Studies of the influence of deep subwavelength surface roughness on fields of plasmonic thin film based on Lippmann–Schwinger equation in the spectral domain

Abstract

In this paper, we consider a line source over a plasmonic thin film with surface roughness. Using layered medium Green’s functions, we derive the Lippmann–Schwinger equation in the spectral domain with scattering potentials for the case of surface roughness over a layered medium. Because of deep subwavelength surface roughness, the scattering potentials are next approximated by the small potential approximation, so that the solutions of fields in the spectral domain can be readily computed. Numerical results are illustrated for the surface fields on the rough surface and the fields in the image plane. For periodic roughness, small periods, on the order of 0.1λ, and small heights, on the order of 0.01λ, are used. For the case of random roughness, we choose the correlation length to be much smaller than a wavelength, on the order of 0.1λ, and height on the order of 0.01λ. The results of the fields on the rough surface in the spectral domain show that subwavelength roughness creates fields with wave vector components that are many times larger than the free-space wavenumber (∼10k0 or larger). In the spatial domain, the imaging is enhanced by the deep subwavelength roughness. Results of the small roughness approximation are in good agreement with that of exact potential and that of the method of moments.