Poincaré Sphere Method for Optimizing the Phase Modulation Response of a Twisted Nematic Liquid Crystal Display

We report an experimental procedure for achieving spatial modulation of the phase of an input wave field with an off-the-shelf twisted nematic liquid crystal display. This method involves illumination of an addressed liquid crystal display (LCD) with circularly polarized light and measurement of the Stokes parameters of the outgoing beam as the applied voltage is changed. The analysis of the distribution of the polarization states in the $S_{1}-S_{2}$ plane suggests a simple way to optimize the liquid crystal phase response by means of a properly oriented quarter wave-plate followed by an analyzer. Laboratory results for a commercial display are presented. A phase modulation depth of 240 $^{\circ}$ is obtained at 514 nm with a residual intensity variation which is lower than 4%.