We consider certain problems in optical wave propagation in linear and nonlinear media in a regime of low-level atmospheric refractive index fluctuations. The perturbation theory hinges on the identification of such perturbing parameters to study its effect on the characteristics of the propagating free-space optical beam. Here, we illustrate the application of the few perturbation methods that are used to track the distorted traversing free-space optical fields. Furthermore, the tracking error is computed for the various approximate solutions in contrast to the numerical solution for comparing the capturing efficiency of the different perturbative analytical techniques. We found that the coordinate straining method efficiently reduces the deviation in the approximate solutions as compared to the regular perturbation expansion method. Furthermore, from the result analysis, it is observed that the tracking reliability of the various approximation solutions for a particular perturbation level depends on the proper choice of the approximation method and the order of the solution.
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