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The field of metasurfaces holds the promise of fundamentally innovating different areas of electromagnetics, optics and photonics. In this talk, we present our recent efforts on some exciting topics at the frontiers of this field, with particular focus on ultra-broadband metalenses and nonlocal meta-optics. We present fundamental bandwidth limits on achromatic metalenses, independent of their implementation, and we discuss potential directions to approach and bypass these bounds. In the second part of the talk, we present our recent efforts on metasurfaces that are both nonlocal and laterally inhomogeneous, which open new opportunities for ultra-compact focusing systems and more advanced functionalities.
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