Photonic crystal with negative index material layers

We consider the one-dimensional photonic crystal composed of an in nite number of parallel alternating layers lled with a metamaterial and vacuum. We assume the metamaterial is an isotropic, homogeneous, dispersive and non-absorptive medium. We use a single Lorentz contribution and assume the permittivity and permeability are equal. Using the time and coordinate Fourier transforms and the Floquet-Bloch theorem, we obtain systems of equations for TE and TM modes, which ones are identical. We consider radiative and evanescent regimes for the metamaterial and vacuum layers and nd sets of frequencies, where the metamaterial has the positive or negative refractive index. We use a numerical approach. As a result, we obtained the photonic band gap structure for different frequency intervals and ascertain how it changes with modification of the system parameters. We observe the non-reflection effect for any directions for a certain frequency but this fails with the layer width modification.