Research Of The Propagating Properties Of Electromagnetic Wave In Isotropic Zero-refractive-index Metamaterial

The transmission properties of the electromagnetic wave propagating in the material mainly depend on two electromagnetic parameters:the permittivity and the permeability. In normal case, both parameters should be positive,i.e. the refractive index of the material is positive. After the metamaterial was proposed and realized in experiment, our traditional knowledge about them has been changed. It produces lots of chances to design new materials with tunable and dispersive permittivity and permeability, which provides new methods for controlling the propagating of the electromagnetic waves. With the development of the theoretical research and constructing technique, the working spectrum of metamaterial gradually increases from microwave to visible light. It deeply influences the electromagnetics, materials and communications, whose research fields have been greatly broadened. Many singular electromagnetic properties have been found for metamaterials, which should be applied in antenna, micro/millimeter wave devices and military cloak, etc.Firstly, we deduce the transmission and reflection coefficient of the negative-zero-positive metamaterial slab using the traditional dielectric film theory, and investigate the transmission and reflection properties of the NZPIM. Some applied potentials in low-pass spatial filter, wave-front reshaping and supercoupling have also been illustrated.Then the transmitted properties in zero-refractive-index point (Dirac point for photon) has been analyzed, and the origin of the Zitterbewegung in NZPIM and photonic crystals has been proposed for the first time. Based on some papers in the journals like Phys. Rev. Lett. proposed the Zitterbewegung in NZPIM and photonic crystals, we explained the origin of the Zitterbewegung with pulse shaping theory with a NZPIM slab sample. We deduced the transmission coefficient of the sample, so we hold that it is the filtering effect of the input spectrum by the transmittance spectral distribution that results in the absence of some spatio-temporal components of the output pulse. Thus the tail oscillations emerge, that is, so-called "Zitterbewegung". Through the theoretical calculations and numerical simulations, the validity of our method has been verified. Furthermore, our method could interpret what can't be interpreted by the method in other papers. And the similar phenomena in two-dimensional photonic crystals can be interpreted in the same way. In addition, the effects of pulse duration, pulse transverse spatial width and slab thickness on the tail oscillations of the transmitted pulse have also been discussed.