Theory of bound-to-continuum infrared absorption in $p$-type quantum wells based on a mapping of the continuum spectrum

Theoretical treatment of the infrared absorption in $p$-type quantum wells (QW’s) is important because of the possibility of selection rule breaking for the in-plane polarized light. Here, we present the theory of the bound-to-continuum $\left(\overrightarrow{B}C\right)$ linear absorption in $p$-type QW’s. The anisotropy of the hole spectra, fully incorporated in the calculations, is responsible for the in-plane optical anisotropy which varies with the layer orientation. In order to simplify the problem of $\overrightarrow{B}C$ absorption it is accepted to put the QW in an artificial additional enclosure. In this way one can reduce the calculational problem to the bound-to-bound one, but the results depend on the artificial parameter, i.e., the size of this enclosure. This problem is known as the “artificial quantization.” The rate of optical excitations is calculated here after mapping the continuum states at the asymptotic limit of an infinitely wide external enclosure. An advantage of this approach is the avoidance of any artificial quantization. Also we eschew computational complexity associated with processes related to the fine energy mesh in a finite enclosure. These processes are replaced by a proper phase parametrization followed by a statistical averaging. As an example we present the polarization-dependent absorption spectra of GaAs/AlGaAs QW’s for both the $〈001〉$ and $〈011〉$ orientations.