deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 3784b85..88320f3 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
\[\widetilde{B}(z)=\widetilde{B}(0)\left(\frac{i \kappa_{ba}}{\beta_c} sin \beta_c z \right) e^{-i \delta z} \] where $\beta_c=\left( \kappa_{ab}\kappa_{ba}+\delta^2\right)^\frac{1}{2}$   Then looking at the power of the two modes when they are completely phase matched, that is when $\delta=0$   \[\frac{P_a(z)}{P_a(0)}=|\frac{\widetilde{A}(z)}{\widetilde{A}(0)}|^2=cos^2 \beta_c z \]   \[\frac{P_b(z)}{P_a(0)}=|\frac{\widetilde{B}(z)}{\widetilde{A}(0)}|^2=sin^2 \beta_c z\] where $\kappa_{ab}=\kappa_{ba}^{*}$ Define the coupling efficiency for a length l as $\eta=\frac{|\kappa_{ba}|^2}{\beta_c ^2} sin^2 \beta_c z$