An exact semi-analytical solution to a scattering problem of evanescent wave incident on a particle is obtained. The evanescent wave is generated by total reflection as an electromagnetic plane wave propagates from an optically denser medium to an optically thinner one. The scattered fields by and internal fields within the particle are expanded in terms of spherical vector wave functions, and an integral representation of spherical vector wave functions over cylindrical ones is used to compute the reflection of the scattered fields on the interface between the optically denser and thinner media. By applying the boundary conditions and projection technique, the unknown expansion coefficients of the scattered fields are determined. The scattering cross sections are evaluated, and the scattering characteristics are analyzed briefly.

获得了入射到粒子上的van逝波散射问题的精确半解析解。an逝波是在电磁平面波从光学密度较高的介质传播到光学厚度较小的介质时通过全反射生成的。利用球形矢量波函数扩展了粒子内部的散射场和内部场，并使用圆柱矢量上的球形矢量波函数的积分表示来计算散射场在光致密物与光学密度之间的界面上的反射。更薄的媒体。通过应用边界条件和投影技术，可以确定散射场的未知膨胀系数。对散射截面进行评估，并简要分析散射特性。