Analysis of 1-D antireflection structured surfaces

Abstract

Over the past two decades, there has been considerable interest in the use of subwavelength-sized surface-relief features to create antireflection surfaces (ARSs). Because the surface features are small compared to the wavelength of the incident light, the incident light averages over the profiles in question and behaves as if it were encountering an effective medium that had optical properties between those of the incident medium and those of the substrate. By properly designing these surface-relief features, one finds that Fresnel reflections can be remarkably reduced from those produced by a smooth surface. In this research, 1-D ARSs possessing continuous triangular and sinusoidal profiles are modeled theoretically. By analyzing the structures using effective medium theory, closed-form solutions for the reflectance from AR surfaces are obtained. The solutions are found by treating the AR surface as a gradient-index medium and applying Maxwell’s equations along with transmission line theory. For the triangular profile, exact solutions are obtained using Hankel functions, while for the sinusoidal profile, a Ricotti differential equation is solved under the condition that the surfaces reflect <1% of the incident light. Numerical analysis of these AR surfaces was also conducted using rigorous coupled wave theory.1,2 Both the theoretical and the numerical treatment reveal that properly designed 1-D AR surfaces are insensitive to the polarization of the incident radiation and exhibit low reflectivities over a wide range of angles and wavelengths.