Comments about Dispersion of Light Waves

Abstract

. 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 v g is usually given as the fi rst derivative of the angular frequency x with respect to the angular spatial frequency k m (or wavenumber) in the medium, whereas it is k m that depends on x . This paper also emphasizes the use of phase index n and group index n g , as inverse of their respective velocities, normalized to 1/ c , the inverse of free-space light velocity. This clari fi es the understanding of dispersion equations: group dispersion parameter D is related to the fi rst derivative of n g with respect to wavelength k , whilst group velocity dispersion GVD is also related to the fi rst derivative of n g , but now with respect to angular frequency x . One notices that the term second order dispersion does not have the same meaning with k , or with x . In addition, two original and amusing geometrical constructions are proposed; they simply derive group index n g from phase index n with a tangent , which helps to visualize their relationship. This applies to bulk materials, as well as to optical fi bers and waveguides, and this can be extended to birefringence and polarization mode dispersion in polarization-maintaining fi bers or birefringent waveguides.