Rate equations analysis of external-cavity quantum cascade lasers

Abstract

We present a comprehensive analysis of an external-cavity (EC) quantum cascade (QC) laser system, which is based on a coupled-mode system with the length of the EC set equal to that of the laser chip and accommodating the large difference in physical cavity length by introducing an effective speed of light for light propagating in the EC. By analyzing the rate equations and discussing the cross sections and losses of the EC QC lasers, numerical results as well as suggestions for a further optimization of the spectral tuning range of the EC system are presented. Besides, the delayed onset of the EC modes with respect to that of the internal Fabry–Perot modes in pulsed operation has been simulated using the rate equations, yielding a good agreement with the experimental data

Beam steering and lateral hole burning in mid‐infrared quantum‐ cascade lasers

“…A small difference between the case in Ref. [8] and the present work is that in Ref. [8] the laser is based on single-LO-phonon relaxation therefore there is only one lower laser level, while in the present work the QC lasers are based on double-LO-phonon relaxation design, which contains two lower laser levels.…”

“…Similar assumption was also made in Ref. [8]. In the following rate equations we describe the lateral hole burning of carriers and diffusion of carriers in the upper laser level (level 3) similar to that in Ref.…”

“…[8] and the present work is that in Ref. [8] the laser is based on single-LO-phonon relaxation therefore there is only one lower laser level, while in the present work the QC lasers are based on double-LO-phonon relaxation design, which contains two lower laser levels. This difference will, however, bring no difference in the rate equation analysis since both lower laser levels in the double-LO-phonon relaxation are assumed to be empty because we assume that the escape rate of both lower levels is high enough.…”

“…2 of Ref. [8]. Electrons are injected into level 3 from the electron reservoir g and the optical transition occurs between level 3 and level 2.…”

Breath analysis using external cavity diode lasers: a review

“…A set of rate equations can describe the time evolution of the photon flux S and the electronic populations of the upper and lower states of the radiative transition ðn 3 ; n 2 Þ. Yang et al 26 conducted rate equations analysis of EC quantum cascade lasers. They considered a four-level quantum cascade laser structure.…”