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

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and
(CA)
with f.b == t(.:.vo) and f./ == f.(2wo). These simplification lead to the relationship
(C.5)
vVe compare this to the relationship between Eb r
and PP) without the zeroth
order expansion, namely
(C.6)
The quantity that we measure is the SHG intensity averaged over all angular frequendes.
:\"ote. this is obviously identical to the SHG intensity averaged over the pulse
duration ..-\s stated previously, the SHG intensity depends on both the bound wave
and free wave fields. The free wave is related to the bound wave by factors that are
independent of w. Therefore, it is sufficient to compare the intensities of the bound
waves with and without the zeroth order phase approximation to determine if the
phase approximation is valid. For GaN (quartz), the discrepancy between the zeroth
order approximation and the full approximation is less than .17% (.06%) over the
fundamental wavelength range of 740 nm to 1 /-lm. Thus, the zeroth order expansion
of w is valid for the coefficients of the bound wave field.
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