The Spiral Spectrum of a Laguerre–Gaussian Beam Carrying the Cross-Phase Propagating in Weak-to-Strong Atmospheric Turbulence

In communication links, the presence of atmospheric turbulence leads to crosstalk between the orbital angular momentum (OAM) states, thereby limiting the performance of information transmission. Thus, knowledge of the effect of turbulence on the spiral spectrum (also named the OAM spectrum) is of utmost importance in the field of optical communications. However, most of the existing studies are limited to weak turbulence calculation models. In this paper, based on the extended Huygens–Fresnel integral, the analytical expression is derived for the mutual coherence function of a Laguerre–Gaussian beam carrying the cross-phase and propagating through weak-to-strong anisotropic Kolmogorov atmospheric turbulence; subsequently, the analytical expression is used to study the behavior of the spiral spectrum. The discrepancies in the spiral spectrum between weak and strong turbulence are comparatively studied. The influences of the cross-phase and the anisotropy of turbulence on the spiral spectrum are investigated through numerical examples. Our results reveal that the cross-phase determines the distribution of the spiral spectrum. The spiral spectrum can be tuned to multiple OAM modes through the adaptation of the cross-phase coefficient. Moreover, increasing the cross-phase coefficient can reduce both the discrepancies of the spiral spectrum under two computational methods and the effects of the anisotropic factors of turbulence on the spiral spectrum.