The influence of second-order dispersion (SOD) on stimulated Raman scattering (SRS) in the interaction of an ultrashort intense laser with plasma was investigated. More significant backward SRS was observed with the increase of the absolute value of SOD ($\mid \kern-1pt\!{\psi}_2\!\kern-1pt\mid$). The integrated intensity of the scattered light is positively correlated to the driver laser pulse duration. Accompanied by the side SRS, filaments with different angles along the laser propagation direction were observed in the transverse shadowgraph. A model incorporating Landau damping and above-threshold ionization was developed to explain the SOD-dependent angular distribution of the filaments.

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.