We introduce a genetic-type tree search (GTTS) algorithm combined with unsupervised clustering for the automatic inverse design of high-performance metasurfaces. With the proposed method, we realize highly directive beam-steering metasurfaces via the cooptimization of the amplitude and phase. In comparison with previous topology optimization approaches, the developed GTTS algorithm optimizes the organization of subwavelength nanoantennas and, thus, is applicable to the design of both passive and active metasurfaces. The optimized beam-steering metasurface specifically exhibits a nearly constant directivity when the steering angle varies from 5° to 30°. Furthermore, the optimized nonintuitive reflectance and phase profiles assist in achieving highly directive beam steering when the phase modulation range is <180°, which was previously challenging. Our approach can diminish the requirements of scattering light properties with substantially enhanced angular resolution of beam-steering metasurfaces, which enables the realization of high-performance metasurfaces that will be promising for a wide range of advanced nanophotonic applications.

Consider a structured matrix factorization model where one factor is restricted to have its columns lying in the unit simplex. This simplex-structured matrix factorization (SSMF) model and the associated factorization techniques have spurred much interest in research topics over different areas, such as hyperspectral unmixing in remote sensing, topic discovery in machine learning, to name a few. In this paper we develop a new theoretical SSMF framework whose idea is to study a maximum volume ellipsoid inscribed in the convex hull of the data points. This maximum volume inscribed ellipsoid (MVIE) idea has not been attempted in prior literature, and we show a sufficient condition under which the MVIE framework guarantees exact recovery of the factors. The sufficient recovery condition we show for MVIE is much more relaxed than that of separable non-negative matrix factorization (or pure-pixel search); coincidentally it is also identical to that of minimum volume enclosing simplex, which is known to be a powerful SSMF framework for non-separable problem instances. We also show that MVIE can be practically implemented by performing facet enumeration and then by solving a convex optimization problem. The potential of the MVIE framework is illustrated by numerical results.

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