Over the last decades, there has been an ever increasing interest in nano-focusing oflight and subwavelength resolution overcoming the classical diffraction limit. Examples
of that are scanning near-field optical microscopy (SNOM) and “perfect lenses”
with negative-index materials. Development of scanning techniques, better performing
probes for SNOM and engineering of effective material parameters depends on
numerical modeling more than ever before. More accurate models and precise simulations
are required to obtain quantitative rather than just qualitative results.
This dissertation discusses numerical challenges of nano-scale structure simulations
with enhanced and strongly localized electric field distributions. In particular,
the thesis focuses on the simulation of scattering-type apertureless SNOM in
the mid-infrared and field distributions in plasmon-enhanced Raman spectroscopy in
the visible range. Although the ideas of field enhancement are similar (sharp, optionally
plasmon-coated, object causing a strong localized enhancement in the vicinity
of an AFM tip), applicable models and the nature of computational and engineering
challenges are different.
For the plasmon-enhanced SNOM, the quasi-static and the full-wave FEM
analyses are compared and a qualitative agreement is shown. The optical response
of the AFM tip is shown to correlate with the amplitude of the local field distribution.
This allows one to use dark field microscopy for tip testing. Several tip designs
proposed in the literature were analyzed using the quasi-static approximation; parametric
analysis and optimization were performed for selected tips.
Numerical challenges due to the multi-scale nature of the problem and multiple
scattering in scattering-type SNOM are exemplified in 3D simulations of a realistic
cantilevered AFM tip in the mid-infrared. The finite element method (FEM) with
adaptive meshing is shown to be a useful tool, but the computation resources of a
standard PC must be stretched to their limits. Near and far fields were analyzed and
an excellent agreement of the direct back-scattered field with experimental results
observed.
A substantial part of the dissertation deals with FLAME ” a generalized FD
calculus. Numerical problems related to high-precision calculation of the coefficients
of the scheme for fine grids are pointed out and overcome. A spurious space of
solutions in the case of multiple possible schemes is discovered and remedies proposed.
Numerical problems of FD for materials with a negative index of refraction are pointed
out and the performance of FLAME is investigated.
Advantages of FLAME over standard schemes for interfaces with negative
index materials (NIM) are demonstrated on an example of a NIM slab in air.