Fig. 1. Experimental setup of the FCPCC with an SI system for the measurement of time synchronization and ΔCEP. A commercial Ti:sapphire mode-locked femtosecond laser provided 10 fs pulses with 20 nJ of energy at a central wavelength of 800 nm. The laser pulse was split by a 50/50 beam splitter (BS), where laser channel 1 passed through a wedge pair for active CEP control, while laser channel 2 passed only through a time delay controller mounted on a PZD stage. Both laser channels were sampled for phase difference measurements based on spectral interference. The remaining portions of the lasers were coherently combined in a tiled-aperture configuration, and the far-field interferogram was captured using a CCD camera. Before combination, the two channels passed through chirped mirrors (CMs) for dispersion compensation.

Fig. 2. Measured pulse durations of the two laser channels. (a) The pulse duration of channel 1 is 10.4 fs. (b) The pulse duration of channel 2 is 10.9 fs. Both pulse durations correspond to approximately four optical cycles at a central wavelength of 800 nm. The Fourier transform limits according to the spectrum are 9.3 fs for both channels, as shown by the dotted lines.

Fig. 3. Spectral interferogram and retrieved phase difference of two laser pulses at different time delays. Each retrieved phase difference (orange curve) from the spectral interferogram is fitted with a quadratic curve (red curve). The symmetry axis (blue dotted line) determines the angular frequency difference Δω = ω₀ – ω_s, from which the time delay (t_d) can be calculated.

Fig. 4. Spectral interferogram and retrieved phase difference of two synchronized laser pulses at different ΔCEP values. When the symmetry axis ω_s of the quadratic curve aligns with ω₀, t_d is determined to be zero; then, the retrieved phase difference at the symmetry axis corresponds directly to the ΔCEP.

Fig. 5. Time delay stability (a) and jitter power spectrum (b) with feedback on and off.

Fig. 6. Measurement results of continuously varying ΔCEPs within a range larger than π while maintaining time synchronization. The blue signal represents the measured time delay, and the orange signal represents the measured ΔCEP. The spikes observed in both signals correspond to instantaneous changes in the time delay and ΔCEP, detected during incremental adjustments of the wedge thickness.

Fig. 7. Far-field interference fringes and efficiency obtained for FCPCC under different ΔCEP values in the tiled- (a) and filled-aperture (f) configurations. The strongest interference fringe in Figure 7(a) gradually shifts with increasing ΔCEP, and the highest combining efficiency (98.5%) is reached only when ΔCEP = 0. For the filled-aperture configuration in Figure 7(f), there is no interference fringe, and the maximum beam combining intensity is also reached when ΔCEP = 0. The solid lines in Figures 7(b) and 7(g) show the experimentally obtained combining efficiency, while the dashed lines correspond to the simulation results based on the experimental parameters. In addition, Figures 7(c)–7(e) and 7(h)–7(j) depict the spatial interference patterns observed at three distinct ΔCEP values identified on the efficiency curves in Figures 7(b) and 7(g), respectively. These patterns further illustrate the dependence of the combining performance on the ΔCEP for each configuration.

Fig. 8. Comparison of the variation in ΔCEP between the measured results and theoretical values. The dotted blue line represents the theoretical ΔCEP variation induced by wedge translation, while the green line is fitted to the mean measured ΔCEP values at each step of Figure 5. The gray line represents the STD of each measurement, in which the mean STD is 40 mrad.

Fig. 9. Experimental spectral phase difference (solid line) and noisy simulated phase (dashed line) considering the impact of the time jitter of multiple pulses.