Computation Of Beam Propagation In Turbulent Field

Turbulent field is characterized by its random refractive index profile,slight change of index gradient and universal existence.The optical systems working in the turbulent field demand high accuracy requirement,hence the analysis of beam propagation in turbulent field is crucial for the design of those optical system.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 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,can 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 requirement for the accurate application of the method is 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.An optimized absorbing boundary(ABL)layer have been developed to reduce the numerical aliasing within the simulation domain.The advancement of this algorithm is an automated selector that figure out the optimal width of boundary layer.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 and the optimal width of boundary layer automatically and much more computationally efficient than the original algorithm.