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nnp:optics:absorption_spectrum
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nnp:optics:absorption_spectrum [2017/02/01 15:43] zoltan.jehn [Physics Model] |
nnp:optics:absorption_spectrum [2017/02/20 21:25] (current) stefan.birner [Eigenvalues] |
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| \[ | \[ | ||
| - | R_{ba} = \frac{2}{V} \sum_{k_a} \sum_{k_b} \frac{2 \pi}{ \hbar} |H_{ba}| ^2 \delta(E_b - E_a -\hbar \omega)(1-f_a) \cdot f_b | + | R_{ba} = \frac{2}{V} \sum_{k_a} \sum_{k_b} \frac{2 \pi}{ \hbar} |H_{ba}| ^2 \delta(E_b - E_a -\hbar \omega)(1-f_a) \cdot f_b, |
| \] | \] | ||
| - | Where the $|H_{ba}|$ depends on the polarization and the $k$ vector. | + | where the matrix element $|H_{ba}|$ depends on the polarization of light and the $\bf k$ vector. |
| ==== Input File ==== | ==== Input File ==== | ||
| Line 18: | Line 18: | ||
| ===== Results ===== | ===== Results ===== | ||
| ==== Transition Matrix Element ==== | ==== Transition Matrix Element ==== | ||
| - | The transition matrix element $H_{ab}(k)$ is plotted in the function of $\vec{k}$ for a 1D structure in figure {{ref>absk}} | + | The transition matrix element $H_{ab}({\bf k})$ is plotted as a function of ${\bf k}=(k_x,k_y)$ for a quantum well structure (1D simulation) in figure {{ref>absk}} |
| <figure absk> | <figure absk> | ||
| ;#; | ;#; | ||
| - | <dataplot dimension=2 xlabel="k_x" ylabel="k_y" ylegends="" 600x400> | + | <dataplot dimension=2 xlabel="k_x (nm^{-1})" ylabel="k_y (nm^{-1})" ylegends="" 600x400> |
| -3.68039679527 -3.68039679527 20.0033226842 | -3.68039679527 -3.68039679527 20.0033226842 | ||
| Line 388: | Line 388: | ||
| </dataplot> | </dataplot> | ||
| ;#; | ;#; | ||
| - | <caption>Transition matrix element in the $\vec{k}$ space</caption> | + | <caption>Transition matrix element in ${\bf k}$ space</caption> |
| </figure> | </figure> | ||
| ==== Eigenvalues ==== | ==== Eigenvalues ==== | ||
| - | The first eigenfunction's energy in the kp-space is plotted in figure {{ref>edisp}} for electrons, and in figure {{ref>hdisp}} for holes. | + | The dispersion of the ground state energy is plotted with respect to $\bf k$ space in figure {{ref>edisp}} for electrons, and in figure {{ref>hdisp}} for holes, respectively. |
| <figure edisp> | <figure edisp> | ||
| ;#; | ;#; | ||
| - | <dataplot dimension=2 xlabel="k_x" ylabel="k_y" ylegends="" 600x400> | + | <dataplot dimension=2 xlabel="k_x (nm^{-1})" ylabel="k_y (nm^{-1})" ylegends="" 600x400> |
| -3.68039679527 -3.68039679527 -1.17995996739 | -3.68039679527 -3.68039679527 -1.17995996739 | ||
| -3.27146363258 -3.68039679527 -1.13216656366 | -3.27146363258 -3.68039679527 -1.13216656366 | ||
| Line 762: | Line 762: | ||
| </dataplot> | </dataplot> | ||
| ;#; | ;#; | ||
| - | <caption>Energy dispersion relation in the $\vec{k}$ space for electrons</caption> | + | <caption>Energy dispersion relation $E(k_x,k_y)$ for the lowest electron eigenvalue</caption> |
| </figure> | </figure> | ||
| Line 768: | Line 768: | ||
| <figure hdisp> | <figure hdisp> | ||
| ;#; | ;#; | ||
| - | <dataplot dimension=2 xlabel="k_x" ylabel="k_y" ylegends="" 600x400> | + | <dataplot dimension=2 xlabel="k_x (nm^{-1})" ylabel="k_y (nm^{-1})" ylegends="" 600x400> |
| -3.68039679527 -3.68039679527 5.32195115805 | -3.68039679527 -3.68039679527 5.32195115805 | ||
| -3.27146363258 -3.68039679527 5.14027884292 | -3.27146363258 -3.68039679527 5.14027884292 | ||
| Line 1132: | Line 1132: | ||
| </dataplot> | </dataplot> | ||
| ;#; | ;#; | ||
| - | <caption>Energy dispersion relation in the $\vec{k}$ space for holes</caption> | + | <caption>Energy dispersion relation $E(k_x,k_y)$ for the highest hole eigenvalue</caption> |
| </figure> | </figure> | ||
nnp/optics/absorption_spectrum.1485963792.txt.gz · Last modified: 2017/02/01 15:43 by zoltan.jehn
