diff options
Diffstat (limited to 'source/know/concept/laser-rate-equations/index.md')
| -rw-r--r-- | source/know/concept/laser-rate-equations/index.md | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/source/know/concept/laser-rate-equations/index.md b/source/know/concept/laser-rate-equations/index.md index c81f02b..feec168 100644 --- a/source/know/concept/laser-rate-equations/index.md +++ b/source/know/concept/laser-rate-equations/index.md @@ -30,7 +30,7 @@ $$\begin{aligned} Where $$n$$ is the background medium's refractive index, $$\omega_0$$ the two-level system's gap resonance frequency, -$$|g| \equiv |\matrixel{e}{\vu{x}}{g}|$$ the transition dipole moment, +$$|g| \equiv |\!\matrixel{e}{\vu{x}}{g}\!|$$ the transition dipole moment, $$\gamma_\perp$$ and $$\gamma_\parallel$$ empirical decay rates, and $$D_0$$ the equilibrium inversion. Note that $$\vb{E}^{-} = (\vb{E}^{+})^*$$. @@ -110,7 +110,7 @@ $$\begin{aligned} Where the Lorentzian gain curve $$\gamma(\omega)$$ (which also appears in the [SALT equation](/know/concept/salt-equation/)) -represents a laser's preferred spectrum for amplification, +represents the laser's preferred spectrum for amplification, and is defined like so: $$\begin{aligned} @@ -139,7 +139,7 @@ $$\begin{aligned} Next, we insert our ansatz for $$\vb{E}^{+}$$ and $$\vb{P}^{+}$$ into the third MBE, and rewrite $$\vb{P}_0^{+}$$ as above. -Using our identity for $$\gamma(\omega)$$, +Using the aforementioned identity for $$\gamma(\omega)$$ and the fact that $$\vb{E}_0^{+} \cdot \vb{E}_0^{-} = |\vb{E}|^2$$, we find: $$\begin{aligned} @@ -218,8 +218,8 @@ $$\begin{aligned} \end{aligned}$$ Where $$\gamma_e$$ is a redefinition of $$\gamma_\parallel$$ -depending on the electron decay processes, -and the photon loss rate $$\gamma_p$$, the gain $$G$$, +depending on the electron decay processes. +The photon loss rate $$\gamma_p$$, the gain $$G$$, and the carrier supply rate $$R_\mathrm{pump}$$ are defined like so: |