Computation of beam propagation in turbulent field

The split-step Fourier method (SSFM) is introduced to analyze the beam propagation in a relatively large-sized turbulent filed, whose refractive-index profile is already detected. The numerical method is achieved by fast Fourier transform (FFT).To obtain the optimal sampling number, we propose an adaptive spread-spectrum method as an optimization. The SSFM is widely used for solving the nonlinear Schrödinger equation [1].The advantage of the SSFM is apparently its simple formalism and suitability to our situation. The direct numerical solution of the Helmholtz equation, derived from this method, yields detailed information of the spatial and angular properties of the propagation beam. On the other hand, a set of approximations restrict its applicability, the requirements for the accurate application of the method are summarized and a set of formulas is generalized in this paper. The efficiency of the SSFM depends on the sampling number, the adaptive spread-spectrum method yields optimal sampling number to increase the computational efficiency .To testify the accuracy of our algorithm, we use graded-index medium as the turbulent filed, for the reason that the beam propagation in turbulent field with random refractive-index profile is ruleless and has no unified reference. The simulation result testifies our algorithm is tremendously accurate, capable of selecting the optimal N automatically and much more computationally efficient than the original algorithm.