Two-Dimensional Numerical Simulations of Photon Scanning Tunneling Microscopy: Fourier Modal Method and R-Matrix Algorithm

Numerical simulation of a two-dimensional probe–object system for photon scanning tunneling microscope is presented. The R-matrix propagation algorithm incorporated into the Fourier modal method was used to achieve an extended capability for modeling of a realistic system consisting of both a probe and a sample. The type of the mode guided through the dielectric probe and the coupling of the near-field to fundamental guiding mode in the probe are discussed. The influence of the probe parameters on the near-field images is investigated. Three different probe shapes were simulated in the constant height scanning mode. The transmitted flux intensity through the probe was found to be strongly dependent on the tip shape. The analysis shows a good agreement of the obtained results with the available theoretical works and confirming experimental results. The proposed numerical scheme can find applications for near-field probe characterization and provides an understanding of the degree of perturbation introduced by a probe tip in the experiment.