Metasurfaces and surface lattice resonances

A collective resonance of a periodic nanoparticle array (plasmonic or dielectric): each particle's resonance couples to light diffracted along the array plane (the Rayleigh anomaly, at λ ≈ period × n at normal incidence). The result is a far narrower and stronger feature than any single particle shows, with quality factors of hundreds instead of about 10.

Surface lattice resonances of metal (gold, silver, aluminum) nanoparticle arrays, where the particles' plasmons couple through the lattice. They give sharp, tunable resonances for sensing, nanoscale lasing and enhanced emission; the strongest form needs the same refractive index above and below the array.

High-index particles (silicon, TiO₂, GaAs) support Mie resonances with little loss: a magnetic dipole when the wavelength inside the particle is about its diameter, then an electric dipole and higher multipoles. A 220 nm TiO₂ sphere in air has its magnetic dipole at 560 nm, electric dipole at 472 nm and magnetic quadrupole at 422 nm. These are the building blocks of all-dielectric metasurfaces and nanoantennas.

A metasurface of dielectric particles whose electric and magnetic dipole resonances are made to overlap. The two dipoles then radiate together forward and cancel backward (the Kerker condition): the layer transmits nearly all light while its phase sweeps through 2π, which lets flat lenses and beam deflectors be built from it. Detuned the other way, the same particles reflect almost perfectly: a square array of 220 nm TiO₂ spheres with 60 nm gaps on glass reflects 99.9 % at 472 nm.

Simulate one unit cell with periodic (Floquet) boundary conditions and ports or perfectly matched layers above and below, and read the reflection and transmission of each diffraction order. For arrays of spheres the T-matrix method with Ewald lattice sums is exact and takes seconds, which makes it a quick design tool and a check for full-wave models.

The diffracted waves that form a lattice resonance travel in the plane of the array; with different refractive indices above and below, the Rayleigh anomalies of the two sides occur at different wavelengths and the collective mode loses strength. Index-matching layers or symmetric embedding restore it.

Metamaterials and metasurfaces built from high-index dielectric particles whose Mie resonances (magnetic and electric dipoles, quadrupoles) set their optical response, instead of plasmonic metals: "Mie-resonant metaphotonics". They give low-loss magnetic responses, directional scattering, flat optics, nonlinear and quantum light sources and sensors, for photonic devices from lenses to lasers.

An air (or low-index) cavity inside a high-index material that supports Mie-like resonances of its own, the inverse of a high-index particle. Arrays of Mie voids in silicon produce vivid structural colours, including in the ultraviolet where solid particles absorb.

The wavelength at which a diffraction order of a grating or array becomes grazing (travels along the surface): λ = period × (n ± sin θ) for a one-dimensional period at angle θ. Transmission and reflection change abruptly there, and lattice resonances form just to its red side.