Degree of unpolarization (DoUP): a single metric for all possible unpolarized beams

Unpolarized light is foundational in many optical technologies, yet current metrics fail to fully capture its complexity, especially when considering hidden or nonuniform polarization states. To overcome this, we introduce the degree of unpolarization (DoUP), a single, comprehensive metric that quantifies unpolarized beams across various sources. The DoUP is developed within a newly conceptualized normalized polarization probability space, termed J-space. This framework allows for precise comparisons of unpolarized beams and standardizes their quantification. Our findings reveal that fully unpolarized beams achieve a DoUP value of unity, while other beams deviate from this ideal, offering critical insights into their polarization behavior. By resolving these nuances, the DoUP metric opens up new avenues for optical technologies, from advanced photonic systems to quantum information science. This advancement promises a deeper understanding of polarization and broader applications in fields that rely on the precise manipulation of light.