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Scattering is a general term for several physical processes in which radiation of some sort changes direction due to an interaction with a particle. Scattering can be classified by the type of radiation (ie, electromagnetic, x-ray, neutron), or by the relative sizes of the wave and the particle (ie, Rayleigh, Mie, geometric).
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Non-square transfer matrix from square scattering matrix
However, for my purposes I can just write out the separate equations resulting from the 3x3 scattering matrices and solve the system brute-force. … TLDR; don't need the transfer matrices, scattering matrices do just fine on their own. …
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Non-square transfer matrix from square scattering matrix
(Image borrowed from http://www.fiberstore.com/images/ckfinder/images/tutorial/1x2_Splitter.jpg)
Currently, I have the entire scattering matrix for my device:
$$
\begin{pmatrix}
A_\text{in}^{(-)}\\ … It seems that generating a transfer-matrix for such a splitter should be quite straightforward, especially since I already have the scattering matrix data. Am I missing something here? …