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Chris Spencer edited untitled.tex
about 9 years ago
Commit id: 157f799714936717a7459936be80a1a3be5b300e
deletions | additions
diff --git a/untitled.tex b/untitled.tex
index 729c484..de1955c 100644
--- a/untitled.tex
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...
\widetilde{B}(z_0)\\
\end{bmatrix}$$
Where $F(z;z_0)$ is the forward coupling matrix and it relates field amplitudes at an intial value of $z_0$ to those at z. For the most simple case when power is launched into only mode a at $z=0$ , giving $\widetilde{B}(0)=0$. With $z=0$
\[\widetilde{A}(z)=\widetilde{A}(0)\left( cos \beta_c z -\frac{i \delta}{\beta_c} sin \beta_c z \right) e^{i \delta z} \]
\[\widetilde{B}(z)=\widetilde{B}(0)\left(\frac{i \kappa_{ba}}{\beta_c} sin \beta_c z \right) e^{-i \delta z} \]