光子晶体缺陷模的带宽与品质因子研究

利用光学传输矩阵法研究了结构参量对缺陷态光子晶体的缺陷模带宽和品质因子的影响.研究发现,当缺陷介质层厚度h₀的值较小时,缺陷模的带宽很小且基本保持不变;当h₀较大时,缺陷模的带宽随h₀的增加而快速增加.另外发现,缺陷模的品质因子在某个h₀处取最大值.但是总体上看,h₀较小时的品质因子要远大于h₀较大时的品质因子.此外,缺陷模的品质因子随光子晶体的周期数增加而急剧增加约4.788倍,而带宽则随周期数的增加而急剧减少约4.788倍.当周期数为13时就可以获得10⁹以上的品质因子值和小于10^-9的相对带宽值.

Investigation on the Bandwidth and Quality Factor of the Defect Mode in a Photonic Crystal with a Defect

The bandwidth and the quality factor of the defect mode of a 1D photonic crystal with a defect are investigated with the optical transmission matrix method. It is found that the bandwidth keeps small and approximately constant when the defect layer is thin. The bandwidth of the defect layer increases rapidly and non linearly with the growth of the thickness of the defect layer when this defect layer is thick enough. The quality factor increases at first, reaches a maximum at a certain thickness of the defect layer, and then decreases with the growth of the defect layer. In general view, the quality factor for a thin defect layer is much greater than that for a thick defect layer. It is also found that, the quality factor increases by a factor of 4.788 and the bandwidth decreases by a factor of 4.788 when the periodic structure at each side by the defect layer increases 1 period. The quality factor is higher than 10 9 and the relative bandwidth is less than 10 -9 for a structure with 13 periods at either side of the defect layer.