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

Appendix A
Justification of First Order Expansion of the Phase
In sections 2AA and 2.4.5, we truncated the expansion of k(w) to first order in
(w - 2wo) for any k(w) which appeared in a phase. In this appendix, we justify this
expansion by demonstrating that the second order term is negligible for the second
harmonic pulse generated in quartz or GaN from a Ti:Ah03 fundamental source. The
calculation follows the analysis developed by Silverstri et al [117].
The first order term in the expansion of k(w) about (w - 2wo) gives rise to the
group velocity mismatch which damps the interference of the bound and free waves.
The second order term in the expansion accounts for the broadening of the pulse
in time. This effect, known as group velocity dispersion (GVD), occurs because the
frequency components of the pulse do not have the same group velocity. The pulse
broadening increases as the distance through which pulse propagates increases or the
dispersion is increased.
In equation (2.42) we defined the general form of the nonlinear ultrafast waves
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