各向异性异质材料中的Goos-Hnchen位移研究

The Goos-Hnchen shift on the surface of anisotropic metamaterials

对单轴各向异性材料中的负折射进行了讨论,并对具有负折射率的准左手介质(NI-QLHM)表面的古斯-汉森位移进行了详细的理论研究,给出了横电(TE)波和横磁(TM)波入射时的古斯-汉森位移d和穿透深度dz的表达式.对TE入射波的情况进行了数值模拟,结果显示,在μz<0的情况下,频率ω分布在4~6GHz之间时,各向异性材料为NI-QLHM.而磁导率分量|μz|越小,在NI-QLHM频率区域越容易实现全反射;随着频率的增加,临界角减小,从而发生全反射的入射角的范围增加,同时也将导致准左手化材料的有效折射率减小.结果还显示,对于同一个入射角,随着频率ω的增加,古斯-汉森位移减小,即随着折射率n的减小,古斯-汉森位移减小.而穿透深度dz与古斯-汉森位移d相对应,穿透深度越大,古斯-汉森位移也越大.

In this paper,we constructed a dissipative uniaxial anisotropic metamaterial,in which the components of the permittivity and the permeability tensor were varying with the frequency.Then,the effective negative refractive index of the uniaxial anisotropic metamaterial,and the Goos-Hnchen（GH）shift on the surface of anisotropic quasi-lefthanded meterial was studied in detail.The expressions of GH shift and penetration depth were given for transverse electric（TE）and transverse magnetic（TM）incident wave.The numerical simulation of the TE incident wave shows that the anisotropic metamaterial can be the quasi-left-handed material with negative refractive index（NI-QLHM）as the frequency is between 4GHz and 6GHz forμz0（i.e.,the relative permeability of the uniaxial material parallel to the optical axial is negative）.Moreover,the smaller of the permeability component｜μz｜,the easier to realize the total reflection in the frequency region of the NI-QLHM.And with increasing the frequency,the critical angle decreases,thus the region of incident angle corresponding to the total reflection increases,which leads to the decrease of the effective refractive index of the NI-QLHM.In what follows,we investigated the GH shifts and the penetration depth of the NI-QLHM.The penetration depth corresponds with the GH shifts,generally,the larger the penetration depth is,the greater the GH shifts are.Meanwhile,the GH shifts of the NI-QLHM are always negative,which is contraryto the ordinary material and is the unique physical property of the NI-QLHM.In the end,the influences of the frequency and the incident angle on the GH shifts and the penetration depth were discussed.The numerical results show that with increasing the frequency,the GH shifts decrease for the same of the incident angle,which means that with decreasing the refractive index,the GH shifts also decrease.It can be concluded that the negative GH shifts can be adjusted by changing the frequency and the angle of incidence.