左右手材料光子晶体能带结构及表面波色散关系

根据平面波展开的传输矩阵理论及布洛赫定理,通过参数匹配的方式,研究零平均折射率及表面含覆盖介质层条件下左右手材料光子晶体的能带结构和表面波的色散关系,结果表明:零平均折射率条件下,左右手材料光子晶体不同于正折射率材料光子晶体,能带结构中出现半封闭状禁带、封闭状禁带和通带,且通带中的分立能级沿着低频方向呈现振荡衰减和多重简并趋势,能带结构沿着波矢绝对值增大方向趋于简并至消逝。添加表面覆盖介质层的左右手材料光子晶体支持正反表面波和反向表面波的传播,部分半封闭状或封闭状禁带边缘出现简并能级分裂,形成禁带中斜率有正有负的分立色散曲线。表面覆盖介质层厚度可调制色散曲线的频率位置和数目,随覆盖介质层厚度增大,分立色散曲线向波矢减小方向移动,且高频区域半封闭状禁带中的色散曲线在覆盖介质层厚度达到一定数值时还出现耦合分裂现象,但覆盖介质层厚度变化对能级的多重简并和通带与禁带的简并态不产生影响。左右手材料光子晶体的能带结构特点和表面波色散特性,可为新型光波导器件的研究和设计等提供指导。

Dispersion relations of energy band structure and surface wave in left-handed and right-handed materials of photonic crystal

The dispersion relations of energy band structure and surface wave of left-handed and right-handed materials of photonic crystal with coating on the surface,as well as zero mean refractive index,are studied based on parameter matching by using the transmission matrix theory of plane wave and Bloch theorem.The results show that there are semi closed band gap,closed band gap and transmission band in the energy band structure of the left-handed and right-handed materials with zero mean refractive index,which is different from materials with positive refractive index.And the discrete energy level in the transmission band attenuates from high frequency to low frequency with oscillation and multiple degeneracy.the energy band structure attenuates and degenerates to zero with the increase of wave vector.The left-handed and right-handed materials of photonic crystal with coating on the surface support the propagation of both forward and reverse surface waves,and degenerate energy level splitting occurs in some of the semi closed or closed band gaps,forming a discrete dispersion curve with positive and negative values in the band gap.The frequency location and number of the dispersion curve can be modulated according to the thickness of coating on the surface.With the increase of coating thickness,the discrete dispersion curve moves to lower wave vector,and coupling splitting appears in the dispersion curve of the semi closed band gap in the high frequency region when the coating thickness reaches a certain value.However,the coating thickness has no effect on the multiple degeneracy of energy level and the degeneracy of transmission band and forbidden band.The characteristics of energy band structure and dispersion of surface waves of left-handed and right-handed materials of photonic crystal can provide guidance for the research and design of new optical waveguide devices.