Alternative derivation of Mie theory with electromagnetic potentials for diffuse particles

Mie's theory of light scattering on spherical particles is being increasingly used in nanophotonics, and these demanding applications have laid bare some shortcomings of Mie theory in its standard formulation. One problem that deserves special attention is the electron spill-out in small metallic nanoparticles, which invalidates the assumption of an abrupt interface. Here we present an alternative derivation of Mie theory without this assumption. To avoid the usual electromagnetic boundary conditions suitable for a hard-wall interface, we set up equations for the electromagnetic potentials instead of the electric and magnetic field. We show that in the limit of a hard-wall interface, the results of the standard Mie theory are recovered. Additionally, a numerical solution scheme is proposed for the equations for the vector potential and the scalar potential. Analysis of the optical cross sections of soft-interface nanospheres shows that the absorption increases and occurs at lower frequencies as compared to hard-walled nanospheres. This effect is rather dramatic in large spheres with large spill-out, due to the disappearance of high-frequency resonance peaks.