摘要
用声学方法构造了折射系数呈余弦变化的一维光子晶体,并在介质无损耗、无电流、无磁性及各向同性假设下,把麦克斯韦方程化为一维薛定谔方程,当折射系数呈余弦变化时,薛定谔方程进一步化为了Mathieu方程。分析表明,在参数(δ,ε)平面上出现了一系列稳定和不稳定区(禁带)。当参数|ε|→0时,这些不稳定区退化为一点,给出了禁带的中心频率,并用摄动法近似地求出了禁带宽度。结果表明,一阶和二阶不稳定区宽度与介质参数和入射光子频率有关。只需适当选择这些参数,就可以有效地调节光子晶体的带结构,并按需要得到不同性能的光子晶体。
The 1-dimension photonic crystal is descripted by using acoustic technique. MaxwellI equation is reduced to Schrodinger equation if assuming free damping, free current, free magnetism and homogeneity for material, but Schrodinger equation is further reduced to Mathieu equation if deflected index is cosine form. It shows that there are a series of stable zones and unstable zones（stop band） in the plane of parameter δ and ε. When , these unstable zones will be reduced to some points in the centre of the stop-bands. The stop-bands widths are obtained by the perturbation techniques. The result shows that the widths of the first order and second order unstable zones depend on the parameters of dielectric and photonic frequency. Only suitable regulating these parameters, the band-structure can be regulated, thus the photonic crystal with a variable properties can be obtained.
出处
《半导体光电》
EI
CAS
CSCD
北大核心
2008年第6期896-898,902,共4页
Semiconductor Optoelectronics
关键词
光子晶体
声子晶体
摄动法
能带
photonic crystal
phononie crystal
perturbation techniques
energy band
