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。
Based on the Zeeman catastrophe machine theory, the critical equation of potential function of Pearceybeams is solved. It is found that the number of roots of the critical equation determines the optical morphogenesis ofPearcey beams. This critical equation has at most three real roots, which correspond to three stable points and threediffraction lines, respectively. By choosing suitable control variables of Pearcey beams, if two of the three real rootsare equal, the two corresponding diffraction lines overlap and the caustic line of Pearcey beams is formed. If threereal roots are all equal, the optical cusp of Pearcey beams is formed. The study not only clarifies the mathematicalmechanism of the generation of caustics and optical cusps of Peareey beams, but also shows the caustic line equationand the position of the optical cusp.
出处
《中国激光》
EI
CAS
CSCD
北大核心
2016年第9期179-183,共5页
Chinese Journal of Lasers
基金
国家自然科学基金(11274278
11674288)
浙江省自然科学基金(Y14D050005)
