Metasurfaces based on resonant subwavelength photonic structures enable novel ways of wavefront control and light focusing, underpinning a new generation of flat-optics devices. Recently emerged all-dielectric metasurfaces exhibit high-quality resonances underpinned by the physics of bound states in the continuum that drives many interesting concepts in photonics. Here we suggest a novel approach to explain the physics of bound photonic states embedded into the radiation continuum. We study dielectric metasurfaces composed of planar periodic arrays of Mie-resonant nanoparticles ("meta-atoms") which support both symmetry protected and accidental bound states in the continuum, and employ the multipole decomposition approach to reveal the physical mechanism of the formation of such nonradiating states in terms of multipolar modes generated by isolated meta-atoms. Based on the symmetry of the vector spherical harmonics, we identify the conditions for the existence of bound states in the continuum originating from the symmetries of both the lattice and the unit cell. Using this formalism we predict that metasurfaces with strongly suppressed spatial dispersion can support the bound states in the continuum with the wavevectors forming a line in the reciprocal space. Our results provide a new way for designing high-quality resonant photonic systems based on the physics of bound states in the continuum.

We develop a multipolar theory of second-harmonic generation (SHG) by dielectric nanoparticles made of noncentrosymmetric materials with bulk quadratic nonlinearity. We specifically analyze two regimes of optical excitation: illumination by a plane wave and single-mode excitation, when the laser pump drives the magnetic dipole mode only. Considering two classes of nonlinear crystalline solids (dielectric perovskite material and III-V semiconductor), we apply a symmetry approach to derive selection rules for the multipolar composition of the nonlinear radiation. The developed description can be used for design of efficient nonlinear optical nanoantennas with reconfigurable radiation characteristics.

Surface electromagnetic waves are characterized by the intrinsic spin‐orbit interaction which results in the fascinating spin‐momentum locking. Therefore, directional coupling of light to surface waves can be achieved through chiral nanoantennas. Here, we show that dielectric nanoantenna provides chiral response with strong spectral dependence due to the interference of electric and magnetic dipole momenta when placed in the vicinity of the metal‐air interface. Remarkably, chiral behaviour in the proposed scheme does not require elliptical polarization of the pump beam or the geometric chirality of the nanoantenna. We show that the proposed ultracompact and simple dielectric nanoantenna allows for both directional launching of surface plasmon polaritons on a thin gold film and their demultiplexing with a high spectral resolution.

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We studied the nonlinear response of a dimer composed of two identical Mie-resonant dielectric nanoparticles illuminated normally by a circularly polarized light. We developed a general theory describing hybridization of multipolar modes of the coupled nanoparticles and reveal nonvanishing nonlinear circular dichroism (CD) in the second-harmonic generation (SHG) signal enhanced by the multipolar resonances in the dimer, provided its axis is oriented under an angle to the crystalline lattice of the dielectric material. We supported our multipolar hybridization theory by experimental results obtained for the AlGaAs dimers placed on an engineered substrate.