Single-step-etched ultra-compact metamaterial grating coupler enabled by a hierarchical inverse design approach

With the concept of metamaterials introduced into integrated photonics,subwavelength structures have gained popularity for their ability to create devices with ultra-compact size,high performance,and versatile functionalities.However,traditional metamaterial design methods are usually based on empirical templates and physical approximations,lacking the ability to design free-form metamaterial structures and optimize entire devices globally.In this work,we propose a hierarchical inverse design approach that combines a conventional effective refractive index based metamaterial structures design with a follow-up global topology optimization.The empirical metamaterial grating coupler design based on effective refractive index engineering faces inaccurate index extraction and insufficient approximation of wavevector matching conditions,which deteriorates coupling efficiency,especially for fully-etched devices with the decreased tapering region.Fortunately,a subsequent overall topology optimization step can well compensate for the negative effect of the shrinking device footprint to increase the efficiency of the metamaterial grating coupler.We demonstrate a 23μm×10μm ultra-compact metamaterial grating coupler with single-stepetched to couple light between a fiber and a 500 nm single-mode silicon waveguide in the O-band.Experimental measurement shows an insertion loss of 3.17 dB and a 3 dB bandwidth of 77 nm,making it the smallest footprint device ever reported.