Holographic modulation of a structured light array through a general 4D redefinable network

Highly flexible phase holograms have significantly advanced the manipulation of various structured light beams and their arrays. Although numerous methods for phase modulation of structured light arrays have been provided, they frequently encounter challenges related to excessive specialization and limited degrees of freedom. Additionally, the generation of phase holograms typically necessitates iterative optimization, which constrains their real-time application potential. This paper introduces ArrayMuxer4D, a strategy leveraging abstract parameter space and neural network Fourier series solver. The core innovation lies in identifying the unique first-order characteristic phase function of structured light and employing a four-dimensional parameter space to uniformly describe different types of structured lights, as opposed to the traditional pixelated definition. Remarkably, the neural network's one-way computation mode ensures high speed, and we further report for the first time that the resolution of the output phase hologram can be decoupled from the network structure, implying that ArrayMuxer4D can natively produce phase hologram of any resolution. Experimental results demonstrate the efficacy of ArrayMuxer4D in generating Airy beam arrays, planar and spatial perfect vortex arrays, multi-channel compound perfect vortex arrays, snowflake intensity arrays, and even specified complex amplitude distributions, all using a standard phase-only spatial light modulator. By meticulously designing the algorithm structure, we achieve high performance in fidelity, speed, and versatility, positioning ArrayMuxer4D as a promising tool for applications in free-space optical communication, structured light microscopy, computational imaging, and parallel laser direct writing.