Adjoint optimization for inverse design of randomly reduced metalens

Metasurfaces have emerged as a powerful platform for manipulating wavefronts, enabling ultrathin, lightweight, and highly efficient optical components. Metalenses provide notable advantages over traditional refractive lenses, including compact form factors and precise phase control. However, reducing structural complexity while maintaining high optical performance remains a key challenge, crucial for large-scale fabrication and cost-effective manufacturing. In this study, we design a single focus metalens based on a hyperbolic phase profile and apply a random reduction strategy to the pillar distribution to simplify the structure while preserving its focusing ability. To compensate for performance degradation caused by pillar removal, adjoint optimization is employed, achieving a focusing efficiency of 58.9%, exceeding that of the original full-density design. Furthermore, we inverse design a dual-focus metalens, using the same random reduction and optimization method, reaching a focusing efficiency of 27.8% at each focal point. By significantly decreasing the number of nanostructures, our method reduces fabrication complexity and cost while enhancing scalability.This work demonstrates the effectiveness of integrating random reduction with adjoint optimization, offering a practical pathway to compact, high-efficiency, and cost-effective metasurface-based optical devices for real-world applications.