Dispersion relation

Summary

Consider the plane waves that solve a linear wave equation. A dispersion relation is the relation between their angular frequency $\omega$ and their wave vector $k$. It determines how waves of different wavelengths travel: their phase velocity and their group velocity. A medium is called dispersive when waves of different frequencies travel at different speeds, so that a pulse spreads out. For light in vacuum the relation is $\omega = c \abs{k}$, and in a medium it is $\abs{k} = n(\omega) \omega / c$ with refractive index $n$.