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

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In particular, this effect could dominant nonlocal effects for samples with large nonlinear
susceptibilities that have components perpendicular to a surface. An example
of such a sample is a film of rod-like nonlinear molecules that lie nearly perpendicular
to a substrate.
It is instructive to analyze this effect on the nonlinear polarization generated in
Si (100). A normally incident wave of the form of equation (7.5) induces a nonlinear
polarization in Si (100) directed along the x direction due to the transverse gradient
of the standard field polarized along the x direction and the anomalous field polarized
along the z direction. We can compare the nonlinear polarization induced by each
effect as
p(2) ,standard
x
pJ2),anomaJous
r ~E2exp( _ x 2 +l 2 )
Wo
- r 2x 3 E2 ( x +,2 ).
2
x=x:: k2wg exp - Wo
xxxx Wo
(7.6)
where Pl2).standard is the nonlinear polarization induced by the transverse gradient
of the standard field, i.e. the first term in equation (7.5), and pp),anamalous is the
nonlinear polarization induced by the transverse gradient of the anomalous field. i.e.
the second term in equation (7.5). The SHG signal detected is simply the SHG
intensity integrated over the area of the SHG beam. Therefore, the ratio of the
intensities is
I(2w)standard 16r2
_..:.-,......:.....,.......,,...--,-- = xxxx (kw )-l
I(2w) polarization 15r2 o·
xzx=
(7.7)
If we assume r =x=x = r xxxx; the fundamental wavelength, A, is 800 nm: and the spot
size, w o , is 3 f.lm, then this ratio is '" 3 X 10 5 • Therefore, the anomalous fundamental
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