Optically isotropic negative index of refraction metamaterial

In early papers of Veselago [1], Mandel’shtam [2], Lamb [3], and Shuster [4], it was pre-dicted that an electromagnetic plane wave in a medium having simultaneously negative permittivity, e < 0, and permeability, µ < 0, would propagate in a direction oppo-site to that of the Poynting vector. This result follows from Maxwell’s curl equations, and not from the wave equation (which remains unchanged). The curl equations provide the proof that the vectors E, H, and k form a left-handed set in the case e < 0 and µ < 0. Since, at the same time, the Poynting vector S = E × H will form with E and H a right-handed set, the Poynting vector and the phase velocity should have opposite directions. Veselago went on to argue, using steady-state solutions to Maxwell equations, that a left-handed medium has a negative refraction index (n). An isotropic n < 0 material has the important property that it exactly reverses the propagation paths of rays within it [5]. Consequently, left-handed materials, or negative-index ma-terials (NIM), have a potential advantage to form highly ef-ficient low reflectance surfaces by exactly canceling the scat-tering properties of other materials. Another potential appli-cation, the perfect lens [6] promised that a planar slab of NIM could focus both the propagating and evanescent com-ponents of an object and achieve sub-wavelength imaging. Since then, great excitement spawned this new field of optics, and many studies were reported. The main diffi-culty in the analysis of negative index metamaterials stems from the fact that such materials still have not been discov-ered as natural substances. There are known natural mate-rials with negative permittivity e < 0 in some frequency range (e.g. metals), but, as follows from theoretical predic-tions [7], a material with µ ≠ 1 is an impossibility in the optical regime. This conclusion stems from the analysis of the problem of spin motion in a magnetic field of the elec-tromagnetic wave [7]. Since the spin can not follow the magnetic field at high optical frequencies, any kind of a material should be principally non-magnetic in the optical regime (µ = 1). Consequently, there is a need for the creation of artifi-cial, man-made materials where e, µ (and, hence, n) can be treated only as some effective parameters e