Infinite-Period Density-Matrix Model for Terahertz-Frequency Quantum Cascade Lasers

In this work, we present a density-matrix model, which considers an infinite quantum cascade laser (QCL) and models transport via a nearest neighbor approximation. We will discuss derivation of output parameters of the model in detail and show the direct mathematical link to the semiclassical rate equation approach. This model can be extended to an arbitrary number of states in the QCL period, without a priori specification of upper and lower lasing level. Application of the model to various QCL structures is possible, including bound-to-continuum structures, which typically employ a large number of states per period. The model has been applied to a 2-THz bound-to-continuum QCL, and a very good agreement with measured V-I characteristics is obtained along with qualitative agreement with measured L-I characteristics in terms of dynamic range.