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Abstract
The evolution law of arbitrary order moments of the Wigner distribution function, which can be applied to the different spatial power spectra, is obtained for partially coherent general beams propagating in atmospheric turbulence using the extended Huygens–Fresnel principle. A coupling coefficient of radiant intensity distribution (RID) in turbulence is introduced. Analytical expressions of the evolution of the first five-order moments, kurtosis parameter, coupling coefficient of RID for general beams in turbulence are derived, and the formulas are applied to Airy beams. Results show that there exist two types for general beams in turbulence. A larger value of kurtosis parameter for Airy beams also reveals that coupling effect due to turbulence is stronger. Both theoretical analysis and numerical results show that the maximum value of kurtosis parameter for an Airy beam in turbulence is independent of turbulence strength parameter and is only determined by inner scale of turbulence. Relative angular spread, kurtosis and coupling coefficient are less influenced by turbulence for Airy beams with a smaller decay factor and a smaller initial width of the first lobe.
Published Version
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