Corrigendum to “Scintillation index analysis of an optical wave propagating through the moderate-to-strong turbulence in satellite communication links” [Opt. Commun. 445 (2019) 255–261]

In laser satellite communications, studies of the scintillation index that are based on the three-layer altitude-dependent turbulence model have paid little attention to the different character of stratospheric turbulence from turbulence in the other two layers. This difference is a consequence of the special power spectrum with a power law exponent of 5. By adopting different wave structure functions at different altitudes in the extended Rytov theory, we analyze the scintillation index along the slant path in the regime of moderate-to-strong turbulence. Our results show that the weak fluctuation theory is limited to a smaller zenith angle, and the scintillation index has a larger maximum value in the focusing regime, when compared to the Kolmogorov model. We also find that the change of the scintillation index with the outer scale of the stratospheric turbulence only appears with moderate-to-strong turbulence, and it weakens with the increase of the turbulence outer scale. Moreover, the impact of the Gaussian beam radius on the scintillation index is different in the downlink and the uplink paths. We can approximate the downlink beam as a plane wave in most cases, but we must optimize the uplink beam to minimize the irradiance fluctuation.