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\[\widetilde{A}(z)=\widetilde{A}(0)\left( cos \beta_c z -\frac{i \delta}{\beta_c} sin \beta_c z \right) e^{i \delta z} \]  \[\widetilde{B}(z)=\widetilde{B}(0)\left(\frac{i \kappa_{ba}}{\beta_c} sin \beta_c z \right) e^{-i \delta z} \]  Then looking at the power of the two modes   $\frac{P_a(z)}{P_a(0)}=\mod{\frac{\widetilde{A}(z)}{\widetilde{A}(0)}}^2$ $\frac{P_a(z)}{P_a(0)}=|{\frac{\widetilde{A}(z)}{\widetilde{A}(0)}|^2$