Thickness dependent behavior of surface plasmon polaritons in layered media

Dependence of the wave vectors of the surface-plasmon-polariton (SPP) to the thickness of the metal or left handed material (LHM) layer is studied in metallic and LHM slabs sandwiched between two different media. A critical thickness for the slab is defined, beyond which the SPP wave vectors for the slab can be accurately approximated by the commonly used wave-vector expression obtained for a dielectric-metal or dielectric-LHM configuration.