Indirect detection phase control algorithms, such as the dithering algorithm and the stochastic parallel gradient descent algorithm (SPGD), have simple system structures and are applicable to filled-aperture coherent combinations with high efficiency. The performances of these algorithms are limited when applied to a coherent combination of pulsed fiber lasers with a low repetition rate (≤5 kHz). Firstly, due to the overlap of the phase noise frequency and repetition rate, conventional algorithms cannot effectively distinguish the phase noise from the pulse fluctuation, and directly applying filtering will result in the phase information being filtered out. Secondly, if the pulse fluctuation is ignored and only the continuous part of the phase information is utilized, it relies on the presetting of conditions to separate the pulse from the continuous part and loses the phase information of the pulse part. In this article, we propose a waveform self-referencing algorithm (WSRA) based on a two-channel near-infrared laser coherent combination system to overcome the above challenges. Firstly, by modelling a self-referencing waveform, a nonlinear scaling operation is performed on the combined signal to generate a pseudo-continuous signal, which removes the intrinsic pulse fluctuation while preserving the phase noise information. Secondly, the phase control signal is calculated based on the pseudo-continuous signals after parallel perturbation. Finally, the phase noise is corrected by optimization. The results show that our method effectively suppresses the waveform fluctuation at a 5 kHz repetition rate, the light intensity reaches an ideal value (0.9939 $I_{\max }$), and the root-mean-square (RMS) phase error is only 0.0130 $\lambda$. This method does not require the presetting of pulse detection thresholds or conditions, and solves the challenge of coherent combination at a low repetition rate, with adaptability to different pulse waveforms.

A novel approach for laser coherent beam combination (CBC) utilizing the self-imaging effect in plasma waveguides is presented in this study, which enables the transmission of ultrashort laser pulses at intensities above the bulk damage threshold of conventional solid optical waveguides. The feasibility of self-imaging-based CBC in plasma waveguides was simulated and verified, demonstrating favorable combining efficiency and beam quality. This work explores the adaptive tuning of waveguide length via dynamic adjustment of plasma density, addressing the critical issue of fabrication tolerances in traditional waveguide systems. With CBC via plasma waveguide, this study offers support for the development of robust, high-power laser systems with enhanced beam quality and operational stability.