Poincaré-sphere representation of phase-mostly twisted nematic liquid crystal spatial light modulators

We establish necessary conditions in order to design a phase-only wave front modulation system from a liquid crystal display. These conditions determine the dependence of the polarization state of the light emerging from the display on the addressing gray level. The analysis, which is carried out by means of the coherence-matrix formalism, includes the depolarization properties of the device. Two different types of polarization distributions at the output of the liquid crystal cells are found. This approach is applied to a twisted nematic liquid crystal display. In this case, an optimization algorithm must be designed in order to select the input polarization state that leads to the required distributions. We show that the Poincaré-sphere representation provides a convenient framework to design the optimization algorithm as it allows for a reduced number of degrees of freedom. This feature significantly decreases the computation time. Laboratory results are presented for a liquid crystal-onsilicon display showing a phase modulation depth greater than 2π radians with an intensity variation lower than 6%. In addition, a hybrid-ternary modulation (HTM), an operation regime employed in holographic data storage, is achieved.