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

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nonlinear waves. This model assumes no multiple reflections of the free waves. Multiple
reflections affect the transmitted intensity by 4%, and are therefore insignificant.
We apply the continuity of E tan and H tan at both quartz/air interfaces (y = 0 and
y = -d) to determine the free wave fields (see section 2.4.1). Here we repeat this
calculation to determine the angular frequency envelopes of the free waves, «(.....:) , and
hence the free waves. Ultimately, we want to calculate the intensity of the transmitted
second-harmonic field, E f2 (r, t), and compare this with the SH intensity generated
from a monochromatic source.
Matching boundary conditions for an ultrafast pulse is complicated by the spread
in frequencies, and hence wavevectors. This dilemma is solved by selecting a specific
..J, which forces the vacuum k to be w/c. In other words, the boundary conditions hold
for each angular frequency of the pulse. vVith this in mind, the continuity equations
at y = 0 are
(fl(W) + (bl(W)
= (fo(w)
(2..16)
kfl (w)(/l (w) + kbl(W)(bl(W) = -kfo(w)(fQCw).
(2..17)
Propagating the fields to y = -d and applying the continuity of the tangential components
of the fields yields
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