Goos–Hänchen and Imbert–Fedorov shifts in a two-dimensional array of gold nanoparticles

Abstract

Using an oblique linearly polarized laser beam, Goos–Hanchen (GH) and Imbert–Fedorov (IF) reflection shifts of a two-dimensional array of gold nanoparticles (NPs) on water substrate are investigated within the framework of a theoretical model. The dependences of spatial ( Δ ) and angular ( Θ ) shifts on the angle of radiation, the polarity of light, the size, and concentration of particles have been studied in detail. It is shown that a grazing p-wave light yields to the highest negative amount of GH shifts, while a 45-deg polarization that radiates at 45 deg would maximize IF shifts. The deviations are sensitive to the particle size linearly and decrease using larger NPs except in the angular out-of-plane shift ΘIF, which has a critical point where its sign and trend change. The curves of ΔGH, ΘGH, and ΘIF for various lattice constant exhibit peaks for a specific arrangement that moves toward smaller values as the particle size increases. On the other hand, ΔIF always has an additive behavior. Accurate monitoring of these parameters may serve as a precise method to determine thickness and aggregation of nanostructured films.