29 September 2017 Modelling of propagation and scintillation of a laser beam through atmospheric turbulence
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The investigation was fulfilled on the basis of the Navier-Stokes equations for viscous heat-conducting gas. The Helmholtz decomposition of the velocity field into a potential part and a solenoidal one was used. We considered initial vorticity to be small. So the results refer only to weak turbulence. The solution has been represented in the form of power series over the initial vorticity, the coefficients being multiple integrals. In such a manner the system of the Navier- Stokes equations was reduced to a parabolic system with constant coefficients at high derivatives. The first terms of the series are the main ones that determine the properties of acoustic radiation at small vorticity. We modelled turbulence with the aid of an ensemble of vortical structures (vortical rings). Two problems have been considered : (i) density oscillations (and therefore the oscillations of the refractive index) in the case of a single vortex ring; (ii) oscillations in the case of an ensemble of vortex rings (ten in number). We considered vortex rings with helicity, too. The calculations were fulfilled for a wide range of vortex sizes (radii from 0.1 mm to several cm). As shown, density oscillations arise. High-frequency oscillations are modulated by a low-frequency signal. The value of the high frequency remains constant during the whole process excluding its final stage. The amplitude of the low-frequency oscillations grows with time as compared to the high-frequency ones. The low frequency lies within the spectrum of atmospheric turbulent fluctuations, if the radius of the vortex ring is equal to several cm. The value of the high frequency oscillations corresponds satisfactorily to experimental data. The results of the calculations may be used for the modelling of the Gaussian beam propagation through turbulence (including beam distortion, scintillation, beam wandering). A method is set forth which describes the propagation of non-paraxial beams. The method admits generalization to the case of inhomogeneous medium.
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Fedor V. Shugaev, Fedor V. Shugaev, Ludmila S. Shtemenko, Ludmila S. Shtemenko, Olga I. Dokukina, Olga I. Dokukina, Oxana A. Nikolaeva, Oxana A. Nikolaeva, Natalia A. Suhareva, Natalia A. Suhareva, Dmitri Y. Cherkasov, Dmitri Y. Cherkasov, "Modelling of propagation and scintillation of a laser beam through atmospheric turbulence", Proc. SPIE 10425, Optics in Atmospheric Propagation and Adaptive Systems XX, 104250N (29 September 2017); doi: 10.1117/12.2278085; https://doi.org/10.1117/12.2278085

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