Numerical Simulations of Plasmonic Nanostructures

Doctoral thesis, 2008

This thesis focuses on the study of metallic nanostructures that support plasmons. Special emphasis is devoted to two specific numerical methods that allow us to predict plasmon characteristics: the discrete dipole approximation (DDA) and the Green's tensor (GT) method. DDA is an approximate method that produces fast and accurate results, but it can only be applied to systems in which the nanostructure is situated in a homogeneous background. In this thesis, DDA has been applied to predict the field enhancement and field decay around nano-rings, showing that the structure is well suited for biosensing; to obtain the spectral characteristics of silver trimers, showing that the actual plasmon modes are closely related to symmetry-adapted coordinates derived from group-theory; and to calculate the optical forces between two spherical particles illuminated by a plane wave, showing that the illumination wavelength determines the separation between the particles. The GT method, on the other hand, is an exact method, in the sense that the system can be solved to arbitrary precision depending on the size of the discretization elements. Its major drawback is the long time it takes to perform the calculations. To tis end, this thesis introduces a novel algorithm, called the top-down extended meshing algorithm (TEMA), that speeds up GT calculations by reducing the number of elements in the discretization process. This decreases the total time needed to perform the calculations, while keeping the precision of the result essentially unaltered. The GT method with TEMA meshes has successfully been used to study single holes of different sizes and shapes (circular and ellipsoidal) in the near- and far-field regime, as well as hole pairs as a function of their separation distance. The results compare very well with experiments, demonstration that the GT method is well suited for predicting the behavior of nano-holes.