbulence representation.

Monte Carlo (MC) simulation of phase front perturbations by atmospheric turbulence finds numerous applications for design and modeling of the adaptive optics systems, laser beam propagation simulations, and evaluating the performance of the various optical systems operating in the open air environment. Accurate generation of two-dimensional random fields of turbulent phase is complicated by the enormous diversity of scales that can reach five orders of magnitude in each coordinate. In addition there is a need for generation of the long "ribbons" of turbulent phase that are used to represent the time evolution of the wave front. This makes it unfeasible to use the standard discrete Fourier transform-based technique as a basis for the MC simulation algorithm. We propose a new model for turbulent phase: the sparse spectrum (SS) random field. The principal assumption of the SS model is that each realization of the random field has a discrete random spectral support. Statistics of the random amplitudes and wave vectors of the SS model are arranged to provide the required spectral and correlation properties of the random field. The SS-based MC model offers substantial reduction of computer costs for simulation of the wide-band random fields and processes, and is capable of generating long aperiodic phase "ribbons." We report the results of model trials that determine the number of sparse components, and the range of wavenumbers that is necessary to accurately reproduce the random field with a power-law spectrum.

In J. Opt. Soc. Am. A 29, 169 (2012), Gerçekcioğlu and Baykal presented an investigation of the dependence of the scintillation index of flat-topped Gaussian beams on the exponent α of the power-law-type spectra of non-Kolmogorov turbulence. In particular, they found that the scintillation index reaches a maximum at α≈3.2. We show that this conclusion is an artifact of their specific calculation, and depends on the choice of the length unit. Gerçekcioğlu and Baykal's calculations are made for the 3<α<5 range of the spectral exponent. We show that for the homogeneous and isotropic turbulence the correct range is 3<α<4, when Markov approximation is used.

This review paper addresses typical mistakes and omissions that involve theoretical research and modeling of optical propagation through atmospheric turbulence. We discuss the disregard of some general properties of narrow-angle propagation in refractive random media, the careless use of simplified models of turbulence, and omissions in the calculations of the second moment of the propagating wave. We also review some misconceptions regarding short-exposure imaging, propagation of polarized waves, and calculations of the scintillation index of the beam waves., (© 2012 Optical Society of America)

We extend our theory of on-axis beam scintillations [Waves Random Media 4, 243 (1994)] for the case of propagation on slant turbulent paths, where turbulence is concentrated in a relatively thin layer near the transmitter. Our technique is based on the parabolic equation for optical wave propagation and the Markov approximation for the calculation of statistical moments of beam intensity. This first of two companion papers presents the details of the path integral formulation of the solution for the fourth-order coherence function. We also discuss in detail two analytic techniques that can be used for the treatment of the path integrals.

On the basis of the analytic techniques presented in the first of these two companion papers [J. Opt. Soc. Am. A27, 2169 (2010)] we present the complete asymptotic analysis of the axial beam scintillation index for coherent Gaussian beams on the ground-to-space propagation paths. The ratio of turbulence layer thickness to overall propagation path length contributes an additional small parameter to the analysis. We show that it is possible to use three dimensionless parameters to describe the problem and that the general arrangement of the asymptotic regions established in our earlier work [Waves Random Media 4, 243 (1994)]) is preserved. We find that on a slant propagation path, collimated beams can experience the unusual double-scattering-dominated scintillation found originally for focused beams.

I present a simple theoretical model for dewarped imaging through a turbulent medium and calculate the degree of superresolution that can be attained by dewarping the distorted instantaneous images registered through a turbulent atmosphere. The estimates show that on 1 km near the ground propagation path, spatial frequencies of the dewarped image can exceed the diffraction limit three times with a probability up to 10%.