# nextnano.QCL - Software for Quantum Cascade Lasers

### nextnano.QCL

Summary and introduction

Software documentation

Examples

### nextnano.MSB

Summary and introduction

### nextnano++

Software documentation

Examples

### nextnano³

Software documentation

### nextnanomat

Software documentation

### nextnano GmbH

nnp:optics:absorption_spectrum

## Absorption Spectrum

With the optics features of nextnano++, the optical absorption spectrum can be calculated for various polarization directions.

### Physics Model

The absorption rate in a semiconductor can be written as

$R_{ba} = \frac{2}{V} \sum_{k_a} \sum_{k_b} \frac{2 \pi}{ \hbar} |H_{ba}| ^2 \delta(E_b - E_a -\hbar \omega)(1-f_a) \cdot f_b,$

where the matrix element $|H_{ba}|$ depends on the polarization of light and the $\bf k$ vector.

## Results

### Transition Matrix Element

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 1

### Eigenvalues

The dispersion of the ground state energy is plotted with respect to $\bf k$ space in figure 2 for electrons, and in figure 3 for holes, respectively.