Spatially Varying Skew Mirrors

Abstract

A skew mirror is an optical reflective device whose reflective axis forms a non-zero angle with the surface normal. A spatially varying skew minor is a skew mirror whose reflective axes vary as a function of lateral position. If a spatially varying skew mirror was subdivided into many pieces, some or all of the many pieces could have a reflective axis that points in a different direction. In some variations, a spatially varying skew minor can act as a focusing mirror that focuses incident light. A spatially varying skew mirror can be made by recording interference patterns between a phase-modulated writing beam and another writing beam or by recording interference patterns between planar wavefronts in a curved holographic recording medium that is later bent or warped.

1 . An electronic device comprising:
 a waveguide configured to propagate light via total internal reflection;   a medium on the waveguide; and   an output coupler on the waveguide and configured to couple the light out of the waveguide, the output coupler being configured to reflect the light about spatially varying reflective axes oriented at non-zero angles relative to a surface normal of the medium, the output coupler including
 a first grating disposed at a location in the medium and characterized by a first grating vector having a first length and pointing in a first direction, and 
 a second grating disposed at the location in the medium and characterized by a second grating vector having a second length and pointing in the first direction, the second length being different than the first length. 
   
     
     
         2 . The electronic device of  claim 1 , wherein the first grating comprises a first volume hologram and the second grating comprises a second volume hologram. 
     
     
         3 . The electronic device of  claim 1 , wherein the light is collimated when incident upon the output coupler and has curved wavefronts after reflection by the output coupler. 
     
     
         4 . The electronic device of  claim 1  wherein the waveguide comprises a substrate layered on the medium. 
     
     
         5 . The electronic device of  claim 4  wherein the waveguide comprises an additional substrate layered on the medium, the medium being interposed between the substrate and the additional substrate. 
     
     
         6 . The electronic device of  claim 1 , wherein the output coupler has a non-zero third-order or higher Zernike coefficient. 
     
     
         7 . The electronic device of  claim 1 , wherein the light comprises a red wavelength, a green wavelength, and a blue wavelength. 
     
     
         8 . The electronic device of  claim 1 , wherein the light carries images. 
     
     
         9 . The electronic device of  claim 1 , wherein the spatially varying reflective axes have orientations that vary smoothly as a function of position across the medium. 
     
     
         10 . An electronic device comprising:
 a medium; and   an optical coupler in the medium, wherein the optical coupler is configured to reflect light about reflective axes that vary across the medium, the reflective axes form non-zero angles relative to a surface normal of the medium, and the optical coupler includes
 a first grating at a location in the medium, the first grating having a first frequency and being oriented a first direction, and 
 a second grating at the location in the medium, the second grating having a second frequency different from the first frequency and being oriented the direction. 
   
     
     
         11 . The electronic device of  claim 10 , wherein the first grating comprises a first volume hologram and the second grating comprises a second volume hologram. 
     
     
         12 . The electronic device of  claim 10 , wherein the light is incident upon the optical coupler within a collimated beam and has curved wavefronts after reflection by the optical coupler. 
     
     
         13 . The electronic device of  claim 10 , wherein the optical coupler has a non-zero third-order or higher Zernike coefficient. 
     
     
         14 . The electronic device of  claim 10 , further comprising:
 a waveguide configured to propagate the light via total internal reflection, the medium being layered on the waveguide.   
     
     
         15 . The electronic device of  claim 14 , wherein the optical coupler is configured to couple the light out of the waveguide. 
     
     
         16 . The electronic device of  claim 14 , wherein the medium is sandwiched between first and second substrates in the waveguide. 
     
     
         17 . An electronic device comprising:
 a waveguide configured to propagate light via total internal reflection;   a medium on the waveguide; and   diffractive gratings in the medium, wherein
 at least one of the diffractive gratings is configured to reflect a first portion of the light having a first wavelength and a first range of incidence angles about a first reflective axis, the first portion of the light being incident upon a surface of the medium at a first location, and 
 at least one of the diffractive gratings is configured to reflect a second portion of the light having a second wavelength and a second range of incidence angles about a second reflective axis, the second portion of the light being incident upon a surface of the medium at a second location, and 
 the first reflective axis differs from the second reflective axis by at least 0.1 degrees. 
   
     
     
         18 . The electronic device of  claim 17 , wherein the first reflective axis and the second reflective axis are each non-parallel to a normal axis of the medium. 
     
     
         19 . The electronic device of  claim 17 , wherein the first range of incidence angles and the second range of incidence angles each span at least 15 degrees. 
     
     
         20 . The electronic device of  claim 17 , wherein the second wavelength differs from the first wavelength by at least 50 nm.