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

Appendix C
Justification of Zeroth Order Expansion of the Coefficients in the
Ultrafast Nonlinear Pulse Calculation
In section 2.4.4, we used a zeroth order expansion of w about the central angular
frequency of the pulse, 2w o , for all coefficients that appear in the wave equation. In
this appendix, we restate the simplified form of the bound wave field and demonstrate
that the simplification leads to a negligible correction to the SHG intensity.
From equation (2.38), we derived the relationship between the bound wave. Eb r
and the second order nonlinear polarization, PP) as
(C.l)
\Ve then simplified this relationship by assuming
w = 2w o • (C.2)
This leads to the approximations
(C.3)
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