The Jones matrices serve as a pivotal tool for connecting the electric field of incident polarized waves with that of outgoing polarized waves, where its two degrees of freedom correspond to the modulation capabilities of amplitude and phase for incident polarized wave. However, due to the complexity of the Jones vector for circularly polarized waves, previous research has predominantly focused on modulating linearly polarized waves, while less attention has been paid to the modulation of circularly polarized waves. This paper proposes an inverse-designed holographic metasurface for circularly polarized waves, enabling independent control of both amplitude and phase in the Jones matrices. The metasurface consists of periodically arranged anisotropic nanorods, with the geometric dimensions and rotation angles of each nanorod obtained through inverse calculation and matching with a meta-atom library, while maintaining a high transmission efficiency exceeding 90 %. As a proof of concept, we integrate a nanoprinting image and two holographic images into a single metasurface, demonstrating independent modulation capabilities across three channels for amplitude and phase in the Jones matrices. As a functional extension, this paper also designs an amplitude-optimized beamforming metasurface capable of precisely deflecting the incident beam to the target elevation and azimuth angles. The metasurface platform presented here provides a significant design reference for multidimensional control of circularly polarized waves, near- and far-field holographic imaging, optical encryption, and other applications.
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