The invention relates generally to optically high transparency and high haze structures and, more particularly, to plastic, e.g., polymer, and glass structures having a sub-wavelength texture formed on a surface thereof, which is effective to impart the optical properties of high transparency and high haze to the structures. The texture is in a grass-like or needle-like form. Additionally, the optically high transparency and high haze structures may include a transparent conductor. Furthermore, the glass structures may exhibit a self-cleaning function.