Accounting for inhomogeneous broadening in nano-optics by electromagnetic modeling based on Monte Carlo methods

Significance The advent of nanotechnology has enabled the study of physical phenomena in structures with nanoscale dimensions. Pushing the limits of fabrication techniques inevitably leads to uncertainties—for example, an array of nanoscale resonators may be designed to be identical, but in fact has a distribution of sizes due to fabrication imperfections, leading to a distribution of responses. In optical experiments involving collections of nanostructures these effects are often acknowledged but rarely quantified. We demonstrate a technique that combines electromagnetic simulations with a Monte Carlo sampling technique to rigorously account for “inhomogeneous broadening” of optical resonances as a result of fabrication or synthesis imperfections. This approach has wide applicability to any experiments involving collections of structures designed to be identical. Many experimental systems consist of large ensembles of uncoupled or weakly interacting elements operating as a single whole; this is particularly the case for applications in nano-optics and plasmonics, including colloidal solutions, plasmonic or dielectric nanoparticles on a substrate, antenna arrays, and others. In such experiments, measurements of the optical spectra of ensembles will differ from measurements of the independent elements as a result of small variations from element to element (also known as polydispersity) even if these elements are designed to be identical. In particular, sharp spectral features arising from narrow-band resonances will tend to appear broader and can even be washed out completely. Here, we explore this effect of inhomogeneous broadening as it occurs in colloidal nanopolymers comprising self-assembled nanorod chains in solution. Using a technique combining finite-difference time-domain simulations and Monte Carlo sampling, we predict the inhomogeneously broadened optical spectra of these colloidal nanopolymers and observe significant qualitative differences compared with the unbroadened spectra. The approach combining an electromagnetic simulation technique with Monte Carlo sampling is widely applicable for quantifying the effects of inhomogeneous broadening in a variety of physical systems, including those with many degrees of freedom that are otherwise computationally intractable.