光子在密度呈正弦变化的一维“声子晶体”中的传播

强调了用声学方法可以获得密度呈正弦平方规律变化的声子晶体，指出了光子在这种声子晶体中的传播等同于电磁波在光子晶体中的传播．描写电磁波运动的麦克斯韦方程化为了熟知的Mathieu方程．数值分析表明，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（禁带）宽度与介质的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．

Propagation of photon in 1-Dimension Phonon Crystal With Sine Density Form

In this paper it is emphasized that the phonon crystal can be obtained by using acoustic technique. It is also pointed out that the propagation of photon in the phonon crystal is equivalent to the propagation of an electro-magnetic wave in photonic crystal. The photonic motion equation is reduced to Mathieu equation. It shows that there are a series of stable zones and unstable zones in the plane of parameter δ and ε. When ｜ε｜ →0, these unstable zones will be reduced to some points in the centre of the stop-bands. The stop-bands＇ widths arc obtained by the perturbation techniques. The results show that the widths of the first order and second order unstable zones depend on the parameters of dielectric and photonic frequency. Only by choosing the suitable parameters, can the band-structure be regulated, and thus the photonic crystal with a variable properties be obtained.