Semi-Continuous Metal Films with Inhomogeneous Broadening: Experiment-Based Statistical Convoluted Models for Plasmonic Colours

Absorption in optical materials is often approximated with a Lorentzian $1/(1+\omega^{2})$ lineshape. The Lorenz oscillators, however, represent a simplified dispersion mechanism, where all the individual microscopic oscillators are coherent, and the lineshape broadening is homogeneous (given with constant $\Gamma$ ). This type of approximation is often valid for transitions in crystalline solids. However, in the presence of amorphous materials, random nanostructures, disorder, or defects in the materials, inhomogeneous broadening plays a significant role in impacting the lineshape, which is classically approximated with the Gaussian (Maxwellian velocity statistics), $\exp[-\omega^{2}\ln 2]$ or Voight (convolution of Lorentzian and Gaussian) profiles. In this study, we characterize the optical constants of semi-continuous Ag and Al films with a statistical convolution approach,