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We assume that a homogeneous plane wave coming from a certain
direction
k_{0} = (k_{x} k_{y} k_{0, z})^{T}
strikes onto a planar homogeneous layer l.
Within the layer the electric field consists of two plane waves
traveling in opposite directions
k_{l}^{+} and
k_{l}^{}.
This situation is schematically illustrated in Figure C.1.
The electric phasor
E_{l}(x) is thus written as

(C.1) 
whereby
E_{l}^{+} and
E_{l}^{} are the wave amplitudes
traveling downwards and upwards the layer. The two wavevectors are
given by

(C.2) 
and the vertical wavevector component

(C.3) 
depends on the wavenumber
k_{l} = k_{0}n_{l} of the layer material with
refractive index n_{l}.
Figure C.1:
In a homogeneous planar layer
with refractive index n_{l} the electric field consists of two plane waves
E_{l}^{+} and
E_{l}^{} traveling downwards and upwards,
respectively.

Due to the transverseness of the plane waves the
vertical amplitude components can be expressed by the lateral ones, i.e.,

(C.4) 
Hence it suffices to study only the lateral field components of
(C.1) given by
In these two equations
E_{l, x}(z) and
E_{l, y}(z) refer to the zdependent
part of the electric field phasor. As can be seen from (C.1)
the complete phasor is obtained by multiplication with the exponential factor
exp(j(k_{x}x + k_{y}y)), which describes the lateral dependence.
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Heinrich Kirchauer, Institute for Microelectronics, TU Vienna
19980417