无衍射Mathieu光束自重建特性的理论和实验研究

Theoretical and experimental studies on the self-reconstruction property of non-diffracting Mathieu beam

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.

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.