Controlling the Coverage of Full Poincaré Beams through Second-Harmonic Generation

Ideal full Poincaré (FP) beams contain all possible polarization states on the surface of the Poincaré sphere and are readily created by linear optical techniques and, more recently, by nonlinear optical processes. An inherent limitation in the latter is the inability to achieve all polarization states, coined coverage, due to modal size, polarization, and modal weighting changes during the nonlinear conversion of the constituent modes. Here, we demonstrate a simple technique to control the coverage of FP beams, using second-harmonic generation as an example, from fully scalar (no coverage) to fully vectorial (full coverage). Our method for determining the coverage confirms the vectorial characteristics of the generated beams and reveals a balancing act between mode order, modal nonlinear efficiency, and initial relative modal weights, all in close agreement with that theoretically predicted. Our findings will hopefully be of value to the communities interested in nonlinear structured light, particularly for vectorial nonlinear modal creators and detectors and control of quantum hybrid entangled states.