Controlling high-$Q$ trapped modes in polarization-insensitive all-dielectric metasurfaces

We reveal peculiarities of the trapped (dark) mode excitation in a polarization-insensitive all-dielectric metasurface, whose unit supercell is constructed by particularly arranging four cylindrical dielectric particles. Involving group-theoretical description we discuss in detail the effect of different orientations of particles within the supercell on characteristics of the trapped mode. The theoretical predictions are confirmed by numerical simulations and experimental investigations. Since the metasurface is realized from simple dielectric particles without the use of any metallic components, they are feasibly scalable to both $\mu \text{m-}$ and nanometer-size structures, and they can be employed in flat-optics platforms for realizing efficient light-matter interaction for multiple hot-spot light localization, optical sensing, and highly efficient light trapping.

Figure 1

Schematic view of an all-dielectric metasurface with the supercell composed of four identical particles having coaxial-sector notch. $a_d$ and $h_d$ are the disks radius and height, respectively, $\theta$ is the radius of the sector midline, $2a_h$ is the notch width, and $\alpha$ is the sector opening angle. The disks are made from a nonmagnetic dielectric having permittivity ${\varepsilon }_d$. All disks are deposited equidistantly with period $d$. The lattice is buried into a dielectric host having permittivity ${\varepsilon }_s$ and thickness $h_s$ to form a whole metasurface (not shown in the figure).

Figure 2

Transmission ($T$) and reflection ($R$) coefficients of an all-dielectric (lossless) metasurface with the supercell composed of (a) solid disks, and particles with notches oriented with symmetry (b) $C_s$, (c) $C_4$, and (d) $C_{4v}$. The geometrical parameters of the disk are $a_d=4.5$ mm, $h_d=2.5$ mm, $\theta =2$ mm, $a_h=1$ mm, $\alpha ={120}^{\circ }$, the period of lattice is $d=22$ mm. The permittivities of disks and host are ${\varepsilon }_d=24$ and ${\varepsilon }_s=1.1$, respectively. The thickness of the host is $h_s=20$ mm. The color maps demonstrate distributions of the polarization current (red arrows) and magnetic field (yellow arrows) calculated within the supercell at the resonant frequency of trapped mode excited by the $x$-polarized incident wave.

Figure 3

Experimental setups for measurements of the (a) transmission and reflection spectra and (b) magnetic near-field distribution.

Figure 4

Simulated (pale lines) and measured (bright lines) transmission and reflection coefficients of the all-dielectric metasurface with the supercell composed of particles oriented with symmetry (a) $C_s$, (b) $C_4$, and (c) $C_{4v}$. In the simulation actual material losses ($tan\delta =1\times {10}^{-3}$) in ceramic disks are taken into account, while the substrate is modeled as a lossless dielectric. The insets demonstrate fragments of the metasurface prototypes. The geometrical parameters of the metasurface are the same as in Fig. 2.

Figure 5

Measured real part of the $H_z$ component of the magnetic near-field (out-of-plane magnetic moments) at the corresponding resonant frequency of trapped mode excited by the $x$-polarized incident wave in the all-dielectric metasurface with the supercell composed of particles oriented with symmetry (a) $C_s$, (b) $C_4$, and (c) $C_{4v}$.

Figure 6

(a) Contributions of four lowest-order multipole moments to the scattering cross section of a single particle irradiated by either $x$-polarized (solid lines) or $y$-polarized (dashed lines) wave, and (b) cross-section patterns of electric field distribution, which are calculated at the corresponding frequencies of the trapped mode and electric dipole mode resonances.