Measuring the non-separability of vector modes with digital micromirror devices

The non-separability between the spatial and polarisation Degrees of Freedom (DoFs) of complex vector light fields has drawn significant attention in recent time. Key to this are its remarkable similarities with quantum entanglement, with quantum-like effects observed at the classical level. Crucially, this parallelism enables the use of quantum tools to quantify the coupling between the spatial and polarisation DoFs, usually implemented with polarisation-dependent spatial light modulators, which requires the splitting of the vector mode into two orthogonal polarisation components. Here we put forward a novel approach that relies on the use of Digital Micromirror Devices (DMDs) for fast, cheap and robust measurement, while the polarisation-independent nature of DMDs enables a reduction in the number of required measurements by 25\%. We tested our approach experimentally on cylindrical vector modes with arbitrary degrees of non-separability, of great relevance in a wide variety of applications. Our technique provides a reliable way to measure in real time the purity of vector modes, paving the way to novel applications where the degree of non-separability can be used as an optical sensor.