Diffraction theory is scalar. How you deal with beam propagation in fourier optics that is sensitive to the to the polarization?
If I have linearly polarized gaussian beam incident on glass surface, how is the polarization included in the propagation code/theory ?
What I am ultimately interested is to have let say linearly polarized input gaussian beam to propagate through a hollow fiber. I will use split step to propagate if that matters. And how is it done if thats not good approach ?
You can have vector diffraction theory as John suggests or, if you want to use just scalar theory, you can use normal modes. In general, you then need to find two orthogonal polarization modes that do not change polarization during the transmission, e.g., polarization parallel and perpendicular to a reflecting surface if you have a glass plate in the way. Then, you write your beam as a linear combination of these two modes and apply scalar diffraction theory on each of them. At the end, you just combine the two output modes (with the weights they have in the input beam) and you have the output beam.
Vector diffraction is a completely standard theory found in any graduate textbook such as Stratton, Jackson, Landau & Lifshits, Born & Wolf, etc. In any case your question has to do with waveguides; from what little you've said, it's not obvious to me that this requires a vector theory.
