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qcl:optics
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qcl:optics [2021/07/12 08:36] thomas.grange |
qcl:optics [2023/07/05 08:36] (current) thomas.grange [Permittivity and gain/absorption] |
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| The bulk relative permittivity, or dielectric constant, is assumed to be given by the [[https://en.wikipedia.org/wiki/Lyddane%E2%80%93Sachs%E2%80%93Teller_relation|Lyddane–Sachs–Teller relation]]: | The bulk relative permittivity, or dielectric constant, is assumed to be given by the [[https://en.wikipedia.org/wiki/Lyddane%E2%80%93Sachs%E2%80%93Teller_relation|Lyddane–Sachs–Teller relation]]: | ||
| - | $$ \epsilon^{\text{bulk}}_{\text{r}}(\omega) = \epsilon_{\infty} + (\epsilon_{\infty}-\epsilon_{\text{static}}) \frac{\omega_{\text{TO}}}{\omega^2-\omega^2_{\text{TO}}}$$ | + | |
| + | $$ \epsilon^{\text{bulk}}_{\text{r}}(\omega) = \epsilon_{\infty} + (\epsilon_{\text{static}}-\epsilon_{\infty}) \frac{\omega_{\text{TO}}}{\omega^2_{\text{TO}}-\omega^2 + i \omega \gamma_{\text{TO}}}$$ | ||
| + | |||
| + | where $\gamma_{\text{TO}}$ is the intrinsic linewidth of transverse optical phonon due to damping into other phonons by anharmonicity of the crystal. It can be set in the input file using | ||
| + | |||
| + | <code> | ||
| + | <Scattering> | ||
| + | … | ||
| + | <PhononDamping Unit="meV">2.0</PhononDamping> | ||
| + | </Scattering> | ||
| + | </code> | ||
| In the self-consistent gain calculation, the quantity which is actually calculated is the a.c. conductivity $\sigma(\omega)$. | In the self-consistent gain calculation, the quantity which is actually calculated is the a.c. conductivity $\sigma(\omega)$. | ||
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| $$ g(\omega) = -\frac{\text{Re}(\sigma(\omega))}{\epsilon_{\text{r}}(\omega)} $$ | $$ g(\omega) = -\frac{\text{Re}(\sigma(\omega))}{\epsilon_{\text{r}}(\omega)} $$ | ||
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qcl/optics.txt · Last modified: 2023/07/05 08:36 by thomas.grange
