Intersubband gain in a Bloch oscillator and Quantum cascade laser

TL;DR

This paper presents a unified quantum mechanical model linking the gain mechanisms in quantum cascade lasers and Bloch oscillators, highlighting dispersive contributions and their effects on intersubband transitions.

Contribution

It introduces a density matrix formalism that accounts for in-plane momentum relaxation, unifying the description of gain in quantum cascade structures and superlattices.

Findings

Dispersive gain exists alongside population-inversion gain.

Gain occurs at photon energies below the Bloch oscillation frequency.

Red-shifted emission results from dispersive gain with small inversion.

Abstract

The link between the inversion gain of quantum cascade structures and the Bloch gain in periodic superlattices is presented. The proposed theoretical model based on the density matrix formalism is able to treat the gain mechanism of the Bloch oscillator and Quantum cascade laser on the same footing by taking into account in-plane momentum relaxation. The model predicts a dispersive contribution in addition to the (usual) population-inversion-dependent intersubband gain in quantum cascade structures and - in the absence of inversion - provides the quantum mechanical description for the dispersive gain in superlattices. It corroborates the predictions of the semi-classical miniband picture, according to which gain is predicted for photon energies lower than the Bloch oscillation frequency, whereas net absorption is expected at higher photon energies, as a description which is valid in the high-temperature limit. A red-shift of the amplified emission with respect to the resonant transition energy results from the dispersive gain contribution in any intersubband transition, for which the population inversion is small.