deletions | additions       diff --git a/section_Four_wave_mixing_Bragg__.tex b/section_Four_wave_mixing_Bragg__.tex  index fdf635d..6cff2ae 100644  --- a/section_Four_wave_mixing_Bragg__.tex  +++ b/section_Four_wave_mixing_Bragg__.tex 
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In the straightforward case of $\epsilon = 0$, i.e., the fields two and two are symmetrical in respect of $\omega_{ZDW}$ (as in figure \ref{fig:cartoon}b ), the $\beta^{(3)}$ term (as well as all the other odd terms of $\kappa$) cancels out, leaving only the contribution from higher order dispersion.  In the approximation $\Delta\Omega \gg \Delta\omega \gg \epsilon$ we obtain a simpler expression for the process momentum conservation  $$ \kappa(\epsilon) L \simeq \beta^{(3)} L  \Delta\omega \Delta\Omega \epsilon + \beta^{(4)}/24 \beta^{(4)}L /24  (8\Delta\omega\Delta\Omega^3) = (\epsilon + \Delta\Omega)/\delta\omega_{bs}$$ in which we can identify the process acceptance-bandwidth $\delta\omega_{bs}$, $\delta\omega_{bs} = (\beta^{(3)} L \Delta\Omega\Delta\omega)^{-1}$,  and the frequency separation from symmetric point $\delta\epsilon = \frac{\beta^{(4)}}{3 \beta^{(3)}} \Delta\Omega^2$ due to higher-order dispersion \cite{Provo_2010}. One prominent feature of FWM-BS, already noticed in \cite{Inoue_1994, Marhic_1996} is highlighted by equation \ref{eq:ph}, that is translation for any given pair of signal and idler frequency can be exactly phasematched by choosing the appropriate pumps: this gives the flexibility of tuning the parameters of the interaction without modifying the nonlinear medium dispersion.