How does light behave in a material whose refractive index vanishes?

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 $ω$⁠, the refractive index $n(ω)$ defines the wavelength $λ$ inside the material as $2 π c / ω n ( ω )$⁠, and the phase velocity $v p = c / n ( ω )$⁠, where $c$ is the speed of light in vacuum.

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