中国激光, 2016, 43 (9): 0905001, 网络出版: 2018-05-25  

Pearcey光束的光学形态形成及其数学机理研究

Optical Morphogenesis of Pearcey Beams and Its Mathematical Mechanism
作者单位
1 浙江师范大学信息光学研究所, 浙江 金华 321004
2 浙江师范大学浙江省光信息检测与显示技术研究重点实验室, 浙江 金华 321004
摘要
基于塞曼突变机构理论,通过求解Pearcey光束势函数的临界点方程,发现Pearcey光束的光学形态由方程根的数目决定。该临界点方程最多有三个实根,分别对应着三个稳态点和三条衍射光线。选取合适的Pearcey光束控制变量,如果三个实根中的两个相等,那么这两个实根对应的两条衍射光线会重叠,进而导致Pearcey光束的焦散线形成;如果三个实根全部相等,则会导致Pearcey光束光学尖点的形成。该研究不仅揭示了Pearcey光束的焦散线及光学尖点形成的数学机理,而且得到了焦散线方程和光学尖点位置。
Abstract
Based on the Zeeman catastrophe machine theory, the critical equation of potential function of Pearcey beams is solved. It is found that the number of roots of the critical equation determines the optical morphogenesis of Pearcey beams. This critical equation has at most three real roots, which correspond to three stable points and three diffraction lines, respectively. By choosing suitable control variables of Pearcey beams, if two of the three real roots are equal, the two corresponding diffraction lines overlap and the caustic line of Pearcey beams is formed. If three real roots are all equal, the optical cusp of Pearcey beams is formed. The study not only clarifies the mathematical mechanism of the generation of caustics and optical cusps of Pearcey beams, but also shows the caustic line equation and the position of the optical cusp.

任志君, 应朝福, 陈波, 杨照清. Pearcey光束的光学形态形成及其数学机理研究[J]. 中国激光, 2016, 43(9): 0905001. Ren Zhijun, Ying Chaofu, Chen Bo, Yang Zhaoqing. Optical Morphogenesis of Pearcey Beams and Its Mathematical Mechanism[J]. Chinese Journal of Lasers, 2016, 43(9): 0905001.

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