Nonlinear response of a quantum cascade laser in a high intensity electromagnetic field

A theoretical study is presented, in which the nonlinear response of a bi-ased Quantum Cascade Laser (QCL) is calculated. The calculations are based on the nonequilibrium Green’s function formalism. Assuming a periodic electromagnetic field in the calculations, this formalism provides not only the stationary behavior Green’s functions, but also the part of the response that varies in time according to the oscillating electromagnetic field. In this work the Fourier components of the response are calculated, and the dynamics of the system is thus expressed in a Fourier series with the fundamental response and its higher harmonics. By including at first only the fundamental and the most prominent harmonics, the ones of low order, we can then increase the accuracy of the method by including even higher harmonics,needed for high intensity calculations. The calculations are done on a four well resonant-phonon QCL that has been studied by Burghoff et al, Applied Physics Letters 98, 061112 (2011), where the gain of the structure was successfully measured. In this work the findings of the simulations are compared to their measurements to find that the high intensity calculations of the nonlinear response agree best with the experimental data. This suggests that the intensity used in the experimental measurements do not correspond to linear response. By relating the response of the system at different biases and external light field intensities, a theoretical connection to gain clamping could also be established, and the output power approaching the operating point calculated and related with good agreement to experiment. In addition, the integrated absorption is calculated, and the relevance of electron-electron scattering and convergence issues are adressed