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

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vVe calculate the effect of GVD on our second harmonic pulse of the form equation
(A.l) that propagates through a 3 mm piece of quartz. vVe used the dispersion
relationship listed in equation (2.67) and Table 2.3. vVe assume the fundamental pulse
has a pulse width of 130 fs. For the parameters stated above, the pulse broadens less
than 2 x 10- 6 % for both the free and bound waves over a fundamental wavelength
range of 740 nm to 1 J..lm for a film thickness of 3 mm. For GaN, the free wave pulse
broadens by .43% and the bound wave pulse broadens by less than 10- 6 % for a film
thickness of 5 J..lm over a wavelength range of 740 nm to 1 J..lm.
These values were
calculated using the Sell meier dispersion relation for GaN with the parameters listed
in Table 4.2.2. This justifies our first order expansion of k with respect to..v. Xote.
since the bound wave propagates with a wavevector twice that of the fundamental
field. the broadening of the fundamental wave can be related to the broadening of the
bound wave by
fundamental"" 8rbound
rout out . (A.8)
Thus. the fundamental wave does not appreciably broaden during propagation
through the Ga~ film or quartz crystal.
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