Method of evaluation of the mutual coherence function of laser beams and its application for symmetric dark hollow beams

In our report, a method of evaluation of the mutual coherence function (MCF) of optical wave propagating in turbulent atmosphere is proposed. The method is based on using inverse Fresnel transform and 2-D Fast Fourier Transformation procedure (FFT) and provides a high accuracy in various propagation conditions from weak up to strong optical turbulence regime. This technique allows significantly reducing the evaluation time of MCF. The proposed method is suitable for optical waves with arbitrary initial distribution of amplitude and phase. Results of investigations on the degradation of coherence of symmetric dark hollow beams (DHB) propagating in turbulent atmosphere are presented. Analysis of evolution of MCF is brought up, and some characteristics of DHB, such as mean intensity distribution, and moments of Wigner distribution are calculated for various kinds of profiles of structural characteristic of refractive index. All of the evaluations for DHB are fulfilled for Kolmogorov spectrum of correlation function of refractive index fluctuations. The comparison between mean intensity calculations within the proposed method and method based on semi-analytical approach using of quadratic approximation of spherical wave structure function, is presented.