We discuss the general theoretical approach for advanced control of light wavefront with full phase and amplitude engineering by using resonant dielectric metasurfaces. We show how efficient functional metadevices, such as lenses, deflectors, vortices or holograms, can be realized at the nanoscale in both linear and nonlinear regime. Our analysis includes but is not limited to the concepts of the resonant phase accumulation, the multipolar decomposition, the Green’s function apparatus and the lattice summation.​ ​

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