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

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where v /2 is the group velocity of the free wave in the sapphire and Vbl is the group
velocity of the bound wave in GaN. We calculated this time by replacing each wavevector
with the inverse of its group velocity. This transformation follows directly from a
first-order expansion with respect to angular frequency of the wavevectors that appear
in phases (see section 2.4.2). Thus, ultrafast effects are included in the D~B wave by
multiplying the phase by a Gaussian centered at the time required to propagate the
wave from point:\. to point B, i.e.
(6.35 )
where ~w is the angular frequency bandwidth of our Ti:AI 2 0 3 laser. The ultrafast
effects are incorporated into the other D waves by similar transformations.
6.4 Second-Harmonic Generation Spectra from GaN / Ah03
In this section we discuss our SHG spectra from GaN / :\.1 2 0 3 in the p-in/s-out and
p-in/p-out polarizations. From these spectra we extract X~~x and :'(~~x' respectively.
In addition, from our rotational symmetry measurements as a function of the angle
of incidence, we determined that the sample miscut does not induce any symmetry
r b'dd l' . . (2) (2)
lor 1 en non meantles, e.g. Xzzx or Xxzx'
In order to accurately calculate the effects of group velocity mismatch in our Ga0;
films, we measured ~w at each wavelength by determining the wavelength distribution
of the pulse with a monochrometer. In practice, group velocity mismatch is most
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