Coherent beam combining (CBC) is one of the most promising techniques for breaking through the output power limit of single channel lasers and has been one of the research hotspots in high-energy laser technology. Traditional CBC includes two schemes, tiled aperture and filled aperture schemes. Tiled aperture CBC has the ability to steer the beam by phase control, but its theoretical efficiency is relatively low in the presence of diffraction sidelobes, while filled aperture CBC can achieve high efficiency but is difficult to achieve beam self-steering. CBC based on multi-plane light conversion (MPLC) is an emerging technology that eliminates the diffraction sidelobes of tiled aperture scheme, and the pointing angle of the combined beam can be adjusted by controlling the piston phases of the sub-beams, thereby achieving efficient beam self-steering without additional optical systems such as deformable mirrors. CBC by MPLC can overcome the limitations of low energy ratio of the main lobe in tiled aperture CBC and the inability of filled aperture CBC for self-steering, and is expected to propel the development and realization of larger-scale and higher-power coherent laser sources. However, there is limited theoretical research, and no numerical analysis of the beam self-steering in filled aperture CBC systems has been reported. In this study, simulations were conducted to verify the CBC of multiple laser channels and high-dimensional mode multiplexing. Moreover, theoretical equations for beam self-steering were derived, and the steering performance under different mode bases was studied.

The principle and method of CBC by multi-plane light conversion were introduced, and the theoretical simulation model was constructed. In the implementation of CBC by MPLC, the design of phase masks at each plane is critical. The input modes of MPLC are the laser array with various phases, and the output modes are supposed to be fundamental Gaussian mode or designed to be high-order modes according to the applications. Based on the wavefront matching method, the input modes are forward propagated while the desired output modes are backward propagated, and the phase mask can be calculated and updated in an iteration process. Numerical simulations were conducted for three different application scenarios: single-mode CBC, high-dimensional mode multiplexing, and beam self-steering. Meanwhile, analytical equations of tilted Gaussian beam decomposed by orthogonal set of Laguerre?Gaussian modes were theoretically derived, demonstrating the feasibility of achieving beam self-steering in mode multiplexing MPLC by phase-only control.

Simulation results for 16-beam single-mode CBC showed that the system combining efficiency was close to 100%, and the beam quality factor was 1.03 (Fig. 3), thus achieving high-quality filled-aperture CBC. In addition, high-dimensional mode multiplexing can be achieved by phase encoding the input beam array, where different phase distributions are mapped to different high-order modes in the process of MPLC design. A simulation of 16 beams combining into 16 Hermite?Gaussian modes was carried out, with an average coupling efficiency of up to 97.4% for each mode (Fig. 5). Finally, the application of beam self-steering was analyzed, and the steering performances of three systems were compared: traditional filled-aperture CBC, single-mode CBC based on MPLC, and mode multiplexing CBC based on MPLC. As shown in Fig. 7, traditional filled-aperture CBC could not achieve beam-steering via phase-only control, single-mode CBC based on MPLC had limited beam-steering capability, while mode multiplexing CBC based on MPLC had good beam-steering capability.

In this work, various CBC scenarios, including single-mode combination, high-dimensional mode multiplexing, and beam self-steering, were simulated and analyzed based on the theoretical model of MPLC coherent combination. The simulation results demonstrate the simple design and excellent performance of the MPLC coherent combining system, which integrates the advantages of traditional schemes to generate high-efficiency, high-quality filled-aperture beams. Moreover, the MPLC-based CBC system can synthesize high-order modes and achieve self-steering of the combined beams through phase-only control, thus expanding the application range of filled-aperture coherent laser systems. Self-steering performance depends on high-dimensional mode multiplexing MPLC, so both the quantity and quality of multiplexed modes should be enhanced by optimizing mode mapping relationships and optical parameters. At the same time, it is necessary to improve control algorithms and accuracy to promote the realization of wide-angle beam steering.