Negative refraction of chemical waves

The refractive index of a material is the factor by which the phase velocity of electromagnetic radiation is slowed relative to vacuum. It is usually given the symbol n, and defined for a material by square root of material's permittivity and permeability.

Both positive (water, glass ...)
Either negative, opaque
Both negative

All known transparent materials possess a positive index because both permittivity and permeability are positive. Many metals (such as silver and gold) have negative permittivity at visible wavelengths. A material having either (but not both) permittivity or permeability negative is opaque to electromagnetic radiation. However, some engineered metamaterials have both negative, (n=>-n, negative refractive index).
Metamaterials with negative index have numerous startling properties:

Snell's law still applies, but ...
The Doppler shift is reversed
group velocity is antiparallel to phase velocity (see demo)

The phase velocity is defined as the rate at which the crests of the waveform propagate; that is, the rate at which the phase of the waveform is moving. The group velocity is the rate that the envelope of the waveform is propagating; that is, the rate of variation of the amplitude of the waveform. It is the group velocity that (almost always) represents the rate that information (and energy).

In most cases this is accurate, and the group velocity can be thought of as the signal velocity of the waveform. However, if the wave is travelling through an absorptive medium, this does not always hold. For example, it is possible to design experiments where the group velocity of laser light pulses sent through specially prepared materials significantly exceeds the speed of light in vacuum (superluminal communication is not possible) It is also possible to reduce the group velocity to zero, stopping the pulse.

A group velocity can be positive or negative. A negative group velocity implies that the individual waves move in a direction opposite to that of the packet as a whole [Lingfa Yang, and Irving R. Epstein, "Chemical wave packet propagation, reflection, and spreading", J. Phys. Chem. A 106(47), 11676-11682 (2002).]