Dispersion of light waves is well known, but the subject deserves some comments. Certain classical equations do not fully respect causality; as an example, group velocity vg is usually given as the first derivative of the angular frequency ω with respect to the angular spatial frequency km (or wavenumber) in the medium, whereas it is km that depends on ω. This paper also emphasizes the use of phase index n and group index ng, as inverse of their respective velocities, normalized to 1/c, the inverse of free-space light velocity. This clarifies the understanding of dispersion equations: group dispersion parameter D is related to the first derivative of ng with respect to wavelength λ, whilst group velocity dispersion GVD is also related to the first derivative of ng, but now with respect to angular frequency ω. One notices that the term second order dispersion does not have the same meaning with λ, or with ω. In addition, two original and amusing geometrical constructions are proposed; they simply derive group index ng from phase index n with a tangent, which helps to visualize their relationship. This applies to bulk materials, as well as to optical fibers and waveguides, and this can be extended to birefringence and polarization mode dispersion in polarization-maintaining fibers or birefringent waveguides.

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关于光波色散的评论

光波的色散是众所周知的，但这个主题值得一些评论。某些经典方程不完全尊重因果关系；例如，群速度 vg 通常作为角频率 ω 相对于介质中角空间频率 km（或波数）的一阶导数给出，而 km 取决于 ω。本文还强调使用相位指数 n 和群指数 ng，作为它们各自速度的倒数，归一化为 1/c，即自由空间光速的倒数。这阐明了对色散方程的理解：群色散参数 D 与 ng 关于波长 λ 的一阶导数有关，而群速度色散 GVD 也与 ng 的一阶导数有关，但现在与角频率 ω 有关。人们注意到，术语二阶色散与 λ 或 ω 的含义不同。此外，还提出了两种新颖有趣的几何结构；他们只是简单地从相位索引 n 中导出组索引 ng 并带有切线，这有助于可视化它们的关系。这适用于块状材料以及光纤和波导，并且可以扩展到保偏光纤或双折射波导中的双折射和偏振模色散。