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

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space representation allows the simplification of the nonlinear wave equation from
a partial differential equation to an algebraic equation. Therefore. we must derive
the generalized second order nonlinear response function in angular frequency space.
This may be effected by Fourier transforming equation (B.1). The Fourier transforms
are defined in the usual way as
(B.3)
and
E(w) = -.
1 100
27r -00
E(t)eiwtdt
(B..1)
with
(B.5)
The frequency space representation of X(2) (t - T1, t - T2) follows as
y(2) (t _ T t _ To ) = 100
100
y(2) (w ., )e-iW1(t-TI )e-iW2(t-T2)dl.J;' d' "
''-Ilk 1, 2 ''-Ilk 1,w2 1 ""'1,
-00 -00
(B.6)
Therefore. the time representation of the nonlinear polarization may be written explicitly
as
(B.7)
Using the Fourier transform equations, equation (B.7) can be expressed as
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