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

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traveling wave, i.e.
(-1.7)
where the wavevectors are
The subscript labels the layer in which the variables are defined. Angles in other
layers are derived from Snell's law. Henceforth, we omit the w dependence of the
wave. Note that equation (4.7) is the general solution to YIa.xwell's equations in each
layer assuming a plane \"ave incident on the film stack with a well defined wavevector.
The formulation of the transmission coefficient is somewhat complicated because
the boundary conditions are expressed in terms of the total tangential field. e.g. £1.
while the propagation of the field from one boundary to another in the same layer is
expressed in terms of the positive and negative going tangential fields. e.g. £~ and
£1. The calculation may be summarized in six steps as follows. First, the tangential
fields across boundary b are related to one another by boundary conditions. Second,
the boundary conditions at interface b are expressed in terms of the positive and
negative going tangential fields in layer 1. Third, the positive and negative going
fields at boundary b are related to the positive and negative going fields in layer 1
at boundary a. Fourth, the positive and negative going waves at boundary a are
expressed in terms of the total tangential fields, and boundary conditions are applied
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