Boundary integral equations for a two-dimensional simulator of a photon scanning tunneling microscope

Boundary integral equations called guided-mode extracted integral equations are applied to simulations of a two-dimensional photon scanning tunneling microscope (2D-PSTM) for an incident TE mode (s polarization). The method presented is global. Complete and rigorous integral equations for a given configuration of the 2D-PSTM are derived. They can be solved numerically by the conventional boundary-element method with high accuracy. To confirm numerical results, three universal laws, i.e., the optical theorem, the energy conservation law, and the reciprocity relation, are derived. Physical characteristics of the interaction between the probe tip and the near held are investigated in detail by using numerical simulations. Many important and interesting physical properties of the 2D-PSTM can be simulated in detail by using the proposed method. (C) 1998 Optical Society of America.