利用准正规模研究有耗纳米结构中的涨落耗散定理和基本光子对易关系
Fluctuation-dissipation theorem and fundamental photon commutation relations in lossy nanostructures using quasinormal modes
摘要：
我们提供的理论和正式的见解格林函数量子化方法的吸收和色散的空间非均匀介质的背景下，电介质。我们表明，一个基本的格林函数的身份，这似乎，例如，在电磁场的基本对易关系中，在非吸收介质的限制下也成立。我们还演示了如何零点场波动产生一个非零的表面项的配置没有吸收，当使用一个更正式的程序的格林函数量子化方法。然后，我们将所提出的方法应用于最近开发的使用准正规模式的光子量子化理论[Franke等人，物理修订版信函122，213901（2019）]用于嵌入无损背景介质中的有限纳米结构。我们讨论了严格的介电限制的准正规模式运营商的交换关系，并提出了不同的方法来获得它们，连接到非吸收，但开放的谐振器的辐射损耗。我们展示了一个完整的三维光子晶体光束腔，包括无损限制，它支持一个单一的准正规模式和讨论的限制的换向关系消失阻尼（无材料损耗和无辐射损耗）的示例性计算。
英文摘要：
We provide theory and formal insight on the Green function quantization method for absorptive and dispersive spatial-inhomogeneous media in the context of dielectric media. We show that a fundamental Green function identity, which appears, e.g., in the fundamental commutation relation of the electromagnetic fields, is also valid in the limit of non-absorbing media. We also demonstrate how the zero-point field fluctuations yields a non-vanishing surface term in configurations without absorption, when using a more formal procedure of the Green function quantization method. We then apply the presented method to a recently developed theory of photon quantization using quasinormal modes [Franke et al., Phys. Rev. Lett. 122, 213901 (2019)] for finite nanostructures embedded in a lossless background medium. We discuss the strict dielectric limit of the commutation relations of the quasinormal mode operators and present different methods to obtain them, connected to the radiative loss for non-absorptive but open resonators. We show exemplary calculations of a fully three-dimensional photonic crystal beam cavity, including the lossless limit, which supports a single quasinormal mode and discuss the limits of the commutation relation for vanishing damping (no material loss and no radiative loss).
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