SNOM theory

SNOM theory is concerned with simulations for investigating the field-distribution and the transmission behaviour of fibertips used for SNOM-imaging. 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 three-dimensional metal-coated 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 FEM-FDTD 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 Helmholtz-equation

     

 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 metal-coated 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 Lippmann-Schwinger equation for successivly solving the Helmholtz-equation 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.

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