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I've implemented the transfer-matrix method to determine the the transmittance and reflectance of a multilayer stack of thin films.

I know that (ignoring scattering) the absorbance of the entire stack can be found using the basic relation, $A = 1 - T - R$, but is there a way to find the absorbance of each layer? I'm trying to model a CCD sensor, and I need the absorption of only the light-sensitive layer (not the oxide layer above).

Initially, I thought that the absorbance of each layer, $A_i$, could be calculated from the transfer matrix associated with each layer, but now I realize that can't possibly be right since $A_i$ must depend on the entire stack, not just one layer.

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You would need to solve for the field at each layer. With the solution of the field, then you can simply calculate the power flow into the specific layer as well as the power flow out of the layer. Then, the absorption inside that specific layer can be obtained.

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  • $\begingroup$ So do you need to make two passes through the stack? One pass (like I'm already doing) to determine the reflectance/transmittance, and then another to evaluate the electric fields given the reflectance/transmittance? $\endgroup$
    – Roy Smart
    Commented Jun 8 at 19:45
  • $\begingroup$ I think that is the correct way. One pass is to find the matrix (or every submatrix), and using all the matrices you can find the fields in each layer. $\endgroup$
    – Jeez
    Commented Jun 8 at 20:01
  • $\begingroup$ Don't you always need two passes, one from the right and one from the left? (If you want the $2\times 2$ scattering matrix with all four parameters, I mean?) Those are two solutions for the fields, one with only incoming field from the right, and for the other from the left. Any solution is a combination of the two, so if you store the values for some layer along the way, you can later combine them (without an explicit extra pass for the new solution). $\endgroup$
    – Jos Bergervoet
    Commented Jun 9 at 6:12

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