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Scattering of electromagnetic waves by subwavelength objects is accompaniedby the excitation of electric and magnetic Mie resonances, that may modifysubstantially the scattering intensity and radiation pattern. Scattered fieldscan be decomposed into electric and magnetic multipoles, and the magneticmultipoles define magnetic response of structured materials underpinning thenew field of all-dielectric resonant meta-optics. Here we review the recentdevelopments in meta-optics and nanophotonics, and demonstrate that the Mieresonances can play a crucial role offering novel ways for the enhancement ofmany optical effects near magnetic and electric multipolar resonances, as wellas driving a variety of interference phenomena which govern recently discoverednovel effects in nanophotonics. We further discuss the frontiers ofall-dielectric meta-optics for flexible and advanced control of light with fullphase and amplitude engineering, including nonlinear nanophotonics, anapolenanolasers, quantum tomography, and topological photonics.

Functional meta-optics and nanophotonics govern by Mie resonances