The long-standing problem of finding a general formulation of optical dispersion for metals, valid over a wide spectral range of photon energy E is tackled. To this end, equations for refractive index n and extinction coefficient k as functions of E are developed. Functions and respectively represent real and imaginary parts of complex index of refraction Previous formulations, most of which are based on various combinations of Drude and Lorentz models, are either useable only over a limited spectral range or do not accurately fit experimental data. The formulation overcomes these shortcomings by exploiting concepts set forth by Forouhi and Bloomer in 1986, 1988 and 2019 publications pertaining to optical dispersion of semiconductors and insulators. These concepts are centered on time-dependent perturbation theory and consistency with principle of causality. The new expression for is based on three types of events initiated by photon-electron interactions in metals: intraband electron dipole transitions; interband electron dipole transitions; inelastic collisions of electrons. Expression for is obtained as Hilbert transform of It is demonstrated that the new dispersion equations satisfy Titchmarsh’s Theorem, a mathematical theorem that conveys the principle of causality, which in turn establishes the theoretical validity of the formulation. Equations for and are fitted to published experimental data of metals encompassing all metal groups of the periodic table. Reported data span various ranges of energy, from far-infrared to extreme-ultraviolet. Excellent fits between calculated and experimental spectra are achieved. Having established consistency with Titchmarsh’s Theorem and by extension, causality, plus agreement with experimental findings suggests this formulation represents a valid description of optical dispersion of metals.

解决了寻找用于金属的光学色散的一般配方并在光子能量E的宽光谱范围内有效的长期问题。为此，建立了折射率n和消光系数k作为E的函数的方程。函数和分别表示复数折射率的实部和虚部以前的配方（大多数基于Drude和Lorentz模型的各种组合）只能在有限的光谱范围内使用，或者不能准确地拟合实验数据。该公式通过利用Forouhi和Bloomer在1986年，1988年和2019年的出版物中提出的与半导体和绝缘体的光学色散有关的概念来克服这些缺点。这些概念集中在与时间有关的扰动理论上，并与因果原理保持一致。的新表达式基于由金属中的光子-电子相互作用引发的三种类型的事件：带内电子偶极跃迁；带内电子偶极跃迁；带间电子偶极跃迁；电子的非弹性碰撞。的表达式作为的希尔伯特变换获得结果表明，新的色散方程满足Titchmarsh定理，这是一个表达因果关系原理的数学定理，进而证明了该公式的理论有效性。对于方程和被装配到金属包含周期表的所有金属组发表的实验数据。报告的数据涵盖了从远红外到极紫外的各种能量范围。计算和实验光谱之间实现了极好的拟合。建立了与Titchmarsh定理的一致性，并由此扩展了因果关系，并与实验结果相吻合，表明该公式代表了金属光学色散的有效描述。