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

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D.2 Derivation of equation (4.21)
The boundary condition for the electric fields at boundary b (equation (4.13)) can be
written as
• co+ • co+ • co-
Z X C,2b = Z X C,lb + Z X C,lb· (0.10)
The boundary condition for the magnetic fields at boundary b can be expressed using
equations ( .. 1.14) and (4.15) as
Hb • co+ - co-
- = Z X C,lb - Z X C,lb.
T/l
(0.11)
Combining equations (D.10) and (D.ll) determines the positive going tangential electric
field in layer 1 at boundary b in terms of the tangential electric and magnetic
fields at boundary b as
(0.12)
The other expressions in equation (4.21) are derived by a similar analysis.
D.3 Derivation of equation (4.33)
In this section, we derive the reflection amplitude from a thin film. The boundary
conditions for the electric and magnetic fields at boundary a are
(z x Eta) + (z x E~) = (z x £~) + (z x E~) (0.13)
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