An intriguing branching of the maximum position of the absorption cross section in Mie theory explained

A potential control over the position of maxima of scattering and absorption cross-sections can be exploited to better tailor nanoparticles for specific light-matter interaction applications. Here we explain in detail the mechanism of an appreciable blue shift of the absorption cross-section peak relative to a metal spherical particle localized surface plasmon resonance (LSPR) and remaining scattering and extinction cross sections. Such a branching of cross sections maxima requires a certain threshold value of size parameter x~0.7 and is a prerequisite for obtaining high fluorescence enhancements, because the spectral region of high radiative rate enhancement becomes separated from the spectral region of high non-radiative rate enhancement. A consequence is that the maximum of the absorption cross section cannot be used as the definition of the LSPR position for x>0.7.