介质折射率对一维光子晶体禁带的影响

Effect of Dielectric Refractive Index on the Forbidden Band-Gap of One-Dimensional Photonic Crystal

利用传输矩阵法推导一维二元周期性光子晶体的色散关系，并进一步推导出禁带宽度与介质折射率之间的数值关系．在设定入射角后，用matlab软件模拟并计算出禁带宽度与介质折射率之间的图象关系．光子晶体的禁带宽度随折射率比值n／n2在0～1之间迅速衰减，但在大于1的范围间缓慢增大．为了光子晶体禁带宽度的可控调制，可以通过限制入射角后调整两种介质的折射率来实现．为获得最大禁带宽度只能在技术可操作性的条件下尽可能增大n1／n2的值．

The dispersion relations of one-dimensional binary periodic photonic crystal using transferring matrix method, and the numerical relationship between band-gap and the refractive index of dielectric were derived. After setting the incidence angle, matlab software to simulate and calculate image was used. The band gap width of photonic crystals reduced rapidly when the ratio in the scope 0- 1. But in the scope of more than 1 the band gap width increased slowly. In order to control modulation of photonic crystal band-gap, the refractive index after choosing a definite incidence angle could be adjusted. If we wanted to obtain the largest band-gap width, we can increase the ratio of refractive index as much as possible according to the feasibility of technical operability .