Surface plasmon broadening for arbitrary shape nanoparticles: A geometrical probability approach

A geometrical probability measure is proposed for calculating the effective conduction electron mean free path of an arbitrary shape convex particle. It is shown that the plasmon widths determined from this mean free path are consistent with exact quantum mechanical widths for simple particle shapes. We use the mean free path formula to evaluate size and shape dependent dielectric functions and extinction spectra for silver spheroids, square prisms, truncated tetrahedrons, and cylinders.