Polarization state vector beam spectrum analyzer using q-plates encoded onto a spatial light modulator

Vector beams where the polarization state is spatially dependent are being examined as new optical communication channels. We demonstrate a vector beam spectrum analyzer capable of simultaneously determining the topological charge and the state of polarization of an input vector beam. We encode a two-dimensional polarization diffraction grating that generates six different q-plate channels from -3 to +3 in the horizontal direction, and each is split in the vertical direction into the six polarization channels at the cardinal points of the corresponding higher-order Poincare sphere. The horizontal q-plate grating is a optimized phase-only grating that produces harmonics of a given input q-plate having a charge of +1 all of which have equal strengths. The vertical polarization grating is specially designed to produce 6 orders where the amplitude and phase of each order can be independently controlled. Different gratings are required for the horizontal and vertical polarizations to create the desired polarization states in each diffracted order. Consequently, we generate 36 different channels in parallel. We demonstrate this polarization diffraction element using a single phase-only liquid-crystal spatial light modulator in a reflective optical architecture. Details are given regarding experimental details on this process. Finally, we demonstrate that this system can act as a vector beam polarization state spectrum analyzer allowing both the topological charge and the polarization state of the input vector beam to be simultaneously determined in a single experiment.