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中文摘要：
首次对无衍射Mathieu光束的自重建特性进行理论和实验研究，利用Mathieu-Hankel波理论分析了Mathieu光束的自重建机理。基于菲涅尔衍射积分理论，推导出了高斯吸收型圆形障碍物部分遮挡后的Mathieu光场重建后的解析表达式，并数值模拟了无衍射Mathieu光束的经圆形障碍物部分遮挡后光场的自重建过程。采用柱透镜-轴棱锥组合光学系统产生近似零阶无衍射Mathieu光束，实验分别验证了轴上和轴外障碍物遮挡时近似零阶无衍射Mathieu光束的自重建特性。理论模拟与实验结果相符。
英文摘要：
Self-reconstruction properties of the Mathieu beam are studied theoretically and experimentally. By means of the Mathieu-Hankel wave＇s theory, the self-reconstruction mechanism of Mathieu beam is analyzed. Based on the Fresnel diffraction theory, an analytical expression for the optical field of a Mathieu beam partially blocked by a circular opaque obstacle is derived, and the self-reconstruction process of Mathieu beam is simulated based on the analytical expression. Using a cylindrical lens and an axicon system to generate Mathieu beam, the self-reconstruction properties of the Mathieu beam partially blocked by a circular opaque obstacle on axis and off axis are verified. Experimental results agree well with the theoretical analysis.
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