Density Matrix Modelling of Terahertz Frequency Quantum Cascade Lasers: Steady State Analysis and Maxwell-Bloch Dynamics

Terahertz frequency quantum cascade lasers (QCLs) are state of the art structures that exploit multiple quantum well (MQW) system to generate emission by radiative transition between very narrow spaced energy levels (∼ 12 meV) through resonant tunnelling quantum mechanical process. The complexity of MQW prevents use of ab initio models, and only models that exploit the periodicity of the structure may be applied. Terahertz frequency devices can have 3 - 12 (and more) states per MQW period, thus there is an interest for a general model that is not dependent on number of states per module. Additionally, the resonant tunnelling process experiences significant issues with typically used semi-classical rate equation (RE) models, by generating discontinuities due to the lack of coherent quantum mechanical transport within these models. The quantum mechanical models such as Non-Equilibrium Green Function (NEGF) and Density Matrix (DM) approaches therefore, need to be applied. NEGF models provide detail analysis of quantum effects, however they typically exhibit very high numerical cost which limits modelling QCLs with large num-ber of states per module. On the other hand, DM approaches have low numerical complexity which allows more versatility of the model applications. This thesis will focus on DM approach that is independent on number of states per module. Both NEGF and DM have been avoided in wide spread use also due to their complicated mathematical formula-tion. One of the main contributions of this work is a detail algebraic simplification of DM model, where its entire construction can be laid out by a single algebraic expression which also allows straightforward numerical implementation, similar to RE models. The low numerical cost of DM approach allows further expansion of the model by coupling the transport model to Maxwell wave equation (creating Maxwell-Bloch (MB) model) and investigating dynamic processes and properties of emitted radiation. This thesis will present the first (to the best of author’s knowledge) dynamic Maxwell-Bloch model for terahertz frequency QCLs, that is independent on number of states per period. In addition to this, MB model will be exten-ded to allow reinjection of optical radiation to the laser cavity which will formulate general model for optical feedback intereferometry that would be capable of studying the self–mixing (SM) effect. Overall, steady–state and dynamics analysis of terahertz frequency QCLs will be discussed through several applications that model experimental current-voltage-power characteristics, acoustic phonon modulation, Maxwell-Bloch dynamics and self-mixing interferometry dynamics. This thesis will also discuss the potential applications of DM model in design of terahertz frequency QCLs, where Chapter 8 will present a novel structure proposal that provides high temperature performance, comparable to the current record designs.