I notice that especially with wide angle lenses, polarizing filters have a tendency to cause vignetting. Why is this?
Some lenses, particularly wide ones, require a slim filter. When such a filter is not used, it will cause vignetting but that has nothing to do with the filter being a polarizer or not. Vignetting is mechanical and appears if something obstructs the view of the lens.
What you will see when using a polarizer on a wide-angle lens is uneven polarization which causes parts of the image to be darker than others, although it can occur in the middle of the frame or edge. The reason it happens is that polarization is strongest at 90° from the sun.
Take as an example a lens with 100° view-angle. If one edge is at 90° from the sun, the other is at 190° and the middle is at 140° and each of these parts of the image will show different polarization.
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
There's a few reasons why it may cause vinetting on your lens.
They tend to be longer than UV as they have 2 rings, one for screwing in, one for rotating. There for they will get in the edges if you're wider than 17mm on a full frame.
If you're referring to entire sides of photos it may be the way the light is reacting with your rotation.
If it's cheap the edges may not be as transparent as the center.