Abstract:In this paper, the dielectric properties of left-handed materials with graphene multilayer structures and the propagation characteristics of planar waveguide TM oscillating modes were studied. The core layer of the waveguide is a multi-layer structure containing graphene, and the coating and substrate are ordinary materials. Calculation results show that:as the normalized waveguide thickness increases, the effective-refractive index of TM modes decreases or increases simultaneously, and up to balance. This property can be realized by adjusting the voltage added on graphene. Besides, the normalized power flow in waveguide can be positive, zero and negative values. Moreover, the change of voltage or frequency has a little influence for the positive power flows, but has great influence on the zero or negative ones.