Taking the random electromagnetic cosh-Gaussian beam as a typical example of random electromagnetic beams, the analytical expressions for the cross-spectral density matrix element of random electromagnetic cosh-Gaussian beams propagating through non-Kolmogorov atmospheric turbulence are derived, and used to study the changes in the states of polarization (degree of polarization, orientation angle and degree of ellipticity) of random electromagnetic cosh-Gaussian beams in non-Kolmogorov atmospheric turbulence. It is shown that the states of polarization of random electromagnetic cosh-Gaussian beams in non-Kolmogorov atmospheric turbulence are different from those in free space. The degree of polarization decreases, and the orientation angle and degree of ellipticity increase with increasing structure constant. The on-axis degree of polarization and the degree of ellipticity appear to have an oscillatory behavior and the orientation angle has a rapid transition for the larger cosh-part parameter of random electromagnetic cosh-Gaussian beams in atmospheric turbulence.
Based on the extended Huygens–Fresnel principle and the definition of second-order moments of the Wigner distribution function, the analytical expression for the kurtosis parameter of partially coherent controllable dark hollow beams in free space is derived, and used to study the influence of beam parameters on the kurtosis parameter. It is shown that the kurtosis parameter increases with increasing the wavelength and the waist width, or decreasing the scaling factor, however, the effect of the beam order and the spatial correlation length on the kurtosis parameter depends on the propagation distance. The results can be interpreted physically.
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