Feasibility of use of lumped elements in anisotropic 2D cloak

Practical realization of an electromagnetic cloak based on the transformation electromagnetics requires the existence of highly anisotropic metamaterial, permittivity and/or permeability of which may have values very close to zero (ENZ and/or MNZ metamaterials). Published experiments on the SRR-based cloaks proved the validity of the basic idea but also showed two significant drawbacks: very complicated design and an extremely narrow bandwidth. Another possible design might use the transmission-line-based metamaterial, which is usually stated as being inherently broadband. Here, it is shown that the bandwidth is actually constrained by the basic physics and not by applied technology. There is always some minimal value of capacitance or inductance that can be achieved within some differential volume of space. Thus, one must use some kind of resonant circuit in order to achieve the ENZ or MNZ behavior. The circuit simulations showed that is indeed possible to construct a 2D TM_z fully anisotropic cloak based on the transmission lines loaded with lumped elements. Such a cloak might have a bandwidth broader than the SRR-based cloak but it is again fundamentally constrained by the bandwidths of used resonant LC circuits.