Periodic pulse solutions and stability in the fast absorber model

It is noted that the mode-locking equations in the theory of passive mode locking with a fast saturable absorber (Haus, 1975) may be satisfied by periodic solutions described in terms of Jacobian elliptic functions. In reexamining these dnoidal solutions, expressions for the system operating points in terms of system parameters are found to be similar to the results of Haus. It is particularly noted that in the case of overlapping pulses the operating point compares to the case of well separated pulses given by Haus. A stability criterion is established. The solutions describe the mode-locked waveform from CW operation to the limit of infinitely separated hyperbolic secant pulses.