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transfermatrix.jl's Issues

Calculate scattering matrix

Right now the transfer matrix method is used. While the current research in transfer matrices tries to mitigate its shortfalls (singularities and numerical instabilities), scattering matrices avoid these from the start. It would probably be more efficient and definitely more broadly useful to the photonics community to use scattering matrices instead of transfer matrices. In any case, once the transfer matrix is calculated, the scattering matrix elements are still calculated in the end to get transmission and reflection. (see this discussion)

Proposal: keep the current transfer matrix code, but write a scattering matrix implementation and have both available.

p-pol, s-pol ordering in 4x4 TMM formalism

Looking through your code, it looks like in your 4x4 transfer matrix formulation has a opposite ordering to Yeh' s book p246 - 247. (Yeh Pochi. 2005. Optical Waves in Layered Media. Hoboken NJ: Wiley.) In Yeh's book, he ordered the s-pol in the upper half of the vector and p-pol in the lower, while your implementation seems to reverse such ordering and hence, your s, p subscripts are swapped compared with Eq. (9.7-23) - (9.7-30) in Yeh's book. I guess it may be helpful to include that in the documentation to avoid confusion? Maybe something like Eq. (9.7-22) in Yeh's book but with your ordering scheme would suffice as a clarification? Thank you.

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