The Effects of Grating Profile on Dispersion Relations of Surface Plasmon Polaritons in Kretschmann-Raether Configuration

The surface plasmon polaritons (SPPs) have been demonstrated with significant advantages in nano-photonic devices due to their ability to control and manipulate light. In this paper, the transmission characteristics of light and field properties of SPPs on the surface of different shapes of gratings in Kretschmann-Raether configurations are studied. With increase of frequency, the strength of SPPs and the light-SPP conversion efficiency decrease, and the conversion efficiency of grating is lower than that of the smooth gold film. The minimum reflection spectrum is obtained through connecting the minimum reflection coefficients corresponding to different incident angles. The valley points of the minimum reflection spectrums are close in gratings with different width while quite different in gratings with different groove depths, which means that the depth of the grooves in grating can regulate the maximum transmission frequency of light. The effective plasma frequency of metal grating is proposed to replace the plasma frequency of the gold film, which shows that the groove depth is negatively relevant to effective plasma frequency of the gold grating and the frequency of SPPs while the groove width does not affect them. Synthesizing the simulation results, we found that the effective plasma frequency of gold grating and dispersion relations of SPPs on the surface of grating change with the propagation trajectory of SPPs. The physical mechanism of this phenomenon is explained through an analogy of the surface wave on grating to slow wave in slow-wave-structure of vacuum electronic devices.