Arbitrary vectorial state conversion using liquid crystal spatial light modulators

There is significant interest in the generation of complex vector beams, where the combined polarisation and phase profile is chosen to have particular properties. These beams have often been implemented in an adaptable manner using liquid crystal spatial light modulators (SLMs). Existing methods have concentrated mainly on the generation of these vector beams from a fixed polarisation state, but there are also applications were conversion between vectorial states is necessary. We discuss the limitations of existing SLM-based modulation systems for conversion between arbitrary vectorial states. Three degrees of freedom are required in principle for transition between two arbitrary states. We show that a three-SLM system can provide conversion between two arbitrary polarisation states, but cannot necessarily provide a full 2π radian phase modulation. Hence, we propose a design using four SLMs that removes these limitations on the phase modulation.