对含石墨烯多层结构左手材料的介质特性及其构成的平面波导TM振荡模的传输特性进行了研究。该波导的芯层为含石墨烯的多层结构，覆盖层和衬底为不同的普通材料。计算结果表明：随着归一化波导厚度的增加，TM振荡模的有效折射率同时具有增加和减小，且两者最终达到平衡的双模简并特性。上述特性可以通过调节石墨烯外加电压的方法实现；进一步研究发现，波导中传输的归一化功率流具有正值、负值和零三种情况。电压或者频率的变化对正功率流的影响较小，对负功率流和零功率流的影响较大。

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.