渗漏效应还是缝宽效应—SPP光子晶体等效理论的误差来源

Leak Effect or Width Effect—the Cause of the Error in Effect Theory of the SPP-Crystal

由两种以上的电介质材料周期性的填充到亚波长金属狭缝中组成的系统被称为是SPP光子晶体.它可以产生带隙结构从而有效调控狭缝中的表面等离激元.对于这个系统,用等效理论计算出来的带隙宽度总是比数值模拟出来的结果要大些.对于这一误差的来源,一种猜测是,光波因能够通过金属壁直接传播而有渗漏效应.本文通过时域有限差分(FDTD)模拟方法计算了SPP光子晶体的带隙结构,发现即使对于理想导体,上述误差仍然存在.因此认为误差来源不是渗漏效应.计算表明,其实是缝宽效应造成了误差,缝宽越小误差越大.我们还发现,当缝宽小于某个临界值时,误差突然增大,等效理论不再适用.

The so called SPP crystal is composed of a metal subwavelength slit filled periodically with two or more dielectrics,in which the photonic band gap（PBG） is generated and consequently the surface Plasmon polariton（SPP） traveling in the slit may be adjusted effectively.The PBG structure can be calculated by the theory of the effective one-dimensional photonic crystal.As the effective theory always gives the PBGs narrower little than the numerical results that are thought as the practical case,one guesstimate of the consequence is leak effect,which means that a small part of SPP penetrates into the walls of the metal slit and transmits through the slit-PP crystal not being scattered.In this thesis the PBG structures are simulated by the finite difference time domain（FDTD） method and the results compared with that got from the effective theory.It is find that even the slit is made of the idea conductor,the difference between the results of the simulation method and the effective theory is still observed.Investigating the detail we found that the difference is caused by the width effect,for instance,the narrower the slit,the bigger the difference.We also found when the slit is narrower than a critical width,the difference will enhance suddenly,the effective theory becomes invalid.