Modeling and simulations of quantum cascade lasers for frequency comb generation

Quantum cascade lasers (QCLs) are unipolar, semiconductor devices emitting coherent radiation in the underdeveloped far- and mid-infrared portions of the electromagnetic spectrum. QCLs achieve lasing in those frequencies by "quantum engineering" of the optical transition in epitaxially grown quantum well heterostructures. Sub-nano scale control over the quantum well thickness ensures that the available conduction band states take only discrete energy values, where the energy spacing between the two lasing levels determines the emitted frequency. The ever increasing complexity of chip-scale devices necessitates correspondingly sophisticated theoretical modeling. In the last two decades, we have seen a steady progress in the design of quantum cascade lasers, resulting in devices with high electrical stability, emitting spectra with various desirable characteristics such as high-power single mode emission, short pulse and frequency comb generation. By contrast, it seems that theoretical or simulation models have struggled to keep up with the pace of experimental progress in the field. For example, to date most theoretical papers reduce the QCL complexity to only two energy levels which, albeit sometimes being able to give qualitative agreement with experiment, is often insufficient to achieve quantitative accuracy or explain some of the relevant physics. In addition, QCLs exhibit highly non-trivial dynamics, stemming from the intricate interplay of various coherent and incoherent processes, nonlinear light-matter interactions and complicated electro-optical phenomena, the understanding of which requires sophisticated theoretical models, unfortunately well beyond the analytically solvable such. To this end, the thesis attempts to outline in greater detail coherent light-matter interaction models, suitable for transient analysis of terahertz (THz) quantum cascade lasers for frequency comb generation. Therefore, there are two main focal points. First, this is the development of sufficiently accurate theoretical models and corresponding algorithms for their solution. And second is the usage of these models to investigate the physics behind frequency comb generation in two main modes of QCL operation, i.e. free running and actively/passively mode locked regime. The thesis begins with a very brief and informal introduction to lasers in general and quantum cascade lasers in particular, before presenting the essential theory on which all subsequent simulations are based. The resulting Maxwell/density matrix model is then discretized and numerical algorithms for its solution are presented, together with theoretical and numerical analysis of their accuracy (consistency) and stability. Next, follow the essential parts of the thesis, and namely the usage of the outlined models for time-domain simulations of QCLs for frequency comb generation. In that context, two different approaches to the production of frequency combs are considered, first by free running devices, where the main mode proliferation mechanisms are a consequence of high order nonlinearities in the device, and secondly by active and passive modelocking, where comb generation is equivalent to the production of a periodic train of pulses in the time domain. Several achievements can be mentioned. For example, this is the extension of the traditional two level Maxwell-Bloch model to multiple level such and subsequent simulations of free running THz QCLs. Importantly, the new model includes coherent tunneling between the injector and upper laser level of QCLs, and its simulation is shown to deliver results in very good agreement with available experiment, both for data in time and Fourier domains. Next, the same model is utilized to emulate laboratory experiments by numerical such, in order to characterize the multimode dynamics of longitudinal optical phonon terahertz QCLs, which results in several important insights about the behavior of these devices. Additionally, the model is adapted to simulate ultrashort pulse generation in the THz with specific emphasis on passive mode locking via a fast saturable absorber. It is also shown how one can exploit the natural "multi-pulse" regime of QCL operation to obtain very stable second and higher harmonic pulse emission. To date, no passively mode locked QCL device has been presented and it remains to be seen if this theoretical possibility could be realized experimentally. The thesis also outlines the beginnings of an extended model, suitable for self-consistent microwave-optical simulations, capturing the interaction dynamics between the intracavity QCL light and the propagating current/voltage along the device. Finally, as a small detour from the main topic, the author also investigates the possibility to engineer metamaterials for slowing down terahertz light, based on the so called tunneling induced transparency effect.