Influence of random surface deformations on the resonance frequencies and quality factors of optical cavities and plasmonic nanoparticles

Abstract

Surface deformations of optical cavities and plasmonic nanoparticles are inevitable in nanophotonics. The random morphology changes of different realizations modify the associated resonance frequencies and quality factors, which may be characterized by specified distributions instead of their nominal values. As an alternative to statistical analyses based on direct numerical calculations, we present an approximate method using first-order perturbation theory with shifting boundaries. For an example resonator in the form of a plasmonic nanowire, the approach explains the bivariate frequency distribution observed in direct numerical calculations involving 1000 realizations of random surface deformations and provides the average and the associated covariance matrix with relatively high accuracy.