包含负折射率材料的多层结构的本征电磁模

摘要

In this paper,eigen electromagnetic modes of photonic crystals containing negative refraction index materials are researched. Using Maxwell equation,we can get wave equations of multilayered structures and transfer matrix. For infinite periodicity structures,the dispersion equation can be deduced by Bloch theorem,and continuous bands and band gap can be given. For finite periodicity stuctures,in the condition of standing,eigen electomagnetic modes and band structures in many kinds of situation such as normal propagation,TE mode in oblique propagation and TM mode in oblique propagation are numerically caculated. It is shown that some new transmission properties appeare in multilayered structures with alternative layers of left-hand materials(LHM) and right-hand materials(RHM),which are different from structures with both layers of RHM.%从Maxwell方程出发,建立了包含负折射率材料的分层介质中的波动方程及电磁波传播的传输矩阵,对于无限的周期性结构,用Bloch定理推出其色散关系,即确定连续的能带与带隙；对于有限的周期性结构,用驻波条件来确定离散的本征值谱.数值计算了由正负折射率材料周期性交替组成的多层膜体系在正、斜入射的TE波,正、斜入射的TM波多种情况下的本征模式及其能带结构.结果表明,与两种材料均为正折射率的多层膜体系相比,由正负折射率材料交替组成的多层膜体系出现了一些新的传输特性.