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# Optical transitions from $`k \cdot p`$ matrix elements
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## Ansatz: Perturbation Hamiltonian for EM wave
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## Matrix elements derived from $`k \cdot p`$ Hamiltonian
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## Spectra
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In order to compare $`k \cdot p`$ results with experimental data, we calculate energy spectra for measureable quantities (absorption, rotation, ellipticity).
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### Filtering transitions
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So far we have calculated all transitions in the system, without taking into account whether their excitation is actually possible.
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A transition can only contribute to the spectrum, if the EM wave excites from a (partially) filled state into a (partially) unfilled state. We use the Fermi distribution function to calculate the filling factors for each state and weight the transition by the filling factors of its states.
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Additionally, only transitions that absorb energy are relevant for most experimental spectra, as inchoerent emission usually can not be measured in the THz regime (energetic scale of HgTe transitions at interest) and stimulated emission does not play a role.
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### Optionally: Calculation of DOS
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### Experimental quantities
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#### Absorption
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#### Ellipticity
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Since a single transition absorbs only left or right circularly polarized photons in our case, we can calculate the ellipticity directly from the absorption.
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# Old notes (archived)
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[Optical transitions pdf W.Beugeling 2018-11-02](uploads/a5c7008408b926d77f72e7f305a368d4/optical-transitions.pdf)
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Old note on optical transition calculation. Note that this does only include a minor subset of relevant matrix elements and fails to reproduce experimental data near the p-type regime. |
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