Dispersion Characteristics of Surface Plasmon Polaritons of Graphene Loaded Three Dimensional Dielectric Gratings

Graphene has been used widely in optical and electronic devices due to its extraordinary electromagnetic characteristics. Recent theories and experiments prove that graphene support surface plasmon polariton (SPPS) and transform it into Terahertz (THz) radiation. In this paper, a dispersion and electric amplitude equations of SPPS of graphene loaded on the three dimensional dielectric gratings excited by parallel moving electron beam are derived by solving the Maxwell's equations. The numerical results show that the frequency of amplified electric amplitude are same as the frequency point where electron beam and dispersion curve meet, which demonstrate theoretical analysis are right. The influence of dielectric gratings width is considered. It is found that the cutoff frequency occurs and rises on the dispersion curve as the width narrowing. The working point frequency is also higher compared with infinite width dielectric gratings. The SPPS of graphene loaded the three dimensional dielectric gratings whose work point is under cutoff frequency can't be excited, even though it can be tuned. The numerical results show the electric amplitude becomes greater with width increasing.