一维周期性增益介质的临界长度

用传输矩阵方法研究了一维周期性增益介质的透射频谱随系统层数的变化规律.研究发现：对层数一定的介质，透射率在某些频率上有很大的峰值；增加层数，尖峰在频谱图上出现的位置会发生移动，且对不同的频段，其位置随介质层数的变化规律是不同的.考察了这种系统中每个频率的光所对应的临界长度，解释了不同频段激光出现位置随层数变化的规律.比较了周期系统和随机系统中临界长度与频率关系的异同，用群速度理论和能带理论对此做了解释.

Critical Length of One-dimensional Periodic Systems with Gain

The relation between the transmission spectrum and the system layers in periodic system with gain was studied by the transfer-matrix method. It is found that, with certain layers, the transmission coefficient is very large at some frequencies,and when the system layers increase, these peaks will move in the spectrum.And for different part in the spectrum, the changes of peaks are different. The critical length of system for different frequencies was studied, which explains the changes of peaks in different part of the spectrum. The relation between the critical length and the frequency in random system was studied next, which shows some differences with this relation in periodic system. The differences can be explained by group velocity theory and energy band theory.