Surface polaritons in grating composed of left-handed materials

In this work, we developed a unique mathematical model to solve dispersion relation for surface polaritons (SPs) in artificial composite materials grating. Here, we have taken two types of materials for analysis. In the first case, the grating composed of epsilon-negative (ENG) material and air interface. In second case, grating composed of left-handed materials (LHMs) and ENG medium interface is considered. The dispersion curves of both p and s polarized SPs modes are obtained analytically. In the case of ENG grating and air interface, polaritons dispersion curves exist for p-polarization only, whereas for LHM grating and ENG medium interface, the polaritons dispersion curves for both p and s polarization are observed.