Inverse design of sub-diffraction focusing metalens by adjoint-based topology optimization

Breaking the diffraction limit to realize imaging at the nanoscale is challenging in scientific research. Traditional sub-diffraction focusing metalens is obtained by arranging artificially selected unit cells, of which the design process is passive and complex. This paper brings up an inverse design idea of planar sub-diffraction focusing metalens based on super-oscillatory theory to solve these problems, starting from a desired focusing performance. The sub-diffraction focusing metalens is then obtained by iterative topology optimization with different initial structures. We introduce the adjoint-based topology inverse optimization into the structural design of sub-diffraction focusing metalens, which provides another way to design a sub-diffraction metalens for far-field unmarked super-resolution imaging. Based on this idea, we achieve a sub-diffraction focusing characterized by a focal radius of 0.75 times the Rayleigh diffraction limit, optimizing from a diffraction-limited focusing metalens. Moreover, focal radii between 0.63 and 0.73 times the Rayleigh diffraction limit are achieved by optimizing 11 sets of random initial metasurface structures with even no focusing performance. The results indicate that our method is independent of the initial structure distribution, which can be extended to the inverse design of other functional metasurfaces in imaging, lithography, and other fields.