Photonic nanojet computation using modified born series

We consider highly localised features of the electromagnetic field, that is, features on the order of a wavelength. Highly localised features are particularly interesting for the computation of plasmonic resonances and the analysis of photonic nanojets. Computing highly localised features of the electromagnetic field is challenging for conventional methods such as FEM because of the need to refine the entire mesh and to use ad hoc numerical solutions to truncate open domains. We define a computational setup and give some theoretical background for the modified Born series approach based on the vectorial Lippmann-Schwinger equation, including a constant overrelaxation parameter, still guaranteeing convergence. We stress that the purpose is to introduce and illustrate a practically computable sufficient method for a constant overrelaxation parameter to make the MBS convergent and not to argue that it is competitive in its present form with the existing methods.