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.
© 2005 Optical Society of America
Original Manuscript: September 30, 2004
Revised Manuscript: December 15, 2004
Manuscript Accepted: December 31, 2004
Published: July 1, 2005
Xueen Wang, Zhaozhong Fan, and Tiantong Tang, "Vector near-field calculation of scanning near-field optical microscopy probes using Borgnis potentials as auxiliary functions," J. Opt. Soc. Am. A 22, 1263-1273 (2005)