Asymmetric Metasurfaces with High-$Q$ Resonances Governed by Bound States in the Continuum

We reveal that metasurfaces created by seemingly different lattices of (dielectric or metallic) meta-atoms with broken in-plane symmetry can support sharp high-$Q$ resonances arising from a distortion of symmetry-protected bound states in the continuum. We develop a rigorous theory of such asymmetric periodic structures and demonstrate a link between the bound states in the continuum and Fano resonances. Our results suggest the way for smart engineering of resonances in metasurfaces for many applications in nanophotonics and metaoptics.

Figure 1

Top: Schematic for the scattering of light by a metasurface. Bottom: Designs of the unit cells of asymmetric metasurfaces with a broken in-plane inversion symmetry of constituting meta-atoms supporting sharp resonances, as considered in Refs. [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15].

Figure 2

(a) A square lattice of tilted silicon-bar pairs with a design of the unit cell. Parameters: the period is 1320 nm, bar semiaxes are 330 and 110 nm, height is 200 nm, distance between bars is 660 nm. (b) Eigenmode spectra and transmission spectra with respect to pump wavelength and angle $\theta$. Error bars show the magnitude of the mode inverse radiation lifetime. (c) Evolution of the transmission spectra vs angle $\theta$. Spectra are relatively shifted by 1.5 units. (d) Distribution of the electric and magnetic fields for both BIC and quasi-BIC.

Figure 3

Effect of the in-plane asymmetry on the radiative $Q$ factor of quasi-BICs. (a) Dependence of the $Q$ factor on the asymmetry parameter $\alpha$ for all designs of symmetry-broken meta-atoms shown in Figs. 1 (log-log scale). (b) Definitions of the asymmetry parameter $\alpha$ for different metasurfaces.

Figure 4

Map of operating wavelengths and quality factors for silicon metasurfaces with tilted-bar pairs for varying orientation of the bars ($\alpha =\sin \theta$) and scaling factor. The radiative part of the total $Q$ factor is evaluated using Eq. (3), the nonradiative part is taken equal $10^5$. All calculations are confirmed by direct numerical simulations with realistic dispersion of silicon (see Supplemental Material [37]). The geometric scaling factor is shown in the upper horizontal axis. Colored rectangles correspond to the structures considered in the previous studies, see Fig. 1.