基于MathieuHankel波理论分析了Mathieu光束经轴棱锥后的聚焦特性，并利用菲涅尔衍射积分理论及稳相法, 推导出Mathieu光束经轴棱锥后的准确解析表达式.数值模拟了无衍射Mathieu光束经轴棱锥线性聚焦后的光场在不同传播距离处的截面光强分布及轴上光强分布.理论分析及数值模拟均表明无衍射Mathieu光束经轴棱锥聚焦后会产生周期性Mathieu光束.研究结果对扩展Mathieu光束的应用范围提供了理论依据.

Based on the MathieuHankel wave′s theory, the focusing characteristics of Mathieu beam propagating through axicon was analyzed .By Fresnel diffraction theory and the method of stationary phase, the optical fields′ formula of Mathieu beam propagating through the axicon was deduced, the transverse intensity distribution in difference propagation distances was numerical simulated. The theoretical analysis and numerical simulation both show that the Mathieu beam passing through axicon can generate periodic Mathieu beam. This result has provided a theoretical basis in application of Mathieu beam.