Metasurfaces based on resonant subwavelength photonic structures enable novel methods 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 an approach to explain the physics of bound photonic states embedded in 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 wave vectors forming a line in the reciprocal space. Our results provide a method 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.

The bianisotropy of meta-atoms is usually associated with their nonlocal response and mutual coupling between electric and magnetic dipole moments induced by an incident field. In this Letter, we generalize the theory of bianisotropy beyond the dipole response to cases of arbitrary high-order multipole resonances. We demonstrate that bianisotropy is fully connected to the geometrical structure of meta-atoms and caused exclusively by the absence of their inversion symmetry, while the strength of the bianisotropy response grows normally with the size of a meta-atom. Applying a group theory analysis, we reveal the explicit criteria when the dipole approximation is enough for the correct description of bianisotropy and when accounting for higher-order multipoles is required. We consider a triangular prism as an illustrative example of a bianisotropic particle and show how accounting for higher-order multipoles prevents the violation of Onsager-Casimir conditions for kinetic coefficients appearing in the dipole approximation. The developed theory is an essential step toward a deeper insight into the scattering properties of nanoantennas and meta-atoms.

Resonantly enhanced Raman scattering in dielectric nanostructures has been recently proven to be an efficient tool for nanothermometry and for the experimental determination of their mode composition. In this paper we develop a rigorous analytical theory based on the Green's function approach to calculate the Raman emission from crystalline high-index dielectric nanoparticles. As an example, we consider silicon nanoparticles which have a strong Raman response due to active optical phonon modes. We relate enhancement of Raman signal emission to the Purcell effect due to the excitation of Mie modes inside the nanoparticles. We also employ our numerical approach to calculate inelastic Raman emission in more sophisticated geometries, which do not allow a straightforward analytical form of the Green's function. The Raman response from a silicon nanodisk has been analyzed with the proposed method, and the contribution of various Mie modes has been revealed.

In this work we study second-harmonic generation of a monocrystalline nanoparticle with a noncentrosymmetric crystalline lattice. It was shown that breaking the symmetry of the nanoparticle’s shape can significantly affect the second-harmonic radiation pattern. We propose a method for explaining and predicting the generated field for arbitrary nanoparticles and provide selection rules for nanoparticles with several different symmetries.