Objective The high- order transverse mode optical field with a special spatial structure utilizes the spatial dimension resources of photons, providing a novel method to address the capacity crisis in optical communication and facilitate the sustainable development and expansion of high-speed,- speed, high- capacity optical communication. As a fundamental high- order transverse mode optical field, the Hermite-Gauss beam is widely used in space quantum measurement in addition to optical communication. Moreover, the Hermite-Gauss beam is also employed in achieving super- resolution imaging. However, due to the lack of an effective Hermite-Gauss mode separation device, it is challenging to surpass the Cram & eacute;r-Rao- Rao measurement lower bound in experiments. Therefore, the generation and mode separation of high- quality higher- order Hermite-Gauss modes play a crucial role in spatial quantum measurement. Hermite-Gauss beams can be generated using phase- plates, specially designed lasers, spatial light modulators, and mode cleaners. However, most of these methods suffer from low conversion efficiency. In 2014, CAILabs in France pioneered multi- plane light conversion (MPLC) technology. The mode division multiplexer based on MPLC solves the problem of low conversion efficiency, enabling the preparation of high- purity high- order mode beams and achieving spatial mode division multiplexing. Subsequently, MPLC has significantly influenced optical communication, quantum cryptography, and quantum computing. Currently, domestic research on MPLC mainly focuses on the modular division multiplexing of linear polarization (LP) mode and orbital angular momentum (OAM) mode, while the preparation and mode decomposition of Hermite-Gauss mode based on MPLC are rarely reported. Methods The laser output infrared light with a wavelength of 1080 nm is coupled into a single- mode fiber after passing through a line polarizer, and the beam is ejected from the optical fiber coupler to be incident into MPLC as a plane wave. Five reflections between the liquid crystal surface and the cavity mirror are achieved to perform continuous phase modulation and optical transformation of Hermite -Gauss beams, resulting in a high- purity, high- order Hermite - Gauss beam. Subsequently, based on the experimental results of beam shaping, we experimentally study Hermite - Gauss mode decomposition. In the experiments, we simulate the superposition light field of high- order Hermite - Gauss modes by shifting the Hermite -Gauss beam, which is used as the input light field to the MPLC. After the multimode light field passes through the MPLC, each mode is decomposed into six spatially separated channels, with each mode separated into a distinct beam. Results and Discussions The conversion efficiency of high- order Hermite-Gauss beams generated by phase- plates, specially designed lasers, spatial light modulators, and mode cleaners is generally low. The MPLC-based- based mode division multiplexer solves the problem of low conversion efficiency and can generate high- order mode light fields with high purity. Using MPLC, we obtain high- order Hermite -Gauss beams with mode purity levels of HG1,0, 1,0 , HG2,0, 2,0 , HG3,0, 3,0 , HG4,0, 4,0 , and HG5, 5, 0 being 93.9 degrees o, 96.8 degrees o, 76.6 degrees o, 88.1 degrees o, and 85.3 degrees o respectively (Fig. 4), and the best conversion efficiency is 71.3 degrees o. The technology for generating and separating high- order Hermite-Gauss modes is crucial in spatial quantum measurement. Currently, there are few reports on the preparation and mode separation of Hermite-Gauss modes based on MPLC in China. In this paper, we build an MPLC to realize 6- channel mode separation of the offset incident Hermite- Gauss beam (Fig. 8), with a maximum crosstalk of-11.9 dB (Fig. 9). Conclusions In our experiments, we develop a mode division multiplexer based on multi- plane light conversion technology that can generate high- order Hermite-Gauss beams with high purity and achieve mode separation of complex light fields. Using the 5- plane transformation, we obtain a high- order Hermite-Gauss light field with mode purity levels of HG1,0, 1,0 , HG2,0, 2,0 , HG3,0, 3,0 , HG 4,0 and HG 5,0 being 93.9 degrees o, 96.8 degrees o, 76.6 degrees o, 88.1 degrees o, and 85.3 degrees o, respectively. Subsequently, we realize a 6- channel mode separation of the offset incident Hermite-Gauss beam using MPLC, with a maximum crosstalk of-11.9 dB. The mode division multiplexer based on multi- plane optical conversion is compact, simple, and flexible, effectively realizing the mode shaping and mode separation of Hermite-Gauss beams. The mode shaping and mode separation techniques of Hermite -Gauss beams are expected to be applied to small displacement measurements in space and super- resolution imaging.
