Enhanced light extraction from textured surfaces with sub-wavelength size features: beyond the ray tracing approximation

Greatly enhanced radiation extraction has been observed through randomly textured interfaces with feature sizes comparable to the wavelength, where ray tracing approaches fail. A numerical tool is introduced based on spectral decomposition and supercritical scattering. A quasi- periodic interface destroys the k_|| invariance, introducing wave-numbers shifted by structure period harmonics, and allows transmission for supercritical incidence. Converting the interface boundary conditions into effective current source terms yield integral formulas for the transmitted fraction including quasi-periodic, sub-wavelength surface features with random variation of the feature size and period.