对含左手材料的三层平面波导的TM振荡模进行了研究。利用麦克斯韦方程组，得到了TM振荡模的色散方程。根据该色散方程，考虑芯层厚度及模阶数对色散特性的影响，画出了相关TM模的色散曲线。从中可以发现，色散特性反常且具有双模简并的特性。此外，对波导中TM模的归一化功率流特性进行了相关的研究。结果显示，在一定的条件下，TM振荡模的归一化功率流具有正、负和零。正的归一化功率流意味着能量在波导中正向传输；负的归一化功率流则说明了能量在波导中向后传输；而零归一化功率流则说明了能量静止于波导中。

A three-layer slab waveguide with left-handed material is investigated. Through Maxwell equations, a dispersion equation for TM oscillating guided modes is obtained and some mode dispersion curves are plotted, respectively. It is found find that they have an abnormal dispersion property and two modes degenerancy near cutoff. Besides, the normalized power flux of TM oscillating guided modes in the slab waveguide is studied. The results reveal their power fluxes have positive value, negative value and zero. The positive or negative power flux means energy in waveguide travels forward or backward. But, zero power flux implies all energy is stored in the slab waveguide.