Deviation characteristics of specular reflectivity of micro-rough surface from Fresnel's equation

Specular reflectivity is an important radiative property in thermal engineering applications and reflection-based optical constant determinations, yet it will be influenced by surface micro-roughness which cannot be completely removed during the polishing process. In this work, we examined the deviation characteristics of the specular reflectivity of micro-rough surfaces from that predicted by the Fresnel's equation under the assumption of smooth surface. The effects of incident angle and relative roughness were numerically investigated for both 1D and 2D micro randomly rough surfaces using full wave analysis under the condition that the relative roughness is smaller than 0.05. For transverse magnetic (TM) wave incidence, it is observed that the deviation of specular reflectivity dramatically rises as the incident angle approaches to the pseudo Brewster's angle, which violates the prediction based on Rayleigh criterion. While for the transverse electric (TE) wave incidence, the deviation of the specular reflectivity is much smaller and decreases monotonically with the increase of incident angle, which agrees with the predication from Rayleigh criterion. Generally, the deviation of specular reflectivity for both TM and TE increases with the relative roughness as commonly expected.