With the experimental setup you describe, you would not observe any intentional polarization dependence, because the light passes only through a beam splitter, not a polarizer.
There can be unintentional polarization due to the nature of optical materials and manufacturing, caused by
- the diffraction grating,
- the polarization contribution of mirror reflections, and
- the diffraction grating slits.
With that out of the way, UV/Vis absorption is polarization dependent. In theory, polarization can occur in any spectroscopic technique where the polarization of the incident EM radiation can be controlled. To quote the Wikipedia article,
In general, any kind of anisotropy in the media results in some sort of change in polarization. Such an anisotropy can be either inherent to the media (e.g., in the case of a crystal substance), or imposed externally (e.g., in the presence of magnetic field in plasma).
Assuming that no other external fields are applied other than your probe beam and your bulk phase has no anisotropy, any differential absorption of polarized light must come from the molecules themselves, namely those that are "optically active". Linear dichroism and particularly circular dichroism are used to describe the differential absorption of linearly and circularly polarized light, respectively. Electronic (UV/Vis) CD is widely applied in the determination of protein secondary structure and the absolute configuration of stereocenters in chiral molecules. An ECD spectrum is usually presented as a difference spectrum between the left- and right-polarized spectra, which themselves are no different from a typical UV/Vis spectrum.
The parent dichroism article is a good starting point for learning about these spectroscopies.
