William Angerer - Department of Physics and Astronomy - University ...

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Equations (4.30) and (4.32) are combined with equations (4.27) and (4.28) to
determine the reflection amplitude as
(z x £~) Eo TloB - C
r=. + =~= .
(z x £Oa) Eo TloB + C
(4.33)
Equation (4.33) is derived in Appendix D. The reflection coefficient is
( 4.34)
Step 6 - Calculate the transmission coefficient.
The transmission coefficient of the thin film is calculated from the reflection coefficient
as
T = 1- R. (4.35)
Equation (4.35) assumes that the layers have real indices of refraction, i.e. the layers
do not absorb light. From equations (4.33) and (4.35), we express the transmission
coefficient as
T =
2T1o(BC· + B*C)
(TloB + C)(TloB + C)*
( 4.36)
The real part of the product BC· is easily determined by performing the matrix
multiplication in equation (4.26) and using the fact that Afl (equation (4.25)) has a
determinant equal to 1, and noting that TIl is real (this is true only for a real index
of refraction). The derivation of the transmission coefficient for a complex TIl, i.e. a
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