J. Eur. Opt. Society-Rapid Publ.
Volume 18, Number 1, 2022
|Number of page(s)
|03 June 2022
Comments about dispersion of light waves
iXblue, 34 rue de la Croix de Fer, 78100 Saint-Germain-en-Laye, France
* Corresponding author: email@example.com
Accepted: 5 April 2022
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.
Key words: Birefringence / Chromatic dispersion / Dispersion / Effective index / First-order dispersion / Group birefringence / Group index / Group velocity dispersion / Index of refraction / Polarization mode dispersion / Refractive index / Second-order dispersion
© The Author(s), published by EDP Sciences, 2022
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