Does the polarization of white light affect its dispersion? The only way to change the oscillation of light waves is through polarization and to the best of my knowledge there are 3 types namely:


*

*Linear Polarization

*Circular Polarization

*Elliptical Polarization


I am trying to find if there's any relationship/difference between dispersion of unpolarized and polarized  light in a given medium (a glass prism in this scenario).
Specifically what I want to achieve is rotating/changing the oscillations of the rays of light such that when I pass the rotated rays through a glass prism the result of the dispersion would be VIBGYOR instead of ROYGBIV?
(As usual, here the letters R, O, Y, G, B, I, and V stand for Red, Orange, Yellow, Green, Blue, Indigo and Violet, respectively.)
 A: This is in principle possible, and the phenomenon is known as birefringence, i.e. the medium refracts light in two different ways, depending on the polarization. Most everyday materials do not exhibit birefringence in usual circumstances, but it's possible to find materials that do.
Now, as to whether you'll be able to find a material that exhibits a normal glass-like refractive-index ramp on one polarization together with an identical-but-inverted ramp on the orthogonal polarization $-$ that's way harder, and I would not bet any money on a material like that existing naturally. It might be possible to achieve using some metamaterial construction, but it'd likely take a great deal of dedicated effort to make.
If you just want the inverted order, though, then the thing to look for is 'anomalous dispersion' (i.e. dispersion which goes in the opposite way to the normal one). I'm unsure whether there are any transparent everyday materials that exhibit anomalous dispersion that can be used to make a prism, but I wouldn't put down any money on that, either.
A: Anomalous dispersion occurs only within the bandwidth of an absorption resonance.  I don't know of any materials with a wide enough and strong enough resonance peak, especially in the visible range, to serve the purpose.  Maybe as Emilio Pisanty suggests it can be done with an optical metamaterial. However: note that an arrangement of beamsplitters and prisms could accomplish something very similar to what you want.  Here, A is a polarizing beamsplitter and B is a non-polarizing beamsplitter.

