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

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Note that the additional subscript, b. denotes that the tangential fields are defined at
boundary b.
Step 2 - Rewrite the boundary conditions at boundary b in terms of the positive and
negative going tangential fields.
In the substrate region. Le. layer 2, only a positive going wave exists. Also note
that boundary b is defined at z = O. Therefore, the boundary conditions at boundary
b may be rewritten as
(-1.13)
and
(-1.1-1)
From 'V x E = _~aa~
we can write equation {4.14} as
(·Llo)
where TJi = ~f) • Equation (4.15) is derived in Appendi.x D.
cos.
Step 3 - Determine the positive and negative going waves at boundary a from the
positive and negative going waves at boundary b in the same layer (layer I).
Boundary a is located at z = -d.
Following equation (4. 7), the positive and
negative going tangential fields at boundary a are defined in terms of the positive and
negative going waves at boundary b as
C'- _ C'- -iOt
"la - "lbe ,
'1.1+ _ '1.1+ eiOt
rLla - Tl.lb , d
'1.J- '1.1- -iOt
an Tl.la = rLlbe (4.16)
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