Wikipedia https://en.wikipedia.org/wiki/Semiconductor_optical_gain proposes the following formula for the material gain in semi-conductor:
$$ g(\varepsilon) = \frac{\nu\mu_0^2}{4\pi\epsilon_0n} \left(\frac{2m_r}{\hbar}\right)^{3/2}\sqrt\varepsilon $$
where $\nu$ a frequency, $\mu_0$ a dipole moment, $\epsilon_0$ the permittivty of vaccum, n the refractive index (non dimensional), $m_r$ is a reduced mass and $\varepsilon$ the energy at which it is computed.
The result is supposed to be in $m^{-1}$ but a dimensional analysis shows that this is in $s^{-1}$.
I wonder if the result should have been divided by $c$ for it to work?