Propagation characteristics of decentered annular beams through non-Kolmogorov turbulence

This paper studies the propagation characteristics related to higher-order moments of decentered annular beams through non-Kolmogorov turbulence. The analytical expressions for the mean-squared beam width w, the skewness parameter A, and the kurtosis parameter K are derived. The analytical expression for the non-Kolmogorov turbulence parameter T' is also derived, and the differences between two non-Kolmogorov turbulence parameters T' and T are examined. It is shown that K depends on both T and T', but w and A only depend on T. K decreases monotonically as the spectral power law exponent α increases, but there exist a maximum of w and a minimum of A when α=3.112. When propagation distance z is long enough, A reaches zero, i.e., the intensity distribution is perfectly symmetric about the centroid position axis. In free space, both A>0 and A<0 may appear on propagation. However, it is always A>0 or A<0 on propagation when turbulence is not weak. On the other hand, in turbulence, the maximum of K increases as the decentered parameter increases and the obscure ratio decreases. In particular, when z is long enough, the beam spot is elliptical in free space, but it becomes circular in turbulence.