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Diffstat (limited to 'content/know/concept/maxwell-bloch-equations')
| -rw-r--r-- | content/know/concept/maxwell-bloch-equations/index.pdc | 15 |
1 files changed, 12 insertions, 3 deletions
diff --git a/content/know/concept/maxwell-bloch-equations/index.pdc b/content/know/concept/maxwell-bloch-equations/index.pdc index ae7d119..020a120 100644 --- a/content/know/concept/maxwell-bloch-equations/index.pdc +++ b/content/know/concept/maxwell-bloch-equations/index.pdc @@ -393,9 +393,18 @@ It is trivial to show that $\vb{E}$ and $\vb{P}$ can be replaced by $\vb{E}^{+}$ and $\vb{P}^{+}$. It is also simple to convert the dipole $\vb{p}^{+}$ and inversion $d$ -into their macroscopic versions $\vb{P}^{+}$ and $D$, -simply by averaging over the atoms per unit of volume. -We thus arrive at the **Maxwell-Bloch equations**: +into their macroscopic versions $\vb{P}^{+}$ and $D$: + +$$\begin{aligned} + \vb{P}^{+}(\vb{r}, t) + = \sum_{n} \vb{p}^{+}_n \: \delta(\vb{r} \!-\! \vb{r}_n) + \qquad \quad + D(\vb{r}, t) + = \sum_{n} d_n \: \delta(\vb{r} \!-\! \vb{r}_n) +\end{aligned}$$ + +We thus arrive at the **Maxwell-Bloch equations**, +which are relevant for laser theory: $$\begin{aligned} \boxed{ |