Eigenfunction analysis of mode-locking process

An active mode-locking process in a homogeneously broadened medium is discussed by using an eigenfunction analysis of a time-varying strongly interacting closed-loop system. This direct time domain analysis is shown to yield a complete set of eigenfunctions or supermodes for steady-state pulse configurations. The kinetics of generated pulses is described in this eigenvector space. The result shows that, depending on the buildup time, the string of detected pulses can differ substantially among themselves. Also, the possibility of using this time domain approach to analyze time-tailoring pulse envelopes is pointed out.