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

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wave at normal incidence is
(7.3)
where k is the wavevector of the fundamental field. The nonlinear polarization expressed
in equation (7.3) cannot radiate a second-harmonic wave into the vacuum.
In contrast, the transverse profile of the Gaussian wave varies appreciably in the
focal plane, and the Gaussian wave induces a nonlinear polarization with components
parallel to the silicon surface, i.e. pP) and P~2).
The nonlinear polarization
induced in Si (100) excited by a x-polarized Gaussian wave at normal incidence, i.e.
equation (7.1), is
(7.-1)
This nonlinear polarization has components along x and y, and can radiate a SH field
into the vacuum. Thus, unlike our SHG spectroscopy of GaN, which is adequately
described by plane waves, SHG microscopy requires a Gaussian waye description.
An additional significant effect in nonlinear optical microscopy is the anomalous
behavior of the polarization of a highly focussed beam. Carter [109. 1101 determined
that tightly focused Gaussian beams consist of a longitudinal field in the focal plane.
l.e.
~ (X2 + y2) . _ x (X2 + y2 )
E(x, y, z = 0) = xEexp - 2 - zZ-k 2 Eexp - 2 .
Wo Wo Wo
( 7.5)
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