Abstract
The concept of metamaterials offers a flexible pathway to manipulate the macroscopic behavior of light by delicately designed microscopic subwavelength structures, which has been recently introduced to integrated photonics to create devices with ultra-compact footprint, excellent performance or versatile functionalities. However, the conventional design approach of metamaterials, including two separated steps of subwavelength structure design and the assembly of unit cells, often encounters challenges when facing extreme design targets. In this work, we propose a hierarchical inverse design approach by cascading a conventional unit-cell-based design with a holistic topology optimization. As a proof-of-concept, we demonstrate ultra-short-range light focusing and mode-size conversion enabled by on-chip meta-lenses. The shortening of tapering region pushes higher numerical aperture of on-chip lenses, leading to the violation of locally periodic approximation used in meta-lens design and thus poor device performance, which fortunately, can be well compensated by the follow-up holistic optimization step. We experimentally realize mode-size squeezing by almost 20 times in a tapering region as short as 8 μm and 5 μm with low insertion loss and broadband performance. The proposed design scheme provides practical guidelines to design metamaterials as flexible on-chip wavefront control and light routing devices for various applications in fiber communication, sensing and optical computing.