Active metamaterials, i.e., coupled systems consist of metamaterials and active or gain media. Modelling the interaction between unconventional electromagnetic response in metamolecules and quantum dynamics of active media in active metamaterials requires the development of a unified and efficient semiclassical model. Here, we propose a semiclassical model based on Langevin Maxwell-Bloch equations and simplified rate equations for a multi-level quantum system. Using the semiclassical model and the finite-difference time-domain (FDTD) algorithm, a methodology for the self-consistent descriptions of both the coherent lasing process and the spatio-temporal spontaneous noise dynamics in active metamaterials is developed. To validate the proposed method, we numerically study the luminescence of QDs hybridized with plasmonic and all-dielectric metasurfaces and compare with the experimental results. The proposed semiclassical method reveals a new approach for developing new types of nanodevices based on active metasurfaces.

中文翻译：

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有源超材料器件的波动和相干动力学建模

有源超材料，即耦合系统由超材料和有源或增益介质组成。模拟超分子中的非常规电磁响应与活性超材料中活性介质的量子动力学之间的相互作用需要开发统一且有效的半经典模型。在这里，我们提出了一个基于 Langevin Maxwell-Bloch 方程和多级量子系统的简化速率方程的半经典模型。使用半经典模型和有限差分时域 (FDTD) 算法，开发了一种自洽描述有源超材料中相干激光过程和时空自发噪声动力学的方法。为了验证所提出的方法，我们数值研究了与等离子体和全介电超表面杂交的量子点的发光，并与实验结果进行了比较。所提出的半经典方法揭示了一种开发基于活性超表面的新型纳米器件的新方法。