We provide a pedagogical introduction to the concept of the local density of optical states (LDOS), illustrating its application to both the classical and quantum theory of radiation. We show that the LDOS governs the efficiency of a macroscopic classical antenna, determining how the antenna's emission depends on its environment. The LDOS is shown to similarly modify the spontaneous emission rate of a quantum emitter, such as an excited atom, molecule, ion, or quantum dot that is embedded in a nanostructured optical environment. The difference between the number density of optical states, the local density of optical states, and the partial local density of optical states is elaborated and examples are provided for each density of states to illustrate where these are required. We illustrate the universal effect of the LDOS on emission by comparing systems with emission wavelengths that differ by more than 5 orders of magnitude, and systems whose decay rates differ by more than 5 orders of magnitude. To conclude we discuss and resolve an apparent difference between the classical and quantum expressions for the spontaneous emission rate that often seems to be overlooked, and discuss the experimental determination of the LDOS.

中文翻译：

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经典天线、量子发射器和光态密度

我们对局部光学状态密度 (LDOS) 的概念进行了教学介绍，说明了其在经典和量子辐射理论中的应用。我们展示了 LDOS 控制宏观经典天线的效率，确定天线的发射如何取决于其环境。LDOS 显示出类似地修改量子发射器的自发发射率，例如嵌入纳米结构光学环境中的激发原子、分子、离子或量子点。详细阐述了光态数密度、光态局部密度和光态局部局部密度之间的差异，并为每个态密度提供了示例以说明需要这些的地方。我们通过比较发射波长相差超过 5 个数量级的系统和衰减率相差超过 5 个数量级的系统来说明 LDOS 对发射的普遍影响。最后，我们讨论并解决了似乎经常被忽视的自发发射率的经典表达式和量子表达式之间的明显差异，并讨论了 LDOS 的实验确定。