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 first derivative of the angular frequency ω with respect to the angular spatial frequency k_m (or wavenumber) in the medium, whereas it is k_m that depends on ω. 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 clarifies the understanding of dispersion equations: group dispersion parameter D is related to the first derivative of n_g with respect to wavelength λ, whilst group velocity dispersion GVD is also related to the first derivative of n_g, 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 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 fibers and waveguides, and this can be extended to birefringence and polarization mode dispersion in polarization-maintaining fibers or birefringent waveguides.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 first derivative of the angular frequency ω with respect to the angular spatial frequency k_m (or wavenumber) in the medium, whereas it is k_m that depends on ω. 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 clarifies the understanding of dispersion equations: group dispersion parameter D is related to the first derivative of n_g with respect to wavelength λ, whilst group velocity dispersion GVD is also related to the first derivative of n_g, 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 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 fibers and waveguides, and this can be extended to birefringence and polarization mode dispersion in polarization-maintaining fibers or birefringent waveguides.

We show that dielectric waveguides formed by materials with strong optical anisotropy support electromagnetic waves that combine the properties of propagating and evanescent fields. These “ghost waves” are created in tangent bifurcations that “annihilate” pairs of positive- and negative-index modes and represent the optical analogue of the “ghost orbits” in the quantum theory of nonintegrable dynamical systems. Ghost waves can be resonantly coupled to the incident evanescent field, which then grows exponentially through the anisotropic media—as in the case of negative index materials. As ghost waves are supported by transparent dielectric media, the proposed approach to electromagnetic field enhancement is free from the “curse” of material loss that is inherent to conventional negative index composites.