ABSTRACT These notes – intended to be self-contained and tutorial – present a direct, macroscopic approach to quantizing light inside a linear-response dielectric material when both spectral dispersion and spatial non-uniformity are present, but the spectral region of interest is optically transparent so that explicit treatment of the underlying physics of the medium is not needed. The approach is based on the macroscopic Maxwell equations and a corresponding Hamiltonian, without the use of Lagrangians or dynamical models for the medium, and uses a standard mode-based quantization method. The treatment covers energy density and flux in a dispersive dielectric; the inverse permittivity formalism; a new derivation of the mode normalization condition; a direct proof of mode nonorthogonality; examples of quantized field expressions for the general case and various special cases; the relationship between group velocity and energy flux; the band approximation and the continuum limit; and quantum optical treatment of waveguide modes.

中文翻译：

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色散结构线性电介质中光的量子理论：宏观哈密顿教程处理

摘要 这些笔记——旨在是独立的和教程——提出了一种直接的、宏观的方法来量化线性响应介电材料内的光，当光谱色散和空间非均匀性都存在时，但感兴趣的光谱区域是光学透明的因此不需要对介质的基础物理进行明确处理。该方法基于宏观麦克斯韦方程和相应的哈密顿量，不使用拉格朗日函数或介质动力学模型，并使用基于标准模式的量化方法。处理包括色散电介质中的能量密度和通量；逆介电常数形式主义；模式归一化条件的新推导；模式非正交性的直接证明；一般情况和各种特殊情况的量化场表达式示例；群速度与能量通量的关系；频带近似值和连续谱极限；和波导模式的量子光学处理。