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The prospect of massive parallelism of optics enabling fast and low energy cost operations is attracting interest for novel photonic circuits where 3-dimensional (3D) implementations have a high potential for scalability. Since the technology for data input–output channels is 2-dimensional (2D), there is an unavoidable need to take 2D-nD transformations into account. Similarly, the 3D-2D and its reverse transformations are also tackled in a variety of fields such as optical tomography, additive manufacturing, and 3D optical memories. Here, we review how these 3D-2D transformations are tackled using iterative techniques and neural networks. This high-level comparison across different, yet related fields could yield a useful perspective for 3D optical design.

Metasurfaces have recently gained extensive interest because of their extraordinary optical behavior as artificial material interfaces with ultrahigh compactness. In this framework, dielectric platforms have newly become very promising for nonlinear nanophotonics, providing opportunities, especially for ultrafast optical switching, and high harmonic generation, opening the research field of nonlinear metaoptics. Up to now, nonlinear metaoptics have been mostly explored using single metasurfaces. However, in a long-term vision, the stacking of optical metasurfaces, very challenging in terms of fabrication, is one key goal of this research field. Here, we demonstrate a three-layer metasurface in the AlGaAs-on-insulator platform, which improves the second harmonic generation efficiency by more than one order of magnitude with respect to its one-layer counterpart. Our achievement paves the way toward phase-shaping multilayer and multifunctional all-dielectric metasurfaces.