Fourth-moment calculation of optical propagation in a turbulent atmosphere with use of the split-step method. I. Plane wave

This paper investigates the spatial dependence of the fourth moment equation as it pertains to turbulent atmospheric optics, using the split-step technique for propagation in a 2-D atmosphere for direct derivation from the fields. The study is aimed at evaluating the effect of inner scales on the fourth moment and quantities like the scintillation index and covariance function, which are related to it. The value of the real and imaginary parts of the fourth moment are shown to be a measure of the inner scales. It is also seen that the intensity scintillation index is not a function of the outer scale of turbulence for the propagation distances under consideration. The simulations can be applied for cross checking the results from numerical methods.