Photonic Non-Separability in the Classical and Quantum Domain

Light is fully described by its three degrees of freedom (DoFs), wavelength/time, space/momentum, and polarization. A deep understanding of the DoFs is central in both classical and quantum optical research. By exploring the unique possibilities that correlations of different DoFs or the correlation of one DoF with other systems offer, new technological opportunities arise. This thesis offers new experimental and theoretical perspectives on optical correlations of laser pulses and photon pairs generated in spontaneous parametric down-conversion (SPDC). This thesis introduces spectral vector beams - light pulses in which wavelength and polarization are correlated. These beams can be used for high-speed spectro-scopic measurements, where the lights spectrum can be obtained from polarization measurements alone. I extend this concept by the third DoF, correlating wavelength, space, and polarization within a single light pulse. I investigate the similarity of the loss of their degree of polarization in imprecise measurements to the loss of coherence of nonseparable quantum systems. Additionally, the thesis explores the conservation of orbital angular momentum (OAM) in photon pairs produced with SPDC. I show, that the OAM of a pump light field is transferred to the photon pair in agreement with the conservation of OAM. For the first time, I demonstrate that this conservation law is also valid for a single-photon pump. This work not only explores fundamental descriptions but also provides the ex- perimental framework to generate light fields with complex hybrid correlations. The research demonstrates the potential for a deeper understanding of light’s versatile DoFs.