There are two canonical routes to sculpturing the columnar shape during growth. The first is to rotate the substrate about the axis normal to the vapor incidence plane. The second is to rotate the substrate about the axis normal to the substrate plane. The former results in a two-dimensional morphology, the latter in a three-dimensional morphology.
As both CTFs and SNTFs have two-dimensional morphologies, their macroscopic electromagnetic properties are quite similar in description. Propagation in both types of thin films is most conveniently couched in terms of a 4 x 4 MODE. An exact analytical solution of this MODE is impossible for SNTFs with arbitrarily specified morphology, so numerical solution procedures must be devised. The solution is used in turn to solve the boundary value problem of reflection and transmission of plane waves by SNTFs of constant thickness. For propagation in the morphologically significant plane, the 4 x 4 MODE breaks up into two 2 x 2 autonomous MODEs, of which one can be solved analytically. The notation developed for CTFs in Chapter 7 turns out to be very useful for SNTFs too.
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