A waveguide display includes a substrate transparent to visible light, a first grating on the substrate and configured to couple display light into or out of the substrate, and a phase structure on the substrate and configured to change a polarization state of the display light after or before the display light reaches the first grating. The first grating is characterized by a polarization-dependent diffraction efficiency. The first grating includes, for example, a surface-relief grating or a volume Bragg grating.