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 semi-classical 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.