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

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X~}k(W
= 2wo) of our GaN samples, a full understanding of interference in these
samples is required.
M. S. Yeganeh [38] developed techniques to analyze nonlinear interference in stacks
of thin slabs using some of the early work of Bloembergen and Pershan [39]. Here
we review the theory for the second-harmonic generated signal transmitted through
a quartz slab at normal incidence.
Fig. 2.2 schematically displays the geometry of second-harmonic generation from
a quartz slab and labels all of the nonlinear fields. The geometry consists of two
semi-infinite linear media, labeled a and 2, separated by a nonlinear slab, labeled 1.
The linear field propagates from the vacuum to the nonlinear quartz crystal, at y = O.
where it generates a second-harmonic field. This field propagates through the crystal
to the second crystal/vacuum interface at y = -d. :\ second-harmonic field is transmitted
through this interface and has a magnitude that depends on the boundary
conditions. Generally the simple Maker fringe model assumes that multiple reflections
of the second-harmonic waves and fundamental waves in the quartz crystal are
unimportant. Even without incorporating these effects in the calculation. the model
captures the oscillation in the SHG intensity from a nonlinear slab. In our model. we
include the effects of a reflected free wave from the quartz/vacuum interface.
\Ve used y-cut quartz as a normalization material in our experiments (for more
detail see section 3.5). In this geometry, the fundamental field couples to the dominant
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