Fractal surface characterization: Implications for plasmon polariton scattering

We compare the scattering of surface plasmon polaritons (SPPs) at relatively smooth and rough surfaces of gold films and relate the difference in the SPP behaviour to the difference in fractality of the studied surfaces. The rough surface, which results in the strong localization of SPPs, is found to have a fractal structure with a normalized fractal dimension D approximate to 2.26 in the spatial range 80-640 nm. It is shown that the smooth surface, which supports well-pronounced propagating SPPs, cannot be viewed as a fractal structure for discretization steps exceeding 80 nm. We conclude that in order for SPPs to be localized by surface roughness, the surface should exhibit a fractal structure in a sufficiently large range of sizes around the SPP wavelength.