Metasurfaces are arrays of subwavelength anisotropic light scatters (optical antennas) that can produce abrupt changes in the phase, amplitude, or polarization of light. Within the last few years, there has been significant progress, including design of metasurfaces that refract and focus light, enabling many unique properties and applications such as holograms, optical vortex generation/detection, ultrathin focusing lens, perfect absorber, etc.

This tutorial will cover the fundamental principles, advanced designs and technological applications of optical metasurfaces, focusing on the topics of (I) High Performance Metasurface Flat Optics: from Components to Systems, (II) Nonlinear Optical Metasurfaces, (III) Electrically Tunable Metamaterials and Metasurfaces for Control of Absorption, Emission and Scattering, and (IV) Optimization and machine learning for metasurface design.

High Performance Metasurface Flat Optics—From Components to Systems 
Federico Capasso, Harvard University

Metasurfaces are leading to the emergence of new optical components that circumvent the limitations of standard refractive and diffractive one by enabling dispersion engineering, which also leads to entirely new functionalities based on the local control of phase amplitude and polarization. Dispersion engineering has led to the demonstration of metalenses with correction of monochromatic aberrations and to achromatic metalenses and hybrid refractive/diffractive doublets across the visible spectrum. The planarity of flat optics will lead to the unification of semiconductor manufacturing and lens-making; recent industrial advances in this direction will be discussed. Polarization optics, polarimeters and polarization sensitive cameras without moving parts and conventional birefringent optics will be presented. Metasurfaces also offer fresh opportunities for structuring light as well as the dark. This session will cover spin to total orbital angular momentum (OAM) converters and  OAM lasing, as well as  flat devices that enable light’s spin and OAM to evolve, simultaneously, from one state to another along the propagation direction. Finally, the demonstration of 2D phase and polarization singularities and the unique applications that they will open will be discussed.

Optimization and Machine Learning for Metasurface Design 
Jonathan Albert Fan, Stanford University

Inverse design, in which the design process is performed through iterative optimization, has the potential to push metasurface performance to the physical limits of composite materials engineering. In this tutorial, we will discuss a range of state-of-the-art numerical optimization methods for metasurface design. We will introduce the objective-first and adjoint variables methods, which are gradient-based optimization concepts that can produce high performance freeform geometries. We will also provide an overview of machine learning techniques as applied to electromagnetics problems and show how generative neural networks can be harnessed as an effective global optimizer for photonic devices.

Electrically Tunable Metamaterials and Metasurfaces for Control of Absorption, Emission and Scattering 
Harry Atwater, California Institute of Technology

Progress in understanding resonant subwavelength optical structures has fueled a worldwide explosion of interest in both fundamental processes and nanophotonic devices for imaging, sensing, solar energy conversion and thermal radiation control. For most nanophotonic materials, the optical properties are encoded and fixed permanently into the nanoscale structure at the time of fabrication. Achieving electronic tunability of the optical properties is an emerging opportunity to bring metamaterials and metasurfaces to life as dynamic objects composed of tunable nanoscale resonators and antennas. Gated field effect tuning of the carrier density in conducting oxides and two-dimensional materials enables the optical dispersion of individual structures to be altered from dielectric to plasmonic, yielding active nano-antenna arrays with electrically tunable absorption, radiative emission and scattering properties.

Nonlinear Optical Metasurfaces: From Enhanced Light-Matter-Interaction to Functional Elements 
Thomas Zentgraf, Paderborn University

For efficient nonlinear processes, the engineering of the nonlinear optical properties of media becomes an important task. The most well-known technique for spatially engineering nonlinear optical properties is the quasi-phase matching scheme for second-order processes like second harmonic generation. However, the widely used technique of periodic polling of natural crystals only provides a binary state for the nonlinear material polarization, which is equivalent to a discrete phase change of π of the nonlinear polarization. The continuous tailoring of the phase of the nonlinear susceptibility would greatly enhance flexibility in the design and reduce parasitic effects. In this tutorial, we will discuss nonlinear metamaterials with a continuously controllable phase of the local effective nonlinear polarizability. We will focus on plasmonic metasurfaces with various designs for the meta-atom geometry together with different polarization states of the light. In particular for circular polarization states, the controllable nonlinearity phase results from the phase accumulation due to the polarization change along the polarization path on the Poincare Sphere (the so-called Pancharatnam-Berry phase) and depends therefore only on the spatial geometry of the metasurface. By using a fixed orientation of the meta-atom, the nonlinear phase can be spatially arbitrarily tailored over the entire range from 0 to 2π. In contrast to the quasi-phase matching scheme, the continuous phase engineering of the effective nonlinear polarizability enables complete control of the propagation of harmonic generation signals, and therefore, it seamlessly combines the generation and manipulation of the harmonic waves for highly compact nonlinear nanophotonic devices. We will discuss the concepts of enhancing nonlinear processes with simultaneous phase engineering for the manipulation of second- and third-harmonic generation from metasurfaces and the restrictions with respect to symmetry and geometry of meta-atoms. Nonlinear metamaterials have fundamental significance in nonlinear optics and for tailored nonlinearities, as they provide a further degree of freedom in the design of nonlinear materials.