Disclosed herein are waveguides comprising at least one scattering surface, a periodicity ranging from about 0.5 μm to about 2 μm, and an RMS roughness ranging from about 20 nm to about 60 nm. Single-layer waveguides having a thickness ranging from about 1 μm to about 100 μm are disclosed herein as well as multi-layer waveguides comprising at least one high index layer and optionally at least one low index layer. Lighting and display devices and OLEDs comprising such waveguides are further disclosed herein as well as methods for making the waveguides.