Nonseparable states of light: From quantum to classical
Controlling the various degrees-of-freedom (DoFs) of structured light at both quantum and classical levels is of paramount importance in optics. It is a conventional paradigm to treat diverse DoFs separately in light shaping. While, the more general case of nonseparable states of light, in which two or more DoFs are coupled in a nonseparable way, has become topical recently. Importantly, classical nonseparable states of light are mathematically analogue to quantum entangled states. Such similarity has hatched attractive studies in structured light, e.g. the spin-orbit coupling in vector beams. However, nonseparable classical states of light are still treated in a fragmented fashion, while its forms are not limited by vector beams and its potential is certainly not fully exploited. For instance, exotic space-time coupled pulses nontrivial light shaping towards ultrafast time scales, and ray-wave geometric beams provide new dimensions in optical manipulations. Here we provide a bird's eye view on the rapidly growing but incoherent body of work on general nonseparable states involving various DoFs of light and introduce a unified framework for their classification and tailoring, providing a perspective on new opportunities for both fundamental science and applications.