Transparent waveguide display with grating lamina that both couple and extract modulated light

An apparatus for displaying an image comprising:

• an input image node for providing image modulated light;
• a first optical substrate comprising at least one waveguide layer configured to propagate the modulated light in a first direction, wherein the at least one waveguide layer of the first optical substrate comprises at least one grating lamina configured to extract the modulated light from the first optical substrate along the first direction;
• a second optical substrate comprising at least one waveguide layer configured to propagate the modulated light in a second direction, wherein the at least one waveguide layer of the second optical substrate comprises at least one grating lamina configured to extract the modulated light from the second optical substrate along the second direction;
• wherein
• the at least one grating lamina of the first optical substrate is configured to couple the modulated light into the first optical substrate;
• the at least one grating lamina of the second optical substrate is configured to couple the modulated light extracted from the first optical substrate into the second optical substrate;
• and
• the at least one grating lamina of at least one of the first and second optical substrates has a k-vector that varies along the respective direction of light propagation.