All-Dielectric Metasurface with a Two-Dimensional Locally Flat Photonic Band

Abstract

Photonic flatbands offer promising light-matter interaction due to their unique slow-light nature. In recent years, flatbands have also attracted significant interest in optical engineering because of their angle-insensitive resonant characteristics. However, to date, no studies have reported the dispersionless behavior of flatbands under arbitrary two-dimensional incident angles. Here, we present a two-dimensional photonic flatband created using a silicon metasurface with a Lieb lattice-inspired structure which demonstrates a locally flat photonic band for both transverse electric (TE) and transverse magnetic (TM) polarized light. Employing Fourier imaging, we analyze the energy-momentum dispersion of the flatband metasurface under arbitrary two-dimensional incident angles, demonstrating dispersionless flatbands with a change in resonance within $\pm2 nm$ up to $\pm24ô$ or $\pm5ô$, depending on the polarization state and incident angle. This geometry can be adapted for various applications in local field enhancement, enhanced photodetection, and augmented reality displays.

Figures (4)

• Figure 1: Flatband metasurface geometry. (a) (left) Crystalline silicon of thickness, h = 230 nm, on a sapphire substrate highlighting the partial etch of Mie voids into the crystalline silicon layer down to a depth h1 = 223 nm. (right) Diagram of the designed metasurface Lieb lattice unit cell of period, a = 309 nm, showing both the major and minor sublattices separated by a spacing, a/2. The minor sublattice is composed of circular voids with radius, r1 = 42.5 nm, and the major sublattice is composed of elliptical voids with semi-minor axis, r2 = 42.5 nm and semi-major axis, r3 = 66.5 nm. (b) Scanning electron micrograph of the fabricated crystalline silicon metasurface.
• Figure 2: (a) Real space and first Brillioun zone representations of the Lieb lattice. (b) Comparison of simulated band structure (top row) with experimentally measured band structure (bottom row) for the Lieb lattice metasurface. Band structures up to the numerical aperture of 0.95 for the objective are shown along the X and M axes in the Brillouin zone for both S- and P-polarizations. White dashed lines indicate flatbands at each polarizations and oblique incident directions. Note a wavelength offset of 10nm between the simulation and experiment, which is most likely due to fabrication imperfection. A change in resonance wavelength within $\sim$$\pm$ 2 nm was considered to be within the flatband extent.
• Figure 3: Extracted bands for simulated and measured S-polarized light as well as for simulated and measured P-polarized light (a and b, respectively). Band surfaces are extracted by fitting Fano resonances to spectra taken at 15$^\circ$ increments in azimuthal and applying a smoothing filter to interpolate a continuous band surface. Results are shown in the vicinity of the $\Gamma$-point up to a numerical aperture of 0.4. While the S-polarized band shows remarkable agreement between simulation and experiment (a), the P-polarized band is more clearly flat in simulation than in experiment (b). Red dashed lines indicate flatband regions at each polarizations.
• Figure 4: Flatband response versus refractive index of the metasurface for (a) P- and (b) S- polarizations. A change in resonance wavelength within $\sim$$\pm$ 2 nm was considered to be within the flatband extent.