In this tutorial we calculate the optical gain upon optical irradiation. The irradiation parameters are the
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 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 as follows, \[ R(E, w) = C_0(E) \int \gamma(E_a-E, w) \cdot H(E_a-E) \cdot [n(E_a) - p(E_b)] {\rm d}E_a {\rm d}E_b, \] where $E$ is the irradiation energy, $w$ is the line width and we assume that the irradiation has the $\gamma(E, w)$ broadening function.
Here $C_0(E)$ is an energy dependent constant, \[ C_0 = \frac{\pi e^2 \hbar}{n_{\rm r} c \epsilon_0 m_0^2 E}. \]
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 = 1.0 # Photon energy in (eV) line_width = 1.0 # Line width in (eV) }
The run
keyword requires solve_optical_device{}
to be included.