Photonic and plasmonic nanostructures almost unavoidably exhibit some degree of surface roughness for which the details depend on the fabrication process. A corresponding quantitative modeling thus requires the separation of numerical errors from the effects of roughness as well as the systematic construction of rough surfaces with prescribed properties. Here, we present a practical approach for constructing meshes of general rough surfaces with given autocorrelation functions based on the unstructured meshes of nominally smooth surfaces. The approach builds on a well-known method to construct correlated random numbers from white noise using a decomposition of the autocorrelation matrix and can be utilized with standard finite-element- and boundary-element-based Maxwell solvers.

As an example application, we demonstrate the impact of surface roughness on the resonance frequencies and quality factors of a plasmonic nano-sphere dimer using direct numerical calculations of the corresponding distributions. Although such direct calculations of the resulting distributions is possible for relatively simple systems, the direct numerical approach is not practically useful for many types of optical cavities or plasmonic resonators in contemporary nanophotonics, for which run-times on the order of hours per realization are not uncommon. As an alternative, we therefore apply a quasi-normal-mode-based perturbation theory with shifting boundaries. This approach, too, can be utilized within a broad range of numerical methods to analyze the effects of surface roughness in various fields of science and engineering.