Nonlinear Mie theory for the second harmonic generation in metallic nanoshells

In this work, Mie theory extended to the specific case of the optical second harmonic generation (SHG) from metallic nanoshells is described. Our model results from a combination of the Mie theory developed for the linear optical response of concentric nanospheres and the Mie theory developed for the SHG from nanospheres. This approach leads to a multipolar expansion of the second harmonic scattered electric fields. The total scattered intensity and the relative contribution of each multipole to the scattered wave are directly calculated within this framework. Our model is then applied to the calculation of the second harmonic cross section for nanoshells made of the most common metals used in plasmonics, namely gold and silver. Finally, the effect of the aspect ratio, i.e., the ratio between the inner and the outer radii of the metallic nanoshell, a parameter that is known to greatly impact the surface plasmon resonance properties of the system, is discussed notably in terms of the tunability of the optical SHG from metallic nanoshells.