High-pulse energy femtosecond lasers with high repetition rates are required in numerous areas such as high-field physics, high-energy terahertz pulse generation, high-fluence attosecond pulse generation, and material processing. Femtosecond pulses with energies above millijoules are generally achieved using solid-state lasers. Heat-related problems limit solid-state laser operation at high average powers. By contrast, fiber lasers are attractive owing to their compactness, flexibility, and low cost. However, the pulse energy of the fiber lasers is limited by their nonlinearity and optical damage. Coherent stacking of numerous femtosecond pulses is a promising technique for generating high pulse energy at a high repetition rate. Temporal stacking can be achieved using cavity stacking, delay-line stacking, or a hybrid of the two. Delay line stacking uses pulses with a repetition rate of 80?100 MHz, corresponding to a pulse separation of 12.5?10.0 ns, or several delay lines with the lengths of multiple times of 3.75?3.00 m for stacking, which makes the system bulky and unstable.

We propose and demonstrate that with a 1 GHz repetition rate pulse train, the delay lines can be significantly shortened so that more pulses can be stacked in a compact structure. The system includes a 1 GHz repetition rate femtosecond fiber laser, a chirped fiber Bragg grating (CFBG) as a stretcher, four fiber amplifiers in series, eight delay line stages, and a grating compressor. The pulses experience intensity modulation that chops the pulse train into bursts of 128 pulses using an electro-optical modulator (EOM). Then, the 128 pulses are stretched using a CFBG and split into two branches. Two EOMs are inserted into each branch to modulate the phases of individual pulses. The phase modulations in 0 or π are added to individual pulses such that after each stacking, the pulse train maintains two polarizations with neighbor pulses that are crossly polarized. In the stacking stage, the first delay line is used to compensate for the path difference in the amplification stages. Then, the remaining seven stages of the delay lines are used to compensate for the time delay between pulses. The stacking strategy used is pulse-train folding. The next stacking stage folds the 128 pulses in the burst into 64 pulses, and the folding process continues until only one pulse remains. A set of control FPGA software and hardware is employed to maintain the stability of the delay lines.

The final amplification delivers a 10 kHz burst train with an average power of 2 W. The energy of each pulse during a burst is 780 nJ. After stacking and compression, the pulse energy of the stacked 256 pulses becomes 100.5 μJ, with a pulse width of 437 fs. The average power of the combined pulse train is stabilized within a fluctuation of 0.45%. The stacking efficiency is 56%. The low stacking efficiency is attributed to the contrast and transmission of the polarization beam splitters.

A coherent stacking of 256 femtosecond pulses is shown from a burst of a 1 GHz pulse train. Although the pulse energy is not high, the stacking technique has the potential to stack a few hundred mJ femtosecond pulses and is expected to find broad applications.