凹形反射面上电磁波传播焦散区奇性分析

Study on Singularities of Caustics of Electromagnetic Wave Propagation in Concave Reflectors

采用辛几何方法分析凹形反射面上电磁波传播的焦散现象.通过引入与原物理空间相同维数的波向量空间,与原物理空间一起组成一个辛空间,在辛空间中分析凹面反射电磁波传播焦散区的奇性.研究表明,凹面反射有折叠、尖点和燕尾三种主要奇性,奇性导致了焦散现象的发生.

The causticals phenomena of electromagnetic wave propagation in concave reflector antennas are studied by Symplectic Geometrical Theory.The new vectors with the same numbers as the original physical vectors are introduced.The new vectors combine with the original physical vectors to form a symplectic space,and the singularities of caustics of electromagnetic wave propagation in concave reflector antennas are studied in the symplectic space.Results of the analysis show that there are three major singularities in concave reflecting: fold,cusp and swallowtail and that singularities give rise to the occurrence of the caustic penomena.