Nematic liquid-crystal polarization gratings by modification of surface alignment

The stylus of an atomic force microscope is used to scribe preferred directions for liquid-crystal alignment on a polyimide-coated substrate. The opposing substrate that comprises the liquid-crystal cell is rubbed unidirectionally, resulting in a twisted nematic structure associated with each micrometer-sized pixel. The polarization of light entering from the uniformly rubbed substrate rotates with the nematic director by a different amount in each pixel, and each of the two emerging polarization eigenmodes interferes separately. Two examples are discussed: a square grating that allows only odd-order diffraction peaks and a grating that combines rotation with optical retardation to simulate a blazed grating for circularly polarized light. The gratings can be electrically switched if used with semitransparent electrodes.