nextnano.NEGF - Software for
Quantum Transport

In this tutorial we present how can be calculated the optical gain upon optical irradiation. The irradiation parameters are the Photon energy of the irradiation, Line width.

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.

\[ R(E, w) = C_0(E) \int dE_a dE_b \gamma(E_a-E, w) \cdot H(E_a-E) \cdot [n(E_a) - p(E_b)] \]

Here $C_0(E)$ is an energy dependent constant: \[ C_0 = \frac{\pi e^2 \hbar}{n_r c \epsilon_0 m_0^2 E} \]

A new keyword has been introduced to handle an optical device, opticaldevice{}

opticaldevice{
	name = "quantum_region_name"
	line_broadening = 1            #Line broadening model (1: Lorentzian)
	photon_energy = 1              #Photon energy in (eV)
	line_width = 1                 #Line width in (eV)
}

An in the run paragraph you have to also add solve_optical_device{} in order to include it the simulation flow.