Tailoring topological nature of merging bound states in the continuum by manipulating structure symmetry of the all-dielectric metasurface

Photonic bound states in the continuum (BIC) promise a versatile platform for construction of optical resonators with highly confined electromagnetic fields and ultralong radiative lifetime. Merging multiple BIC can enable suppression of out-of-plane radiative losses and further boost the quality (Q) factor of the resonance state. However, current studies on merging BIC (M-BIC) are primarily restricted to the elementary BIC with topological charge $\pm 1$, which hinders further improvement of the performance of optical resonators. Here, an all-silicon terahertz metasurface (THz-MS) is investigated that supports the symmetry-protected BIC (SP-BIC) with topological charge $-2$ and accidental BIC (A-BIC) with topological charge $\pm 1$ simultaneously. Empowered by the topological nature of BIC, we merge twelve A-BIC with a higher-order SP-BIC at the $\mathrm{\Gamma }$ point. By tailoring in-plane mirror symmetry of the THz-MS, we achieve M-BIC at almost arbitrary position in the momentum space. Unlike original isolated BIC, M-BIC manifests the dramatic enhancement of the Q factors of nearby resonances and are robust against radiation losses introduced by fabrication imperfections. Our work presents a paradigm for realizing higher-order at-$\mathrm{\Gamma }$ M-BIC and momentum-steerable M-BIC that can substantially enhance light-matter interaction and further improve the performance of terahertz optoelectronic devices.

Figure 1

(a) Left panel: Schematic view of a conventional THz-MS with a hexagonal

lattice of etched circular holes standing in free space. Right panel: Top view of the hexagonal-lattice unit cell. (b) Numerically simulated TE-like band structure. The inset shows the first Brillouin zone of the triangular lattice and irreducible contour for circular-hole THz-MS (shaded triangle area). (c) Calculated radiation loss ($\gamma$) normalized by the value near the light cone (${\gamma }_0$), $\gamma /{\gamma }_0$, along both $\mathrm{M}\text{−}\mathrm{\Gamma }$ and $\mathrm{\Gamma }\text{−}\mathrm{K}$ direction as a function of $k(a/2\pi )$. The inset shows mode profile of the $z$ component of the magnetic field $H_z$, highlighting $B_1$ irreducible representation for the SP-BIC and $B$ irreducible representation for the A-BIC on the ${\mathrm{TE}}_1$ band, respectively. (d) Simulated 2D brightness map of evolution of radiative Q factor for the ${\mathrm{TE}}_1$ band along the $\mathrm{M}\text{−}\mathrm{\Gamma }\text{−}\mathrm{K}$ direction wave vector with the variation of the THz-MS thickness.

Figure 2

Numerically calculated Q factors (a), polarization vectors of far-field radiation (b), and the distribution of absolute value of the nodal lines of $c_x$ (c) and $c_y$ (d) near the $V$ point in the momentum space at $t=210\mu \mathrm{m}$ (before merging), $t=197.5\mu \mathrm{m}$ (at merging), and $t=190\mu \mathrm{m}$ (after merging). When the slab thickness is reduced from 210 to $190\mu \mathrm{m}$, twelve A-BIC with topological charge $\pm 1$ at distance $|k{}_{\mathrm{BIC}}|=0.272\pi /a$ from the origin are gradually merge into an isolated SP-BIC with topological charge $-2$.

Figure 3

Simulated radiative Q factors (dotted lines) and the corresponding fitting curves (solid lines) at $t=210\mu \mathrm{m}$ (before merging), $197.5\mu \mathrm{m}$ (at merging), and $190\mu \mathrm{m}$ (after merging). The Q factors of M-BIC configuration (blue) are orders of magnitude higher than the other isolated BIC design (red and dark green) along both the $\mathrm{\Gamma }\text{−}\mathrm{M}$ and $\mathrm{\Gamma }\text{−}\mathrm{K}$ directions due to the scaling rule changes to $Q\propto 1/k^8$.

Figure 4

(a) Schematic drawing of the unit cell with elliptic air holes. The semimajor axis of the ellipse $D_1=120\mu \mathrm{m}$ and the semiminor axis $D_2=100\mu \mathrm{m}$. (b) Numerically simulated dispersion relation for a symmetry-reduced THz-MS at $t=210\mu \mathrm{m}$. (c) Calculated radiation loss ($\gamma$) normalized by the value near the light cone (${\gamma }_0$), $\gamma /{\gamma }_0$, along the highly symmetrical $\mathrm{M}\text{−}\mathrm{\Gamma }\text{−}\mathrm{K}$ direction as a function of $k(a/2\pi$). Owing to the reduced symmetry of the system, the SP-BIC at the $\mathrm{\Gamma }$ point splits into two off-$\mathrm{\Gamma }$ BIC in the $\mathrm{\Gamma }\text{−}\mathrm{M}$ direction. (d) The evolution trajectory of BIC in momentum space with variation of the slab thickness.

Figure 5

Numerically calculated radiative Q factors (a) and far-field polarization state distribution (b) around BIC in the $k$ space at $t=210\mu \mathrm{m}$ (before-merging), $t=221.4\mu \mathrm{m}$ (at merging), and $t=225\mu \mathrm{m}$ (after merging). As the slab thickness $t$ increases, two S-BIC with topological charge $-1$ first approach each other along the $\mathrm{\Gamma }\text{−}\mathrm{M}$ direction, then merge at the origin for $t=221.4\mu \mathrm{m}$, and finally bouncing off each other along the $\mathrm{\Gamma }\text{−}\mathrm{K}$ direction. (c) Calculated Q-$k$ relationship (dotted lines) and the corresponding fitting curves (solid lines) for three different THz-MS thicknesses. Compared to the original isolated BIC, M-BIC shows an ultrahigh Q-factor distribution over a broad wave-vector range.

Figure 6

Numerically calculated radiative Q factors (a) and far-field polarization state distribution (b) around BIC in the $k$ space at $t=209\mu \mathrm{m}$ (before merging), $t=207.1\mu \mathrm{m}$ (at merging), and $t=200\mu \mathrm{m}$ (after merging). When the slab thickness $t$ is tuned from 209 to $207.1\mu \mathrm{m}$, two S-BIC with topological charge $-1$ merge with two A-BIC with topological charge $+1$. Further increasing $t$, A-BIC and the S-BIC with opposite topological charges annihilate each other and then transform into quasi-BIC modes with high Q factor. (c) Calculated radiative Q factors (dotted lines) and the corresponding fitting curves (solid lines) for three different THz-MS thicknesses. Unlike the isolated BIC case, the M-BIC case shows considerable enhancement of the Q factor for nearby states over a broad wave vector.

Figure 7

(a) Schematic drawing of a triangular-lattice THz-MS of elliptic-shaped air holes with the major axis rotated by $\theta$. Numerically calculated normalized radiative lifetime Q (b) and far-field polarization states distribution (c) around BIC in the $k$ space for isolated BIC with $t=210\mu \mathrm{m}$ and $\theta ={20}^{\circ }$, M-BIC at ($k_x=\pm 0.068\pi /a$, $k_y=\pm 0.164\pi /a$) with $t=206.5\mu \mathrm{m}$ and $\theta ={20}^{\circ }$, and M-BIC ($k_x=\pm 0.085\pi /a$, $k_y=\pm 0.144\pi /a$) with $t=205.5\mu \mathrm{m}$ and $\theta ={32}^{\circ }$.