Backward waves in a grounded bilayer slab containing double-negative   (DNG) and double-positive (DPS) metamaterials
  Simple dispersion relations for the guided modes in a grounded DNG/DPS bilayer slab are given in terms of normalized parameters. Relations corresponding to the grounded single-layer DNG slab are refound as specific cases. Numerical examples are given showing dispersion curves of the lower order modes and the respective total normalized power carried on the propagation direction. Snapshots obtained by the finite-difference time-domain method are provided showing the electromagnetic field inside the grounded DNG/DPS bilayer slabs. Since an important characteristic of the guided modes in the slab containing a DNG layer is the existence of a turning point (TP) at which the power carried by each mode of order m>0 equals zero and changes the sign, we present implicit relations at the TP for the normalized parameters of the guided modes in the grounded DNG/DPS and DNG slabs. We show that a thin DPS layer coating on the grounded DNG slab produces a shift of the TP on the dispersion curve. 
E. Cojocaru
physics.optics