deletions | additions       diff --git a/section_Four_wave_mixing_Bragg__.tex b/section_Four_wave_mixing_Bragg__.tex  index 6c1ced1..2f62882 100644  --- a/section_Four_wave_mixing_Bragg__.tex  +++ b/section_Four_wave_mixing_Bragg__.tex 
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- \para{-\frac{\Delta\omega}{2} +\Delta\Omega}^4 \right]   \end{align}  and simplifies to   $$ \label{eq:ph} \kappa = \frac{\beta^{(3)}}{6} \left[ 3 \Delta\omega \epsilon (\epsilon-2\Delta\Omega) \right ]+ \right]+  \frac{\beta^{(4)}}{3} \left[\Delta\omega (\epsilon-2\Delta\Omega) \para{\Delta\omega^2+4\Delta\Omega - 4\Delta\Omega\epsilon + 4\epsilon^2} \right]  $$