求解分析了有损耗情况下二维金属光子晶体的能带结构。在无损耗自由电子模型下，利用界面算子法得到了横磁模式和能带结构。考虑有损耗的Drude模型，并引入同伦法对本征频带进行修正，得到其相应的虚部。结果表明，损耗在表面等离子体频率处存在一个极大值；当频率改变时，损耗急剧减小，并随着倒格矢量值的变化而改变。即使考虑金属损耗，实部频率变化不明显。界面算子法与同伦法的结合为金属光子晶体的研究提供了较好的技术支持。

The energy band structure of a lossy 2D metallic photonic crystal is solved and analysed. The transverse magnetic mode and energy band structure are obtained under the non-lossy free-electron model with the interfacial operator approach. When the Drude model with loss is considered and the homotopy method is employed to correct the eigen-frequency, the corresponding imaginary parts are obtained. The results show that the loss reaches the maximum value at the surface plasma frequency. When the frequency changes, the loss diminishes rapidly and varies with the change of reciprocal-lattice vector value. Even though the metal loss is considered, the real part of the eigen-frequency changes a little. The combination of the interfacial operator approach and the homotopy method provides an efficient technique support for the study of metallic photonic crystals.