A Random Phase Approximation Method for the Generation of Complex Beams and Its Verification via Phase-Only Digital Metasurfaces

Complex beams hold significant value in radar and communication systems due to their distinctive propagation characteristics. Digital metasurfaces, which can dynamically control electromagnetic (EM) waves, play an important role in realizing complex beams. Conventional analytic and optimization methods face challenges in synthesizing complex beams of low-bit digital metasurfaces due to the quantization error and the high computational complexity. Here, we propose a statistical method to realize complex beams with phase-only digital metasurfaces. To this end, we introduce tailored quantization probabilities to design the discrete random phase distributions, which approximate the continuous excitation coefficients derived from analytic methods. Based on the proposed method, we analyze the error between the realized and target patterns. These findings offer critical insights into the accuracy of random quantization. Complex patterns with cosecant, prescribed null, flat-top, and dual-beam are designed and validated in combination with a 2-bit phase coding digital metasurface. The experimental results are in good agreement with the theoretical analysis. This work pioneers the application of random phase approximation and statistical synthesis in digital metasurfaces, providing a fast and efficient route for realizing complex beams in modern radar and wireless communication technologies.