Quantum-limited timing jitter in actively modelocked lasers

Expressions for the quantum-limited timing jitter in an actively modelocked fiber laser are derived. We identify a set of characteristic constants that govern the timing jitter for the cases using amplitude modulation (AM) and phase modulation (PM) as the active modelocking elements. We find that when using AM, the Gordon-Haus jitter is proportional to the square of the group-velocity dispersion and reaches a minimum value for the case of low dispersion. Using PM, the Gordon-Haus jitter increases only linearly proportional to group-velocity dispersion, and there exists an optimum group-velocity dispersion that minimizes the jitter. We compare the theory to recent experiments of the timing jitter for an active harmonically modelocked fiber laser.