Angular-modulated spatial distribution of ultrahigh-order modes assisted by random scattering

In designing an optical waveguide with metallic films on a nanometer scale, the random scattering by the natural roughness of the thin film is always ignored. In this paper, we demonstrate that for the ultrahigh-order modes (UOMs) in the symmetric metal cladding waveguide, such a scattering leads to drastic variations in their spatial distribution at different incident angles. Owing to the high mode density of the UOMs, the random scattering induced coupling can be easily related to different modes with different propagation directions or wavenumbers. At small incident angles, the intra-mode coupling dominates, which results in a spatial distribution in the form of concentric rings. At large incident angles, the inter-mode coupling plays the most important role and leads to an array-like pattern. Experimental evidence via optically trapped nanoparticles support the theoretical hypothesis.