deletions | additions       diff --git a/newcommand_para_1_left_1__.tex b/newcommand_para_1_left_1__.tex  index 761f27c..0aafed7 100644  --- a/newcommand_para_1_left_1__.tex  +++ b/newcommand_para_1_left_1__.tex 
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In the straightforward case of $\epsilon = 0$, 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  $$ \kappa(\epsilon) * L \simeq \beta^{(3)} \Delta\omega \Delta\Omega \epsilon + \beta^{(4)}/24 (8\Delta\omega\Delta\Omega^3)  = $$ (\epsilon + \Delta\Omega)/\delta\omega_{bs}$$  in which we can identify the process acceptance-bandwidth $\delta\omega_{bs}$, 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 [Inoue94,Marhic96] is highlighted by equation \ref{eq:ph}, that is translation for any given pair of signal and idler frequency can be exacly exactly  phasematched by choosing the appropriate pumps: this gives the flexibility of tuning the parameters of the interaction without the modifing modifying  the dispersion of the nonlinear medium.