As you know, a polarizing filter darkens the blue sky and this causes clouds to stand out in bold relief. The polarizing filter will increase the vividness (color saturation) of a vista without changing the overall color balance. Additionally the polarizing filter is able to cut through haze -- thus they are a valued asset for aerial photography and landscapes with distant mountains. The polarizing filter mitigates reflections that plague on glass and water and most non-conductive surfaces.

Light from the sun arrives un-polarized. As it transits the earth’s atmosphere is becomes polarized. This name comes from the observations of early scientists who tried to explain this phenomenon. They surmised that light, being electromagnetic radiation, had a positive (+) and a negative (-) content and that the polarizing filter separated the beam into two magnetic poles. This was later proven to be a false observation, however the name stuck.

The polarizing filter reduces reflections from glass depending on the angle which is 57° for glass and 53° for water. When it comes to blue sky, the angle of maximum effect is 90°. Since the wide-angle lens envelopes a super wide view, much of the expanse of a mundane sky will display different levels of strength as to the effect of polarization. This lack of uniformity is not a true vignette, however if it looks like a duck, it’s a duck.

Add to this that a filtered wide-angle lens is prone to display a vignette. This is likely due to the constraint of the inside circumference of the filter blocking peripheral rays. Also, the wide-angle lens suffers from cosign error. This causes the edges of the image to receive weaker image rays than the center of the image. This is comparable to the difference in intensity of a flashlight shining directly vs. shining obliquely. In other words a circle of light is brighter than an oval of light. The indirect flashlight beam is oval -- thus it has more surface area. This causes the intensity of the oblique rays to spread out over a larger area -- thus they are actually dimmer. This is a true vignette that plagues when a wide-angle lens is mounted