Behavior of surface plasmon polaritons at the interface of metal and a non-integer dimensional (NID) dielectric medium

The behavior of surface plasmon polaritons (SPPs) at a planar non-integer dimensional dielectric-metal interface has been studied for the first time. The dimension of the interface is shown to have a strong effect on the behavior of SPPs. Dimensions of both the half spaces are different from each other which can be used to distinguish between them besides their different wavenumbers. Lossless dielectric medium has non-integer dimensions while metal has integer dimension. Surface plasmon polaritons (SPPs) only exist for p-polarization and no surface modes exist for s-polarization because the partnering non-integer dimensional dielectric material is homogeneous (Polo and Lakhtakia, 2011). Two methods are used in order to verify the proposed idea. First method is named as so-called indirect method, by using this method, it has been observed that SPP waves are excited only at one incident angle [θi=54.87°] for p-polarized incidence. It has been investigated that the behavior of SPPs changes with change in order of non-integer dimension. The absorption of SPPs increases by decreasing dimensionality for p-polarization at the excitation angle. Second method is named as so-called direct method, according to this method, by solving the presented idea directly using SPP waves fields expressions in NID space, it is conceived that SPPs with same polarization state, but with different phase speeds, attenuation rates, along with propagation lengths can be directed by such interface which incorporates metal and a non-integer dimensional dielectric medium. The results achieved by both methods (so-called indirect and direct methods) complement each other tremendously, validating the efficiency of our proposed concept regarding propagation of SPP waves at a planar non-integer dimensional dielectric-metal interface. Furthermore, the effect of relative permittivity of non-integer dimensional dielectric medium on SPPs is also discussed. The conventional results for integer dimensional space can be recovered as a special case.