Scatterers Near an Infinite Plane Surface

Another common configuration in plasmonics is a particle upon or near semi-infinite substrate. This substrate may have no plasmonic properties by itself, e.g. glass, but it still modifies the light scattering properties of the nanoparticle. The FDTD, the FIT, and the FEM can naturally handle such problems, because the effect of the interface is automatically accounted by the part of the substrate falling into the computational domain, when appropriate absorbing boundary conditions are used [11,13]. 

Alternative way to approach this scattering problem by the DDA in their standard form is a brute-force discretization of a large block of substrate together with the particle [32, 33]. Finite size of this block does introduce certain artifacts in the computed results. However, they can be diminished by using either the Gaussian beam with size smaller than that of the block [34] or by using empirical compensation formula [32], which also uses result of simulations for truncated substrate without the particle. Similar ideas should, in principle, be also applicable to the BEM. 

Finally, periodic scatterers and particles on a substrate, discussed above, are the simplest examples of the scattering problem in a complex background. Real applications may present more elaborate configurations, like multi-layered substrate or periodic array in a film. However, this presents no qualitative difference. In particular, using a proper Green s tensor for the complex background [35], the standard DDA or BEM can be used, discretizing only the scatterer itself. 

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