Negative Refraction - Negative Phase Velocity

Negative Phase Velocity

Negative phase velocity (NPV) is a property of light propagation in a medium. There are different definitions of NPV, the most common being Veselago's original proposal of opposition of wavevector and (Abraham) Poynting vector, i.e. E×H; other common choices are opposition of wavevector to group velocity, or to energy velocity. The use of "phase velocity" in the naming convention as opposed to the perhaps more appropriate "wavevector" follows since phase velocity has the same sign as the wavevector.

A typical criterion used to determine Veselago NPV is that the dot product of the Poynting vector and wavevector is negative (i.e. that ); however this definition is not covariant. Whilst this restriction is rarely of practical significance, the criterion has nevertheless been generalized into a covariant form. For plane waves propagating in a Veselago NPV medium, the electric field, magnetic field and wave vector follow a left-hand rule, rather than the usual right-hand rule. This gives rise to the name "left-handed (meta)materials". However, the terms left-handed and right-handed can also arise in the study of chiral media, so this terminology is best avoided.