基于宏观Maxwell-Bloch方程的光电子器件模拟
Optoelectronic device simulations based on macroscopic Maxwell-Bloch equations
摘要：
宏观Maxwell-Bloch（MB）方程由于其直观性、灵活性和相对的数值效率，被广泛应用于描述离散能级量子系统介质中的光传输和相干光-物质相互作用的半经典、半唯象模型。本文重点介绍该模型在量子级联和量子点激光器等先进光电子器件中的应用。Bloch方程在这里被视为一个密度矩阵模型的驱动量子系统的两个或多个离散的能级，其中耗散是由Lindblad项。此外，严格推导了半导体波导结构和光纤的一维MB方程。特殊的解析解和合适的数值方法。由于MB方程在计算电动力学中的重要性，重点放在不同的数值方案的比较上，无论有没有旋转波近似。实现额外的效果，可以成为相关的半导体结构，如空间烧孔，不均匀的加宽和局部场校正，进行了讨论。最后，链接到微观模型和适当的Lindblad形式主义的扩展进行了简要说明。
英文摘要：
Due to their intuitiveness, flexibility and relative numerical efficiency, the macroscopic Maxwell-Bloch (MB) equations are a widely used semiclassical and semi-phenomenological model to describe optical propagation and coherent light-matter interaction in media consisting of discrete-level quantum systems. This review focuses on the application of this model to advanced optoelectronic devices, such as quantum cascade and quantum dot lasers. The Bloch equations are here treated as a density matrix model for driven quantum systems with two or multiple discrete energy levels, where dissipation is included by Lindblad terms. Furthermore, the one-dimensional MB equations for semiconductor waveguide structures and optical fibers are rigorously derived. Special analytical solutions and suitable numerical methods are presented. Due to the importance of the MB equations in computational electrodynamics, an emphasis is placed on the comparison of different numerical schemes, both with and without the rotating wave approximation. The implementation of additional effects which can become relevant in semiconductor structures, such as spatial hole burning, inhomogeneous broadening and local-field corrections, is discussed. Finally, links to microscopic models and suitable extensions of the Lindblad formalism are briefly addressed.
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