In recent years, high-energy few-cycle femtosecond laser pulses have demonstrated significant application value in strong-field physics research. However, restricted by multiple factors, the output power of single few-cycle pulse lasers faces bottlenecks in further enhancement. Coherent beam combining of multiple low-energy few-cycle lasers becomes a feasible solution to improve pulse power. Given that the instantaneous power of few-cycle laser pulses is significantly influenced by carrier-envelope phase (CEP), the CEP difference and time delay difference between sub-pulses are crucial for the beam combining efficiency. Traditional CEP measurement and control technologies are complex and cumbersome, limiting the application of multi-beam combining. To simplify the optical path and measurement adjustment process in beam combining and maintain high beam combining efficiency, this study proposed a novel CEP measurement and control scheme.

This study used spectral interference data to measure the CEP difference and time delay difference between combined sub-pulses and conducted theoretical analysis. The results showed that for pulses to be combined with second-order dispersion difference, the time delay difference between the two pulses could be determined through the parabolic characteristic of the spectral interference phase, from which the phase value at the pulse center frequency and the CEP difference between the two pulses could be obtained. By measuring and adjusting the CEP difference and time delay difference between the two optical pulses to approach zero, high beam combining efficiency was achieved. A measurement and control system for CEP difference and time delay difference was established, and experimental studies were conducted. As shown in Fig.1, two sub-pulses, denoted as beam 1 and beam 2, entered the spectral interferometer to generate interference, where inter-beam CEP difference and time delay difference were two main factors affecting the interference fringes. By analyzing the interference pattern, the CEP difference and time delay difference between beam 1 and beam 2 were obtained. Based on this, the computer sent two electrical signals: one to adjust the CEP of beam 1, and the other to adjust the time delay of beam 2. The specific optical path was shown in Fig.2. The laser emitted from the femtosecond laser was split by a 5:5 beam splitter into two sub-pulses, with the transmitted sub-pulse designated as beam 1 and the reflected sub-pulse as beam 2. beam 1 passed through a pair of optical wedges, and the position of one of the optical wedges was adjusted by a computer-controlled piezoelectric transducer, thereby changing the CEP of beam 1 and simultaneously altering its optical path length. In the propagation path of the reflected Beam 2, a delay optical path was added, and the optical path length of beam 2 was adjusted through another piezoelectric transducer.

Multiple groups of feedback adjustment experiments were conducted, with results of two groups shown in Fig.4, Fig.5, and Fig.6. Fig.4 illustrated the time delay difference variation between two-beam pulses before and after feedback system activation. Before feedback activation, the time delay difference between the two beams exhibited random changes with large fluctuations. The main reasons included the following two aspects. (a) Although the optical system was placed on a vibration-isolation platform, which could effectively suppress most vibrations, the vibration of two optical components were not completely consistent. The optical paths of two beams continuously changed, causing random fluctuations of time delay. As shown in Fig.4, before feedback system activation, the time delay difference between the two beams was within ±2 fs, corresponding to an optical path difference within ±600 nm. (b) Before feedback adjustment, to stabilize the spectral interference image, manual commands were sometimes sent to adjust the optical path, causing changes in the time delay of the two beams. Following the activation of the feedback adjustment, the time delay difference between the two beams was stabilized within ±62 as, showing very high stability. Fig.5 showed the CEP difference variation between two-beam pulses before and after feedback system activation. After activating the feedback adjustment, the CEP difference between the combined sub-pulses was basically stable within ±50 mrad. Fig.6 showed the variation in beam combining efficiency between two-beam pulses. After activating the feedback control, the combining efficiency remained stable above 95%, reaching a maximum of 98.5%.

The scheme proposed in this study avoids the problem of individually controlling the CEP of each beam in traditional few-cycle laser pulse beam combining processes, thereby simplifying the optical setup and control process. Additionally, it suppresses the impact of optical component vibration on the optical path length, while maintaining high beam combining efficiency during the combining process. This provides innovative insights and solutions for coherent beam combining of multi-beam few-cycle laser pulses.