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

在本研究项目中，我们主要对中红外(MIR)和太赫兹(THz)波段的量子级联激光(QCL)频率梳进行建模。QCL是一种用途极其广泛的光源，它在半导体纳米结构的导带中使用了人工设计的光学跃迁，而不是电子-空穴复合。通过这种方式，可以打开紧凑型半导体激光器无法达到的频率范围。此外，QCL纳米结构还可以集成巨大的光学非线性，该纳米结构最近被用来实现紧凑的MIR和THz频率梳状源。它们提供了一个等距的线谱，作为频域中的标尺，使得许多创新的应用在计量学和光谱学中，例如在化学传感中。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。与以前使用的摄动解不同，我们设想了一种完全依赖于时间的数值处理。通过将所得到的数值格式与系综蒙特卡罗(EMC)载流子输运模拟相耦合，我们得到了不需要经验输入参数的自洽方法。这样，就得到了一个包含四波混频、色散和空间烧孔等所有相关效应的定量数值模型。具体地说，这种全数值方法不仅提供了频率梳操作的准确描述，而且允许我们确定形成稳定梳子所允许的参数区域，并研究仅延伸到激光模式的一小部分的不完美梳子。具体而言，该提议涉及开发一种稳定而高效的数值格式来求解麦克斯韦-布洛赫方程，适合于消除瞬变所需的长期模拟。在此基础上，通过将该方案耦合到EMC仿真，将建立一个自洽的建模工具。此外，我们将在我们的模型中包括共振隧穿，它主要在THzQCL结构中扮演着重要的角色，并可以显著影响光谱梳状特性。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THz梳子，并开发具有扩展频谱带宽等改进的梳状源。另一个目标是从理论上评估宽带太赫兹梳子的可行性，例如，通过对MIR梳子进行下转换而获得的。这涉及到发展一种稳定和有效的数值方法来求解Maxwell-Bloch方程，而不需要通常使用的旋转波近似。

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.