nextnano.NEGF - Software for
Quantum Transport

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===== Optical Gain =====

In this tutorial we present how can be calculated the generated carriers upon optical irradiation.
The irradiation parameters are the //poynting vector magnitude//, //Mid energy of the irradiation//,  //Line width//. 

==== Physics model ====
The transition rate per volume element can be expressed with the following sum:
\[
R = R_{ab} - R_{ba} = \frac{2}{V} \sum_{k_a} \sum_{k_b} \frac{2 \pi}{ \hbar} |H_{ba}| ^2 \delta(E_b - E_a -\hbar \omega)(f_a-f_b)
\]

In order to make evaluate the sum much faster we calculate the $H_{ba}$ matrix element at $k_a = 0; k_b = 0$(Remark: $k_a = k_b$), and we neglect the k dependence of it. 
Then we can simplify the sum in the following form, if the irradiation has the $\gamma(E, w)$ broadening function, where $E$ is the irradiation energy, and $w$ is the line width. 

\[
R(E, w) = C  |(S)| \int dE_a dE_b \gamma(E_a-E, w) \cdot  H(E_a-E) \cdot  [n(E_a) - p(E_b)]
\]

Here $C$ is an energy independent constant. and $|S|$ is the magnitude of the Poynting vector.

nextnano.NEGF - Software for Quantum Transport

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nextnano.NEGF - Software for
Quantum Transport