In this paper, a novel Modal decomposition (MD) method based on the Wigner representation of fiber modal field is developed. An important distinction between this work and some others is that it can allow either fully or partially spatial coherent modal contents to be decomposed into guided modes. When the Wigner representation is reconstructed, based on the orthogonal property of guided modes and Moyal identity rule, the modal weights and possible relative phases can be obtained in an exact way. Further, the validity and reliability of the method are demonstrated with the numerical simulations.
The flow field around a hemispherical/cylindrical structure at Mach number of Ma=0.4 is calculated, and the distributions of temporal root mean square value of velocity and density in the wake are presented. Further more, the optical path difference and aero-optical phase are calculated according to density field, and then the impact of the wake on adaptive optics systems with a point source and a plane-wave source beacon is studied respectively. It is found that there are plentiful turbulent structures in the wake, and the maximum values of the temporal root mean square of density and velocity both decrease 84% when the distance from the calculated position to the center of the structure varies from 0.43 m to 1.5 m. The spatial root mean square of optical path difference varies dramatically over time, and its time average gain two times while the angle of projection varies from 120°to 148°. The hemispherical/cylindrical wake has little impact on the adaptive optics system when the beacon is point source. While the wake has great impact when the beacon is plane-wave source, and the impact gets worse when the angle of projection gets larger. The Strehl ratio of the main laser decreases from 0.72 to 0.33 when the angle of projection increases from 120°to 148°.
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