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authorPrefetch2022-04-01 10:10:31 +0200
committerPrefetch2022-04-01 10:10:31 +0200
commit2677f9bd104515b598fa49d1ae78fa112d879e8d (patch)
tree6b31ac33a95454a05249ad436b45d49f705b4c6d /content/know/concept/coupled-mode-theory
parenta77d159d6a7f73252308459fe121a28df99b6df2 (diff)
Update "uses" page. Probably last commit for several months.
Diffstat (limited to 'content/know/concept/coupled-mode-theory')
-rw-r--r--content/know/concept/coupled-mode-theory/index.pdc5
1 files changed, 3 insertions, 2 deletions
diff --git a/content/know/concept/coupled-mode-theory/index.pdc b/content/know/concept/coupled-mode-theory/index.pdc
index 5a44d6e..c9e9ad4 100644
--- a/content/know/concept/coupled-mode-theory/index.pdc
+++ b/content/know/concept/coupled-mode-theory/index.pdc
@@ -190,8 +190,9 @@ $$\begin{aligned}
&\quad\; + S_\ell^\mathrm{in} (S_\ell^\mathrm{out})^* - \beta_\ell^* |S_\ell^\mathrm{in}|^2
+ (S_\ell^\mathrm{in})^* S_\ell^\mathrm{out} - \beta_\ell |S_\ell^\mathrm{in}|^2
\\
- &= - (|\beta_\ell|^2 + \beta_\ell + \beta_\ell^*) |S_\ell^\mathrm{in}|^2
- + (1 - \beta_\ell) S_\ell^\mathrm{in} (S_\ell^\mathrm{out})^* + (1 - \beta_\ell^*) (S_\ell^\mathrm{in})^* S_\ell^\mathrm{out}
+ &= - (|\beta_\ell|^2 + \beta_\ell + \beta_\ell^*) |S_\ell^\mathrm{in}|^2 - |S_\ell^\mathrm{out}|^2
+ \\
+ &\quad\; + (1 - \beta_\ell) S_\ell^\mathrm{in} (S_\ell^\mathrm{out})^* + (1 - \beta_\ell^*) (S_\ell^\mathrm{in})^* S_\ell^\mathrm{out}
\end{aligned}$$
This equation is only satisfied if $\beta_\ell = -1$.