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Correlations of the phase gradients of the light wave propagating in a turbulent medium in the regime of strong scintillations

V. A. Bogachev, I. V. Kolokolov, V. V. Lebedev, A. V. Nemtseva, F. A. Starikov

Abstract

We investigate analytically and numerically correlation functions of the phase of light waves that propagate through turbulent media. We examine the case of strong scintillations that occur at large values of the Rytov dispersion, $σ^2_R$. Then, it is possible to relate the pair correlation function of phase gradients to the known pair correlation function of the envelope dependent on the distance $r$ assuming Gaussianity of the envelope of the beam. Our direct numerical simulations show that the profile of the pair correlation function for phase gradients gradually approaches the theoretical expression as the value of $σ_R^2$ increases, if $r<r_0$ where $r_0$ is the Fried length. For larger $r$ the behavior of the computed correlation function is quite different because of destroying the Gaussianity.

Correlations of the phase gradients of the light wave propagating in a turbulent medium in the regime of strong scintillations

Abstract

We investigate analytically and numerically correlation functions of the phase of light waves that propagate through turbulent media. We examine the case of strong scintillations that occur at large values of the Rytov dispersion, . Then, it is possible to relate the pair correlation function of phase gradients to the known pair correlation function of the envelope dependent on the distance assuming Gaussianity of the envelope of the beam. Our direct numerical simulations show that the profile of the pair correlation function for phase gradients gradually approaches the theoretical expression as the value of increases, if where is the Fried length. For larger the behavior of the computed correlation function is quite different because of destroying the Gaussianity.
Paper Structure (6 sections, 30 equations, 3 figures)

This paper contains 6 sections, 30 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Main relations
  3. Analytic derivation
  4. Numerics
  5. Explanation
  6. Conclusion

Figures (3)

  • Figure 1: The output intensity as a function of $x,y$ (the upper graph) and its dependence on $x$ at $y=0$ (the lower graph) for $\sigma_R^2 =5.73$, $r_0=0.62$ cm. The dashed line represents the ideal intensity profile that would be observed in the absence of turbulence.
  • Figure 2: The normalized pair correlation function of the envelope (\ref{['paircorrfu']}) as a function of $r/r_0$ for $\sigma_R^2=1.05$, $r_0=2.94$ cm (the upper graph) and $\sigma_R^2=5.73$, $r_0=0.62$ cm (the lower graph. The solid line is drawn using the analytic expression (\ref{['BKLS24']}) and the filled squares represent the numerical data extracted from the simulations.
  • Figure 3: The off-diagonal component $Q_{xy}$ of the pair correlation of the phase gradients (\ref{['kgrph1']}) multiplied by $-r_0^2$ taken at $x=y$ as a function of $r/r_0$, for $\sigma_R^2=1.05$, $r_0=2.94$ cm (the upper graph), $\sigma_R^2=3.1$, $r_0=1.28$ cm (the middle graph), $\sigma_R^2=5.73$, $r_0=0.62$ cm (the lower graph). The solid line represents the analytical expression obtained from the zeroth order of the perturbation theory, the dashed line is drawn by using the expression (\ref{['kgrph18']}), and the filled squares represent the numerical data extracted from the simulations.