Waveguide for an augmented reality or virtual reality display

A system, comprising:

• a waveguide;
• and
• an output element of the waveguide, the output element including a plurality of discrete optical structures arranged in an array of a plurality of rows and columns to form a plurality of overlaid diffractive optical elements in or on the waveguide, the plurality of discrete optical structures and the plurality of overlaid diffractive optical elements arranged to receive light input into the waveguide from an input direction and to diffract a first portion of the received light that is input into the waveguide into diffraction orders that are further diffracted in a plane of the waveguide within the output element, and to diffract a second portion of the received light that is input into the waveguide into a diffraction order that is coupled out of the output element of the waveguide towards a viewer without the second portion of the received light internally reflecting in the waveguide, and the plurality of discrete optical structures having respective shapes in a plane view of the waveguide that include a plurality of substantially straight sides having respective angles relative to one another.