Efficient multi-channel holography with three-dimensional multiplexed metasurfaces using the integrated modified gradient descent algorithm

Terahertz metasurfaces have recently garnered significant attention as an effective platform for holographic imaging due to their subwavelength resolution capabilities. Nonetheless, efficient multi-channel holography continues to pose considerable challenges. Although inverse design methodologies and multi-dimensional multiplexing strategies have been proposed to address these limitations, existing approaches struggle to optimize channel capacity and computational efficiency simultaneously. In this paper, we propose an innovative method that integrates an Integrated Modified Gradient Descent (I-MGD) inverse algorithm with three-dimensional multiplexing to achieve a 12-channel holographic metasurface. The I-MGD algorithm facilitates efficient optimization of phase distributions by incorporating second-order smoothing coefficients, thus ensuring stable and rapid convergence. Furthermore, the proposed I-MGD method effectively reduces channel crosstalk and noise by introducing background-noise loss and an orthogonality constraint term. In comparison to the long design times typically associated with forward design methods, our inverse design approach significantly expedites the metasurface design process, requiring merely 51 s to calculate the corresponding metasurface configuration. By employing a single-cell structure, our method simplifies the fabrication process and eliminates the cumbersome procedure of finding suitable units inherent to forward designs. The proposed metasurface uniquely integrates circular polarization, frequency, and spatial multiplexing, thereby enabling the generation of 12 distinct holographic images under diverse conditions, including left-hand circular polarization/right-hand circular polarization (LCP/RCP) incidence, dual-frequency operations, and three separate imaging planes. The resultant holographic images demonstrate an average peak signal-to-noise ratio (PSNR avg ) of 16.14 dB. Numerical simulations substantiate the effectiveness and robustness of our design, illustrating high-quality holography with enhanced information capacity. This work significantly contributes to the advancement of terahertz metasurfaces by providing a streamlined and efficient solution for multi-dimensional multiplexing, with promising potential applications in optical encryption, augmented reality systems, and high-density data storage technologies.