Enhancing optical nonlinearity: Intense pulses of light interacting with a dielectric material can induce optical nonlinear behavior, whereby the frequency of the output light can be doubled or tripled or excited to even higher harmonics of the input light. Usually this interaction is weak and occurs over many thousands of wavelengths, typically requiring the combination of bulk volumes of material with a confining cavity. Using a mechanism of light confinement called bound states in the continuum, Koshelev et al. show that enhanced second-harmonic generation can be obtained in nanoscale subwavelength cylinders of a dielectric material. The results on these optical nanoantennas offer a platform for developing integrated nonlinear nanophotonic devices. Science , this issue p. 288

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 reveal the existence of a type of surface electromagnetic wave supported by hyperbolic metasurfaces, described by a conductivity tensor with an indefinite signature. We demonstrate that the spectrum of the hyperbolic metasurface waves consists of two branches corresponding to hybrid transverse electric–transverse magnetic waves with a polarization that varies from linear to elliptic or circular depending on the wave frequency and propagation direction. The shape of the equal-frequency contours drastically depends on the frequency and changes from the elliptical to hyperbolic—a topological transition takes place. We derive asymptotic formulas describing the losses of the surface waves for capacitive, inductive, and hyperbolic regimes of the metasurface. We analyze numerically the generation of surface waves by a point electric dipole placed in the vicinity of the metasurface with numerical simulations, and also reveal wave-front peculiarities in strong anisotropic hyperbolic and $\sigma$-near-zero regimes of the metasurface.