Modeling of quantum cascade laser frequency combs in the mid-infrared and terahertz spectral region

在本研究项目中，我们重点研究了中红外（MIR）和太赫兹（THz）波段的量子级联激光（QCL）频率梳的建模。QCL是一种非常通用的光源，采用人工设计的半导体纳米结构导带中的光学跃迁，而不是电子-空穴复合。通过这种方式，打开了紧凑半导体激光器无法达到的频率范围。此外，巨大的光学非线性可以集成到QCL纳米结构中，该结构最近被用于实现紧凑的MIR和太赫兹频率梳源。这些提供了等距线谱，作为频域的标尺，使计量学和光谱学中的许多创新应用成为可能，例如化学传感。为了描述潜在的相干非线性光学现象，我们使用麦克斯韦-布洛赫方程。与以前采用的微扰解相反，我们设想了一个完全依赖于时间的数值处理。通过将所得到的数值格式与集成蒙特卡罗（EMC）载流子输运模拟相结合，我们得到了一种不需要经验输入参数的自洽方法。通过这种方法，得到了一个包含四波混频、色散和空间孔燃烧等所有相关效应的定量数值模型。具体地说，这种完全数值化的方法不仅提供了频率梳的精确描述，而且还使我们能够确定形成稳定梳的允许参数范围，并研究仅在一小部分激光模式上延伸的不完美梳。详细地说，该建议涉及到求解Maxwell-Bloch方程的稳定和有效的数值格式的发展，适用于需要消除瞬态的长时间模拟。在此基础上，将该方案与电磁兼容仿真相结合，建立自一致的建模工具。此外，我们将把共振隧道效应纳入我们的模型，它主要在太赫兹QCL结构中起重要作用，并且可以显著影响频谱梳特性。在与实验小组的密切合作下，我们将使用建模工具来分析基于qcl的MIR和太赫兹梳，并开发改进的梳源，例如，扩展频谱带宽。进一步的目标是从理论上评估宽带太赫兹梳的可行性，例如通过MIR梳的下变频获得。这涉及到发展一种稳定和有效的数值方法来解决麦克斯韦-布洛赫方程，而不需要常用的旋转波近似。

In this research project, we focus on the modeling of quantum cascade laser (QCL) frequency combs in the mid-infrared (MIR) and terahertz (THz) regimes. The QCL is an extremely versatile light source, employing artificially engineered optical transitions in the conduction band of a semiconductor nanostructure rather than electron-hole recombination. In this way, frequency ranges are opened up which are otherwise inaccessible to compact semiconductor lasers. In addition, giant optical nonlinearities can be integrated into the QCL nanostructure, which has recently been exploited for the realization of compact MIR and THz frequency comb sources. These provide an equidistant line spectrum which serves as a ruler in the frequency domain, enabling many innovative applications in metrology and spectroscopy, e.g., in chemical sensing.To describe the underlying coherent nonlinear optical phenomena, we use the Maxwell-Bloch equations. In contrast to previously employed perturbative solutions, we envisage a fully time dependent numerical treatment. By coupling the resulting numerical scheme to ensemble Monte Carlo (EMC) carrier transport simulations, we obtain a self-consistent approach which does not require empirical input parameters. In this way, a quantitative numerical model including all relevant effects, such as four-wave mixing, dispersion and spatial hole burning, is obtained. Specifically, such a fully numerical approach not only provides an accurate description of frequency comb operation, but also allows us to identify the allowed parameter regime for the formation of stable combs and to investigate imperfect combs extending only over a fraction of the laser modes.In detail, the proposal involves the development of a stable and efficient numerical scheme for solving the Maxwell-Bloch equations, suitable for long-time simulations as required to eliminate transients. Building on this, a self-consistent modeling tool will be set up by coupling the scheme to EMC simulations. Furthermore, we will include resonant tunneling into our model, which plays an important role primarily in THz QCL structures and can significantly affect the spectral comb characteristics. In close collaboration with experimental groups, we will use the modeling tool for the analysis of QCL-based MIR and THz combs and the development of improved comb sources with, e.g., extended spectral bandwidth. A further goal is to theoretically assess the feasibility of broadband THz combs, e.g., obtained by down-conversion of MIR combs. This involves the development of a stable and efficient numerical approach for solving the Maxwell-Bloch equations without the commonly used rotating-wave approximation.