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

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Fourier transform to E /2 (r, w) as
( ? _.;:Kl --)
vVhen k/ is used as a coefficient, (2.51) is the appropriate equation. .-\ first-order
expansion,
(2.56)
, is required for any k / which appears in a phase. The second term in equation (2.56)
contains an expression for the free wave group velocity in the quartz crystaL
8kl
8w 2w o
1
(?_.;) --) I
The functional form of (bl (w) is determined by the calculations in section 2..!..! as
(2.58)
with Po is defined by equation (2.34). Csing equations (2.27), (2.50), (2.54), (2.55).
(2.56), and (2.58), the a part of the frequency space representation of the transmitted
nonlinear field can be Fourier transformed to the time domain in the following steps.
The a integral can be expressed as
(2.59)
Integration of equation (2.59) with respect to w yields
(2.60)
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