Wang Xueen, Fan Zhaozhong, Tang Tiantong
School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
J Opt Soc Am A Opt Image Sci Vis. 2005 Jul;22(7):1263-73. doi: 10.1364/josaa.22.001263.
A new boundary integral equation method for solving the near field in three-dimensional vector form in scanning near-field optical microscopy (SNOM) using Borgnis potentials as auxiliary functions is presented. A boundary integral equation of the electromagnetic fields, expressed by Borgnis potentials, is derived based on Green's theorem. The harmonic expansion in rotationally symmetric SNOM probe--sample systems is studied, and the three-dimensional electromagnetic problem is partly simplified into a two-dimensional one. The boundary conditions of Borgnis potentials both on dielectric boundaries and on perfectly conducting boundaries are derived. Relevant algorithms were studied, and a computer program was written. As an example, a SNOM probe-sample system composed of a round metal-covered probe and a sample with a flat surface has been numerically studied, and the computational results are given. This new method can be used efficiently for other electromagnetic field problems with round subwavelength structures.
提出了一种新的边界积分方程方法，该方法以博尔尼希势作为辅助函数，用于求解扫描近场光学显微镜（SNOM）中三维矢量形式的近场。基于格林定理推导了由博尔尼希势表示的电磁场边界积分方程。研究了旋转对称SNOM探针 - 样品系统中的谐波展开，将三维电磁问题部分简化为二维问题。推导了博尔尼希势在介质边界和理想导电边界上的边界条件。研究了相关算法并编写了计算机程序。作为示例，对由圆形金属包覆探针和平坦表面样品组成的SNOM探针 - 样品系统进行了数值研究，并给出了计算结果。这种新方法可有效地用于其他具有圆形亚波长结构的电磁场问题。
