  Increasing the complexity of a light field through the advanced manipulation
of its degrees of freedom (DoF) provides new opportunities for fundamental
studies and technologies. Correlating polarization with the light's spatial or
spectral shape results in so-called spatial or spectral vector beams that are
fully polarized and have a spatially or spectrally varying polarization
structure. Here, we extend the general idea of vector beams by combining both
approaches and structuring a novel state of light in three non-separable DoF's,
i.e. space, wavelength, and polarization. We study in detail their complex
polarization structure, show that the degree of polarization of the field is
only unveiled when the field is narrowly defined in space and wavelength, and
demonstrate the analogy to the loss of coherence in non-separable quantum
systems. Such light fields allow fundamental studies on the non-separable
nature of a classical light field and new technological opportunities, e.g.
through applications in imaging or spectroscopy.
