Discretizing electrodes in phase modulators for enhanced signal modulation and multi-angle spatial multiplexing

Modulators require separate regions for phase and intensity modulation, with phase modulators using the electro-optic effect and intensity modulators relying on phase interference. Here, we combine both functionalities into a single unit by applying a phase gradient across discrete electrode units controlled by a spatiotemporal matrix. The matrix consists of "0" and "1" elements, where the number of columns corresponds to the number of electrodes, and the rows represent the time sequence for each electrode. Our design decouples phase and intensity modulation. Phase modulation is determined by the initial phase of the sinusoidal voltage, while intensity is controlled by the amplitude, which is set by the number of ``1" elements in each matrix column. The method also enables momentum modulation, allowing the signal to either propagate within the waveguide or radiate into free space. Our experiments demonstrate that the design effectively suppresses higher-order spacial harmonics, improving spectral efficiency. Additionally, we achieve multi-angle beam shaping for spatially multiplexed information transmission. Our work expands the modulation capabilities and opens new possibilities for advanced applications in wireless communication, optical field control, and wavefront engineering.