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

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fields at the lh interface to the known tangential electric and magnetic fields at the
adjacent (j_l)th interface. In general. optical properties are described by a complex
index of refraction, ii = n + i/'i,. However. our CaN thin films are characterized by
a real index of refraction over the spectral range probed in our experiments. Thus.
we derive our transmission theory assuming a real index of refraction of Ca~. The
more general transmission theory with complex indices of refraction, which describes
transmission and reflection including effects of absorption, is discussed in Appendix D.
\Ve first describe the method for the transmission of p-polarized light through a single
layer. \Ve then generalize the theory to multiple layers and apply it to our case of
light transmission through the CaN / Al 2 0 3 sample.
Fig. 4.6 displays the geometry of light incident on a single thin film. By applying
boundary conditions at each interface, a relationship is developed between the tangential
components of the fields on each side of the interface. In addition. fields at
different locations within the same layer are related to one another via a phase factor.
From these relationships, the transmission coefficient of the thin film is calculated.
In the following analysis, we use bold faced letters, e.g. E, to denote total fields. and
script letters, e.g. £, to denote tangential fields.
:\. single thin film consists of three layers: the incident layer. the thin film layer.
and the substrate layer. In layer 1, the electric field consists of a positive and negative
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