Simulation Of The Phase’s Evolution Of The Propagation Of Gaussian Laser Beam Through A Long Distance In Space

Based on satellites, gravity recovery and spatial gravitational wave detection are thecutting-edge scientific research tasks. The former (GRACE) has launched the K-bandsatellites, and its further plan (GRACE Follow on) will use laser to substitute the microwave.It and the latter (LISA) are to measure the displacement between the satellites for gravityrecovery of the earth or gravitational wave detection through the laser interferometer. Inthese research tasks, laser propagates between two satellites. How the errors from mastersatellite are transferred to another satellite? And how much effect the changing ofthe refractive index of the medium in which laser propagates has on the measurement? Theseproblems are the research focuses of this thesis.Various models can be utilized to simulate the long-distance beam propagation, includingFast Fourier Transformation method (FFT-BPM), finite difference method (FD-BPM) andthe finite element method (FE-BPM). Comparing the advantages and disadvantages of thesecalculation methods, as well as taking my research goal into account, FFT-BPM is thechoice.This paper analyzes the theory of FFT-BPM, and uses MATLAB for programming.Comparing the calculation results with the ideal Gauss beam propagation equations, ourcalculation method is reasonable. Then add the refractive index in the ionosphere, thecalculated results agree well with the theoretical conclusions: refractive index in this papercan be neglected in the calculation. Then add the initial wavefront distortion, which isdescribed by Zernike polynomials and geometric aberration respectively. The calculation ofthe transfer of the distortion under different divergence angle cases leads to the conclusionthat the bigger the divergence angle, the smaller the effect of the initial wavefront distortionon the calculated results, and we analysis this conclusion theoretically. We find, in theory,that although the increase of the divergence angle can benefit in reducing the effect ofwavefront distortion, it also increase the inherent wavefront curvature of the Gaussian beam.In future work, we need further analysis of divergence angle selection.