3www.intechopen.com 2 Will-be-set-by- IN-TECH seriously, the dispersion is related with some very basic limitations of this world, e.g.t h e causality limitation that the group velocity in metamaterial should be less than the vacuum light speed. If our design of devices is based on the metamaterials which violate these basic limitations, the design surely can not work since such metamaterial could not exist in this world. From this view, the group velocity picture is not only needed in understanding and explanation, but also required in research of some topics and design of devices. For instance, in the research of the limitation of the cloak [7,8] and abnormal phenomena on the interface of the hyperbolic metamaterial[9], if we neglect the dispersion of material, from group velocity picture we will immediately find that we have fallen into a superluminal trap, since the energy velocity in such artificial systems is divergent. So, the group velocity picture can help us avoid such traps.As a basic value for revealing the complex propagating process, abnormal group velocity has been studied for decades. In the early 1960's the group velocity in material has been studied by Brillouin[10] and the group velocity in strongly scattering media is investigated by J. H. Page, Ping Sheng et al. in 1996[11], which indicate that the physical origin of the remarkably low velocities of propagation lies in the renormalization of the effective medium by strong resonant scattering. So far, metamaterials generally are composite of "photonic atoms" which can scatter light coherently. And all abnormal properties of metamaterials, e.g. these strange beams, are from these complex coherent scattering. Another byproduct of these scattering is the (abnormal) group velocity. In other words, the strange beam and the abnormal group velocity are two sides of a same coin. Further more, with some abnormal group velocity, such as the extremely slow light, we can design new signal-processing devices or new detecting devices. Hence, exploring the group velocity in metamaterial is very vital for revealing mechanism and the design of the real optical devices.The numerical simulation takes an important role in research for modern photonics. For metamaterial, since the difficulties of experimental realization, the numerical tools become very essential for researchers. But, in some frequency domain simulation softwares, the dispersion is neglected totally. As we discussed above, we think such softwares can misleading researchers to some imaginary metamaterial which can not exist in this world. Such as for cloaking study, these softwares could present perfect invisibility very easily, but from our study [7,8], that is misleading one. We strongly recommend the time-domain softwares, such as finite-difference time-domain (FDTD) method or finite-element time-domain(FETD) method.Their simulating results are much more convincible since they are generally with physical dispersion in the simulation and fit for metamaterial studies. This paper is organized ...