Superluminal group velocity in CRLH transmission line metamaterials

Since the pioneering works of Brillouin and Sommerfeld [1], the intriguing concept of group velocity has generated a lot of academic excitement. In particular, many papers, both theoretical and experimental, have reported superluminal group velocity and have explained this phenomenon in the context of Einstein's relativity [2]-[7]. In general in these papers, superluminal group velocity is associated with anomalous dispersion (∂n / ∂ω < 0) and occurs in a strongly absorptive band (stop-band) of the propagation medium, where extremely little transmission is achieved. In fact, such superluminal transmission occurs in many engineering devices, such as in microwave filters, but has then little practical interest because both of high distortion (due to high dispersion) and low transmission (due to stop-band). As pointed out by Brillouin and Sommerfeld, the group velocity under these conditions do not have a real physical meaning, since no information can be transmitted (the input pulse so much distorted that its detection at the output is impossible.) and should rather be replaced by the more meaningful concepts of energy velocity or front velocity.