SNOM theory is concerned with simulations for investigating the fielddistribution and the transmission behaviour of fibertips used for SNOMimaging. For the simulations we use finite element (FE) and Green's function methods.
FEM calculations using the full set of Maxwell's equations


Electric field energy density 
Poynting vector 
Simulation of a fully threedimensional metalcoated fibertip with an aperture of about 100 nm. The tip is modeled completly with mantel and core consisting of two dielectrica. The coating is modeled as an ideal metal. The simulation was done using the FEMFDTD package MAFIA from CST . The underlying grid consists of nearly 1.5 million points and the calculation took about one night on the SUN Ultra Enterprise of the computing center of the university.
Simulations using Green's function technique for solving the Helmholtzequation
Scattered electric field Electric field distribution  real part 
Scattered electric field (square of the amplitude) Electric field distribution  imaginary part part 
Material distribution (real part) Material distribution (imaginary part) 
Simulation of the electric behaviour of a fibertip modeled out of a metalcoated dielectricum. The aperture is about 100 nm. There's a little mirror in front of the aperture. The incoming focused wave has a wavelenght of 633 nm. This simulation was done using the Green's function method in two dimensions. The method uses the LippmannSchwinger equation for successivly solving the Helmholtzequation for the Green's function of the problem. The calculation shown here is only twodimensional. The underlying grid consists of 10000 points, but only the object needs to be discretized, so here only about 2000 source points are used. The calculation took about 15 minutes on the SUN Ultra Enterprise.