A waveguide configured for an augmented reality or virtual reality display, comprising: a photonic crystal comprising a plurality of optical structures ; wherein the plurality of optical structures are arranged in an array to provide at least two diffractive optical elements, wherein 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; wherein each optical structure of the plurality of optical structures respectively have a cross 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 and wherein adjacent optical structures in the array are spaced apart from each another by a gap in a direction parallel to the diffractive optical elements, wherein the optical structures have a physical extent that extends in the direction parallel to the optical elements, wherein a lattice constant is defined by a sum of the physical extent and the gap, and the gap is defined as a ratio of the lattice constant; wherein each optical structure of the plurality of optical structures is arranged in the photonic crystal in a corresponding unit cell having a parallelogram shape when viewed in the plane of the waveguide, wherein the lattice constant defines one side of the unit cell; wherein the arrangement of the plurality of optical structures in the array has hexagonal symmetry; and an input diffractive optical element, separate from the at least two diffractive optical elements overlaid on one another in the waveguide, configured to couple light into the waveguide and to provide light to the plurality of optical structures in the array in the input direction. a photonic crystal comprising a plurality of optical structures ; wherein the plurality of optical structures are arranged in an array to provide at least two diffractive optical elements, wherein 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; wherein each optical structure of the plurality of optical structures respectively have a cross 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 and wherein adjacent optical structures in the array are spaced apart from each another by a gap in a direction parallel to the diffractive optical elements, wherein the optical structures have a physical extent that extends in the direction parallel to the optical elements, wherein a lattice constant is defined by a sum of the physical extent and the gap, and the gap is defined as a ratio of the lattice constant; wherein each optical structure of the plurality of optical structures is arranged in the photonic crystal in a corresponding unit cell having a parallelogram shape when viewed in the plane of the waveguide, wherein the lattice constant defines one side of the unit cell; wherein the arrangement of the plurality of optical structures in the array has hexagonal symmetry; and an input diffractive optical element, separate from the at least two diffractive optical elements overlaid on one another in the waveguide, configured to couple light into the waveguide and to provide light to the plurality of optical structures in the array in the input direction. <EOS>