In this talk we discuss our theoretical and experimental studies of a family of null solutions to Helmholtz equation in 3D free space - optical vortices, or zero lines of complex amplitude in a propagating light field. When multiple light beams overlap in three-dimensional space, their interference produces tangled lines of complete darkness – optical vortices that can form closed loops – links or knots. We design all-dielectric optical metasurfaces – nanostructures enabling unprecedented control over the amplitude, polarization and phase of optical fields, for generation of optical knots, and study their stability, evolution, and third-harmonic generation using knots as a fundamental wave. Knotted electromagnetic fields may find applications in three-dimensional optical manipulations or as potential candidates for new information carriers in classical and quantum communication systems.
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