User Tools

Site Tools


Sidebar

nextnano.NEGF

nextnano.MSB

Summary and introduction



nextnano++

Software documentation

Examples



nextnano³

Software documentation



nextnanomat

Software documentation



nextnano GmbH

qcl:optics

Optics: gain/absorption calculation

Permittivity and gain/absorption

The bulk relative permittivity, or dielectric constant, is assumed to be given by the Lyddane–Sachs–Teller relation:

$$ \epsilon^{\text{bulk}}_{\text{r}}(\omega) = \epsilon_{\infty} + (\epsilon_{\infty}-\epsilon_{\text{static}}) \frac{\omega_{\text{TO}}}{\omega^2-\omega^2_{\text{TO}}}$$

In the self-consistent gain calculation, the quantity which is actually calculated is the a.c. conductivity $\sigma(\omega)$.

The complex relative permittivity which is output is then:

$$ \epsilon_{\text{r}}(\omega) = \epsilon^{\text{bulk}}_{\text{r}}(\omega) - i \frac{\sigma(\omega)}{\omega \epsilon_0} $$

Finally the gain reads

$$ g(\omega) = -\frac{\text{Re}(\sigma(\omega))}{\epsilon_{\text{r}}(\omega)} $$

qcl/optics.txt · Last modified: 2020/09/08 15:58 by thomas.grange