Abstract

Frequency combs generated by trains of pulses emitted from mode-locked lasers are analyzed when the center time and phase of the pulses undergo noise-induced random walk, which broadens the comb lines. Asymptotic analysis and computation reveal that, when the standard deviation of the center-time jitter of the nth pulse scales as $n^{p∕2}$, where p is a jitter exponent, the linewidth of the kth comb line scales as $k^{2∕p}$. The linear-dispersionless $(p=1)$ and pure-soliton $(p=3)$ dynamics in lasers are derived as special cases of this time-frequency duality relation. In addition, the linewidth induced by phase jitter decreases with power $P_{\mathrm{out}}$, as $(P_{\mathrm{out}}{)}^{-1∕p}$.

© 2006 Optical Society of America

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