Backward-wave propagation in Metamaterials?

[Jimmy Johnson]

Ok so I am currently doing a research project on reconfigurable polarization sensitive metamaterials. Namely trying to manually control/determine where electrical and magnetic resonance within the structure will occur dependent on geometrical parameters, so it can then be used with some active components to 'tune' the output response as desired.

I have encountered a phenomena described as backward-wave propagation. I have been able to find little on the matter online that adequately explains or details what it actually is.

From my understanding I believe it is a matter of a difference of opinion between academics, where backward wave propagation could essentially be described as a 'backwards travelling' wave, so an EM wave impinging on the metamaterial could exhibit what would normally be described as a Negative Refractive Index (due to negative permittivity and permeability? where permittivity is negative due to resonance causing the metal to behave as a plasma? unsure if this is the same for the permeability or not).

The difference of opinion stems from the incident wave not exactly being refracted, i.e. the wave is attenuated rather than reflected, so since it has different properties (phase velocity, group veloctiy etc) it isn't entirely accurate to be described through a negative refractive index?

The reason for the question is because it is confusing me, some papers detailing NRI while others discuss backward waves, are they essentially the same thing? With NRI being say accepted convention, and backward wave propagation being meticulous about the underlying phenomena?

 

[DrDu]

I would consider both things to be equivalent, although I consider neither negative refractive index nor backward wave as particularly lucky nomenclature for the underlying phenomenon. In a medium with negative refraction, group velocity and phase velocity have different sign. At an interface, there shouldn't be accumulation of energy, hence the group velocity in both media should point in the same direction (precisely true only for the case of perpendicular incidence). In a material with negative refraction, this will then lead to the wave vector to have opposite direction in comparison with usual materials.
Personally, I prefer to think of these materials in terms of a nonlocal index of refraction rather than in terms of permittivity and permeability.