There is disclosed a waveguide for use in an augmented reality or virtual reality display. The waveguide comprises a plurality of optical structures in a photonic crystal. The plurality of optical structures are arranged in an array to provide at least two diffractive optical elements. Each of the two diffractive optical elements is configured to receive light from an input direction and couple it towards the other diffractive optical element which can then act as an output diffractive optical element, providing outcoupled orders towards a viewer. The plurality of optical structures respectively have a shape, when viewed in the plane of the waveguide, comprising twelve substantially straight sides, six of the sides having respective normal vectors at a first angle, and the other six of the sides having respective normal vectors at a second angle which is different to the first angle.