Displays with dispersion-compensating interleaved gratings

A head mounted display device comprising:

• a waveguide having a planar surface;
• an input coupler that includes a first diffractive grating configured to couple light into the waveguide, the first diffractive grating having a first pitch and being characterized by a first grating vector with a first grating vector projection onto the planar surface of the waveguide;
• and
• an output coupler configured to couple the light out of the waveguide, the output coupler comprising:
• a second diffractive grating having a second pitch and characterized by a second grating vector, wherein the second grating vector has a second grating vector projection onto the planar surface of the waveguide and the second grating vector projection is oriented at an angle with respect to the first grating vector projection, and
• a third diffractive grating that at least partially overlaps the second diffractive grating, that has the second pitch, and that is characterized by a third grating vector, wherein the third grating vector has a third grating vector projection onto the planar surface of the waveguide and the third grating vector projection is oriented at a negative of the angle with respect to the first grating vector, wherein
• the second pitch is constant,
• the second pitch is equal to twice the first pitch times a cosine of the angle, and
• the second and third diffractive gratings each diffract the image light.

A display comprising:

• a waveguide configured to propagate light via total internal reflection;
• a first diffractive grating configured to couple the light into the waveguide, wherein the first diffractive grating has a first pitch and is characterized by a first grating vector that has a first projection onto a lateral surface of the waveguide;
• a second diffractive grating configured to couple at least some of the light out of the waveguide, wherein the second diffractive grating has a second pitch, the second diffractive grating is characterized by a second grating vector that has a second projection onto the lateral surface of the waveguide, and the second projection is oriented at an angle with respect to the first projection;
• and
• a third diffractive grating configured to couple at least some of the light out of the waveguide, wherein the third diffractive grating has the second pitch, the third diffractive grating is characterized by a third grating vector that has a third projection onto the lateral surface of the waveguide, and the third projection is oriented at a negative of the angle with respect to the first projection, wherein
• the second pitch is constant,
• the second pitch is equal to twice the first pitch times a cosine of the angle, and
• the second and third diffractive gratings each diffract the image light.