title: Vector near-field calculation of scanning near-field optical microscopy probes using Borgnis potentials as auxiliary functions.
abstract: 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.
authors.affiliation: School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
authors.forename: Xueen
authors.initials: X
authors.lastname: Wang
authors.forename: Zhaozhong
authors.initials: Z
authors.lastname: Fan
authors.forename: Tiantong
authors.initials: T
authors.lastname: Tang
mesh_terms: D000465:Algorithms; D019544:Equipment Failure Analysis / Q000379:methods; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D020527:Microscopy, Scanning Probe / Q000295:instrumentation* / Q000379:methods*; D014159:Transducers