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

在本研究计画中，我们主要针对中红外及太赫兹波段的量子级联雷射频率梳进行模拟。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的导带中的光学跃迁，而不是电子-空穴复合。以这种方式，打开了否则紧凑型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，这是最近被利用的紧凑的MIR和太赫兹频率梳源的实现。这些提供了用作频域中的标尺的等距线频谱，从而实现了计量和光谱学中的许多创新应用，例如，为了描述潜在的相干非线性光学现象，我们使用Maxwell-Bloch方程。与以前采用的微扰解相比，我们设想了一个完全依赖于时间的数值处理。通过耦合所得到的数值方案系综蒙特卡罗（EMC）载流子输运模拟，我们得到了一个自洽的方法，不需要经验输入参数。这样，一个定量的数值模型，包括所有相关的影响，如四波混频，色散和空间烧孔，得到。具体地说，这种完全数值方法不仅提供了频率梳操作的精确描述，而且还允许我们识别形成稳定梳的允许参数区域，并调查仅在一小部分激光模式上延伸的不完美梳。适用于消除瞬变所需的长时间模拟。在此基础上，一个自我一致的建模工具将建立耦合的计划，EMC模拟。此外，我们将包括共振隧穿到我们的模型中，它主要在太赫兹QCL结构中起着重要的作用，可以显着影响光谱梳特性。在与实验小组的密切合作中，我们将使用建模工具来分析基于QCL的MIR和THz梳，并开发改进的梳源，例如，扩展的光谱带宽。另一个目标是从理论上评估宽带太赫兹梳的可行性，例如，通过MIR梳的下转换获得。这涉及到一个稳定的和有效的数值方法来解决麦克斯韦-布洛赫方程的发展，而不常用的行波近似。

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.