In recent years, metasurfaces have emerged as revolutionary tools to manipulate the behavior of light at the nanoscale. These devices consist of nanostructures defined within a single layer of metal or dielectric materials, and they offer unprecedented control over the optical properties of light, leading to previously unattainable applications in flat lenses, holographic imaging, polarimetry, and emission control, amongst others. The operation principles of metaoptics include complex light-matter interactions, often involving insidious near-field coupling effects that are far from being described by classical ray optics calculations, making advanced numerical modeling a requirement in the design process. In this contribution, recent optimization techniques used in the inverse design of high performance metasurfaces are reviewed. These methods rely on the iterative optimization of a Figure of Merit to produce a final device, leading to freeform layouts featuring complex and non-intuitive properties. The concepts in numerical inverse designs discussed herein will push this exciting field toward realistic and practical applications, ranging from laser wavefront engineering to innovative facial recognition and motion detection devices, including augmented reality retro-reflectors and related complex light field engineering.

Optimization of the performance of flat optical components, also dubbed metasurfaces, is a crucial step towards their implementation in realistic optical systems. Yet, most of the design techniques, which rely on large parameter search to calculate the optical scattering response of elementary building blocks, do not account for near-field interactions that strongly influence the device performance. In this work, we exploit two advanced optimization techniques based on statistical learning and evolutionary strategies together with a fullwave high order Discontinuous Galerkin Time-Domain (DGTD) solver to optimize phase gradient metasurfaces. We first review the main features of these optimization techniques and then show that they can outperform most of the available designs proposed in the literature. Statistical learning is particularly interesting for optimizing complex problems containing several global minima/maxima. We then demonstrate optimal designs for GaN semiconductor phase gradient metasurfaces operating at visible wavelengths. Our numerical results reveal that rectangular and cylindrical nanopillar arrays can achieve more than respectively 88% and 85% of diffraction efficiency for TM polarization and both TM and TE polarization respectively, using only 150 fullwave simulations. To the best of our knowledge, this is the highest blazed diffraction efficiency reported so far at visible wavelength using such metasurface architectures.