Critical Length of One-dimensional Periodic Systems with Gain
一维周期性增益介质的临界长度

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.