Sharp electromagnetic resonances play an essential role in physics in general and optics in particular. The last decades have witnessed the successful developments of high-quality (Q) resonances in microcavities operating below the light line, which however is fundamentally challenging to access from free space. Alternatively, metasurface-based bound states in the continuum (BICs) offer a complementary solution of creating high-Q resonances in devices operating above the light line, yet the experimentally demonstrated Q factors under normal excitations are still limited. Here, we present the realizations of quasi-BIC under normal excitation with a record Q factor up to 18 511 by engineering the symmetry properties and the number of the unit cells in all-dielectric metasurface platforms. The high-Q quasi-BICs exhibit exceptionally high conversion efficiency for the third harmonic generation and even enable the second harmonic generation in Si metasurfaces. Such ultrasharp resonances achieved in this work may immediately boost the performances of BICs in a plethora of fundamental research and device applications, e.g., cavity QED, biosensing, nanolasing, and quantum light generations.

We propose an ultra-thin metamaterial constructed by an ensemble of the same type of anisotropic aperture antennas with phase discontinuity for wave front manipulation across the metamaterial. A circularly polarized light is completely converted to the cross-polarized light which can either be bent or focused tightly near the diffraction limit. It depends on a precise control of the optical-axis profile of the antennas on a subwavelength scale, in which the rotation angle of the optical axis has a simple linear relationship to the phase discontinuity. Such an approach enables effective wave front engineering within a subwavelength scale.

Toroidal multipole moments are usually underestimated as they are quite weak in most cases of light-matter interaction. Herein, we reveal a strong link between the toroidal dipole resonance and the bound state in the continuum in the context of all-dielectric metasurfaces. We introduce the concept of toroidal dipole bound states in the continuum, in which two eigenmodes of the silicon metasurface exhibit an intrinsic toroidal dipolar character and have an infinite lifetime. They can be classified as transverse (trivial) and longitudinal (nontrivial) toroidal dipole modes, which correspond to symmetry unprotected and protected bound states in the continuum, respectively. We demonstrate that such toroidal bound states in the continuum supported by the symmetry metasurface can be turned into ultrahigh-Q resonances with a dominant toroidal dipole excitation, which validates their physical origin associated with the ultrahigh-Q toroidal dipole leaky resonances. A full multipole decomposition with dispersive, lossy, and substrate effects further validates that the proposed concept is general and can also be generalized to other structures.

Metamaterials are effectively homogeneous materials that display extraordinary dispersion. Negative index metamaterials, zero index metamaterials and extremely anisotropic metamaterials are just a few examples. Instead of using locally resonating elements that may cause undesirable absorption, there are huge efforts to seek alternative routes to obtain these unusual properties. Here, we demonstrate an alternative approach for constructing metamaterials with extreme dispersion by simply coiling up space with curled channels. Such a geometric approach also has an advantage that the ratio between the wavelength and the lattice constant in achieving a negative or zero index can be changed in principle. It allows us to construct for the first time an acoustic metamaterial with conical dispersion, leading to a clear demonstration of negative refraction from an acoustic metamaterial with airborne sound. We also design and realize a double-negative metamaterial for microwaves under the same principle.

We introduce the concept of tunable ideal magnetic dipole scattering, where a nonmagnetic nanoparticle scatters light as a pure magnetic dipole. High refractive index subwavelength nanoparticles usually support both electric and magnetic dipole responses. Thus, to achieve ideal magnetic dipole scattering one has to suppress the electric dipole response. Such a possibility was recently demonstrated for the so-called anapole mode, which is associated with zero electric dipole scattering. By spectrally overlapping the magnetic dipole resonance with the anapole mode, we achieve ideal magnetic dipole scattering in the far field with tunable strong scattering resonances in the near infrared spectrum. We demonstrate that such a condition can be realized at least for two subwavelength geometries. One of them is a core-shell nanosphere consisting of a Au core and silicon shell. It can be also achieved in other geometries, including nanodisks, which are compatible with current nanofabrication technology.