deletions | additions       diff --git a/section_Four_wave_mixing_Bragg__.tex b/section_Four_wave_mixing_Bragg__.tex  index 7eae425..57c0c21 100644  --- a/section_Four_wave_mixing_Bragg__.tex  +++ b/section_Four_wave_mixing_Bragg__.tex 
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Fig. 1. Cartoon of FWM-BS. A) Energy level depiction. B) Dispersion picture.  FWM-BS interactions are driven by two strong pump fields, whose frequency separation Δω define the amount of frequency translation between signal and idler (see fig. 1) []. 1).  The efficiency of the translation process is , $\\eta=r^2/k_{bs}^2 \sin(k_{bs} L)$,  where $r = 2\gamma P$  is the coupling strength term, $k_{bs} = sqrt{\kappa^2+r^2} $  the scattering wavevector, and γ, L $\gamma$, $L$  and P $P$  respectively the medium nonlinearity, the interaction length and the pump power. $\kappa = \beta(\omega_s) - \beta(\omega_i) - \beta(\omega_1) + \beta(\omega_2)$  is the phasematching term: it is convenient to describe all fields expand the wavevector $\beta(\omega)$  in respect of the zero dispersion frequency $\omega_{ZDW}$  of the nonlinear medium (i.e. and ), $\beta^{(2)}(\omega_{ZDW}} = 0$) so that $\beta(\omega) = \beta^{(3)} (\omega-\omega_{ZDW})^3 + \beta^{(3)}/6 \cdot (\omega- \beta^{(3)}/24 \cdot \omega_{ZDW})^4$,  and to introduce the average pump frequency $\Delta \Omega = ..$  and the signal offset $\epsilon$  so that the frequency and idler signal $\omega_s = \epsilon -\Delta\Omega + \Delta\omega/2$  and $\omega_s = \epsilon -\Delta\Omega - \Delta\omega/2$  (see figure 1b). The phasematching now reads and simplifies to   In the straightforward case of = 0, the term (as well as all the other odd terms) cancels out, leaving only smaller contribution from higher order dispersion.