Calculation of internal and scattered fields of axisymmetric nanoparticles at any point in space

We present a method of simultaneously calculating both the internal and external fields of arbitrarily shaped dielectric and metallic axisymmetric nanoparticles. By using a set of distributed spherical vector wavefunctions that are exact solutions to Maxwell's equations and which form a complete, linearly independent set on the particle surface, we approximate the surface Green functions of particles. In this way we can enforce the boundary conditions at the interface and represent the electromagnetic fields at the surface to an arbitrary precision. With the boundary conditions at the particle surface satisfied, the electromagnetic fields are uniquely determined at any point in space, whether internal or external to the particle. Furthermore, the residual field error at the particle surface can be shown to give an upper bound error for the field solutions at any point in space. We show the accuracy of this method with two important areas studied widely in the literature, photonic nanojets and the internal field structure of nanoparticles.