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

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waves is 0.15 J1.m. Our Ti:Ah03 beams have a spot size of ",100 J1.m, and therefore
"walk-off" is insignificant in our experiment.
Ultrafast effects are incorporated into the theory by modifying the phases of the
nonlinear waves to include the finite duration of the pulses. The transmitted SHG
wave is composed of a sum of waves that propagate through the film stack with
various phase velocities. For example, we can rewrite a transmitted second-harmonic
wave, E sp (2w o ), to explicitly display its phase dependence as
(6.33)
Comparison of equation (6.33) with equations (6.25) - (6.29) reveals that the D coefficients
consist of X~;~,
E y , Fresnel coefficients, dielectric constants. and wavevectors
in air, Ga?'J, and sapphire. D~B corresponds to the wave that propagates from point
A to point B in Fig. 6.4 and has a phase that depends on the bound wavevectors in
Ga?'J. The other D coefficients are defined similarly. The time required for the D~-\B
and D~B waves to propagate to point B and the D~-\c
and D~c waves to propagate
to point C is contained in the phase of each wave (i.e. a group velocity is associated
with each wavevector). For example, the time required for the D~B wave to propagate
from point A to point B is
~ d cos ()bl
t=-+---
v /2 Vbl
(6.34)
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