Passive repetition-rate stabilization for a mode-locked fiber laser by electro-optic modulation

We report a passive stabilization of the repetition rate for a mode-locked fiber laser by using an electro-optic modulator in a phase-biased nonlinear amplifying loop mirror. The underlying mechanism, in contrast to active feedback operations, lies in the cross-phase modulation between electrical and optical pulses within an electro-optic crystal. The resulting spectral shift can automatically compensate the cavity-length drift via the group velocity dispersion. Consequently, the artificial actuator enables to obtain a capture range up to 2.3 mm, much longer than that achieved by index changes of the modulator. A robust and tight locking for the repetition rate is then realized with a standard deviation as low as 9 $\mu$Hz with a 1-s sample time over 11 hours, corresponding to a fractional instability of 4.3$\times$10$^{-13}$. Furthermore, a dynamic optical sampling by repetition-rate tuning has been manifested with a fast refresh rate at 100 kHz and a broad scanning range over 305 ps. The demonstrated passive servo action may provide a simple yet effective way to stabilize the repetition rate with high precision, large bandwidth and wide tunability.