A femtosecond laser metrology with nanometer precision and dynamic range of centimeter incorporating time-stretch interferometry and phase delay retrieval method is proposed and experimentally demonstrated. Displacement encoded phase-sensitive temporal interferogram is generated when phase stabilized femtosecond laser pulses transmitting through a time-stretch interferometer. To avoid the chirp of temporal interferogram due to high-order dispersion, time-to-frequency mapping is established to transform the temporal interferogram to the spectral interferogram for high-speed detection. The phase delay of spectral interferogram corresponding to specific displacements is retrieved and accumulated for linear fitting. The fitted slope is the time delay between two arms in the interferometer therefore displacement can be calculated. For precision verification, the preset displacements are measured. Mean error and standard deviation are presented after sliding average of measured results in 4 μs.

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We numerically study on the key factors and their influences which affected the generation and interaction of solitons in the figure-9 fiber laser based on nonlinear amplifying loop mirror (NALM) mode-locking mechanism. Our simulation used a more authentic approach, which tracing the pulse propagation within the loop cavity. It could act like a saturable absorber which exactly followed the working principle of the NALM. For this reason, the study on the self-starting of mode-locked operation could be carried out systematacially. The simulation results showed that the phase shift difference of the non-reciprocal phase shifter, the splitting ratio of the coupler in the Sagnac loop, and the strength of the pump power all played a role in enabling the mode-locking establishment. Further, multipulse generation were also studied by changing the pump power, and the final steady state presented that all solitons had the same pulse properties. Soliton interactions including attraction, repelling, collision and annihilation could also be observed. In addition, we explored the pump hysteresis phenomena in our simulations. The numerical results verified that the parameters affecting the self-starting of mode-locked operation, the mechanism of multisoliton formation and the interactions between solitons in figure-9 fiber laser, which would enlighten more various experiments and study of solitons dynamics.

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