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矩形光阑限制下高斯光束的衍射特性分析
Analysis of the diffraction characters of the Gaussian beams restricted by a rectangular aperture
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摘要: 为了研究矩形光阑边长与透镜像方焦面处光束光斑尺寸以及光斑内所包含功率的关系,根据高斯光束经矩形光阑和透镜变换后在透镜像方焦面的衍射场分布表达式,采用MATLAB进行数值计算的方法,进行了理论分析。结果表明,当光阑对光束的衍射影响明显时,光束衍射场的中央亮条纹的宽度随着光阑边长的增大而减小;当光阑对光束的衍射影响极小时,中央亮条纹的宽度随着光阑边长的增加而阶跃变化,中央亮条纹强度的半最大值宽度随着光阑边长的增大而减小;当光阑对光束衍射影响极小时,中央亮条纹半最大值宽度趋近于一定值。给出的中央亮条纹强度半最大值宽度与矩形光阑边长关系的拟合表达式,可为激光应用装置的设计提供理论支持。Abstract: Based on the expression of diffractive field distribution of the Gaussian beams restricted by a rectangular aperture and focalized by a lens, the relationship between the width of the rectangular aperture and the spot size of the restricted beam, as well as the relationship between the aperture width and the power in the bucket,was numerically calculated with MATLAB. It was illuminated that the width of the centre bright fringe decreased along with the increasing width of the rectangular aperture when the effect of the aperture on the beam couldn't be ignored, however, the width of centre bright fringe step changed with increase of the size of the aperture when the effect could be ignorable, the width of the half maximum intensity of the centre bright fringe decreased along with the accretion of the width of the aperture and then it tends to a constant. The piecewise function of the relationship between the full width at half maximum(FWHM) of the centre bright fringe and the rectangular aperture width was put forward as well. The conclusions are useful for the design of a laser facility.
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