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

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The bound wave, which propagates as a pulse with twice the wavevector of the
fundamental pulse, kb = 2won(wo)/c, propagates through the crystal and arrives at
the crystal/quartz interface before the free wave, which propagates with a wavevector
k f = 2won(2wo}/c.
There have been several theoretical investigations of ultrafast nonlinear pulse propagation
[42, 43, 44, 45]. The focus of these papers is to calculate conversion efficiencies
for nonlinear optical crystals. In general, the papers include the effects of group velocity
mismatch and GVD. Comly and Garmire [43] solve the problem of ultrafast
nonlinear pulse propagation by summing over a series of discrete plane wave modes.
vVe develop our theory from first principles to calculate the nonlinear pulse propagation
for any geometry. Our goal is to develop a theory that accurately predicts the
response of nonlinear materials to an ultrafast excitation in the low conversion limit.
This theory is useful for interpretation of our nonlinear optical spectroscopic data.
The remainder of this section is organized as follows.
First we calculate the
nonlinear polarization induced by an ultrafast fundamental field. Next, we calculate
the bound wave field from the nonlinear polarization. The free wave field generated
from an ultrafast fundamental pulse is then calculated.
Finally, the transmitted
second harmonic field is calculated.
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