The refractive index of a material describes how fast light travels through it. The index is the dimensionless ratio of light’s speed in a vacuum to its speed, or phase velocity, in the material. For a light wave whose temporal variation is given by a frequency $\omega $, the refractive index $n(\omega )$ defines the wavelength $\lambda $ inside the material as $ 2 \pi c / \omega n ( \omega ) $, and the phase velocity $ v p = c / n ( \omega ) $, where $c$ is the speed of light in vacuum.

Both of those quantities dictate how light changes shape in space. Following Snell’s law, $n(\omega )$ determines the angle $\theta $ at which an incident wave is refracted at an optical interface between two materials: $ n 1 sin \theta 1 = n 2 sin \theta 2 $. And in...