Effective dipolar polarizability of amorphous arrays of size-dispersed nanoparticles

Inhomogeneity of nanoparticle size, shape, and distribution is ubiquitous and inherent in fabricated arrays or may be a deliberate attempt to engineer the optical response. It leads to a spread of polarizabilities of interacting elements and phases of scattered light, and quantitative understanding of these effects is important. Focusing on random/amorphous arrays of optical antennas, we combine T-matrix calculations and an analytical approach based on an effective dipolar polarizability within a film of dipoles framework to quantify the spectral response as a function of the particle inhomogeneity and stochastic clustering. The interplay of position-dependent stochastic coupling and size distribution of antennas determines the optical properties of such arrays as a function of mean/standard deviation of diameter and minimum separation. The resonance wavelength, amplitude, and scattering-to-absorption ratio exhibit oscillations around their size-averaged values with periods and amplitudes given by average structural factors.