Characterizing the statistical distribution for transmission coefficient of turbulent optical orbital-angular-momentum channels

The instantaneous transmission coefficient, i.e., instantaneous transmittance, of a turbulent optical orbital-angular-momentum (OAM) channel is mathematically formulated as a weighted integration and is found to range between 0 and 1. Common probability distribution models for optical irradiance fluctuations with a support from 0 to ∞ are not strictly proper for statistical description of the fluctuating transmission coefficient. The novel dual Johnson S B distribution is proposed to model the statistical behavior of the fluctuating transmission coefficient. Its applicability is verified by making comparisons between the histograms of transmission-coefficient samples generated by Monte Carlo simulations and the corresponding fitted probability density functions; the values for its four independent control parameters under different conditions are obtained by the fit of the dual Johnson S B distribution to relevant simulated transmission-coefficient samples. It is found that each of the four independent control parameters of the dual Johnson S B distribution can be considered as a function of three quantities, viz., the OAM index, the Fried's atmospheric coherence width, and the ratio of the root-mean-square (RMS) OAM-beam radius to the Fried's atmospheric coherence width. The results demonstrate that the statistical distribution of the fluctuating transmission coefficient depends less on the first two quantities than on the last one. Finding a model for direct mapping from these three quantities to the four control parameters of the dual Johnson S B distribution deserves future study.