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Fan JX, Li ZL, Xue ZQ, Xing HY, Lu D et al. Hybrid bound states in the continuum in terahertz metasurfaces. Opto-Electron Sci 2, 230006 (2023). doi: 10.29026/oes.2023.230006
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Abstract
Bound states in the continuum (BICs) have exhibited extraordinary properties in photonics for enhanced light-matter interactions that enable appealing applications in nonlinear optics, biosensors, and ultrafast optical switches. The most common strategy to apply BICs in a metasurface is by breaking symmetry of resonators in the uniform array that leaks the otherwise uncoupled mode to free space and exhibits an inverse quadratic relationship between quality factor (Q) and asymmetry. Here, we propose a scheme to further reduce scattering losses and improve the robustness of symmetry-protected BICs by decreasing the radiation density with a hybrid BIC lattice. We observe a significant increase of radiative Q in the hybrid lattice compared to the uniform lattice with a factor larger than 14.6. In the hybrid BIC lattice, modes are transferred to Г point inherited from high symmetric X, Y, and M points in the Brillouin zone that reveal as multiple Fano resonances in the far field and would find applications in hyperspectral sensing. This work initiates a novel and generalized path toward reducing scattering losses and improving the robustness of BICs in terms of lattice engineering that would release the rigid requirements of fabrication accuracy and benefit applications of photonics and optoelectronic devices. -
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References
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Fan JX, Li ZL, Xue ZQ, Xing HY, Lu D et al. Hybrid bound states in the continuum in terahertz metasurfaces. Opto-Electron Sci 2, 230006 (2023). doi: 10.29026/oes.2023.230006
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Figure 1.
Hybrid BIC lattices. (a–c) Schematic diagram of a symmetry-protected BIC lattice without radiation channel (a), a uniform quasi-BIC lattice with radiation channel open by breaking symmetry of all the resonators (b), and a hybrid quasi-BIC lattice with C2 symmetry preserved in the neighboring resonators along x-axis in a supercell (c). (d) A double gap split ring resonator as the unit cell of the metasurface. (e, f) Simulated (e) and experimental (f) transmission amplitude spectra for the three-type lattices. The same asymmetry degree (α = 4.95%) was applied for U-qBIC and Hx-BIC metasurfaces.
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Figure 2.
Interpretation of hybrid BIC from reciprocal space. (a, b) Brillouin zones of monoatomic and diatomic supercells at α = 0 when the periods were chosen with a and 2a in the x direction. (c) Illustration of Brillouin zones for monoatomic and diatomic supercells showing the band folding operation where X and M points in the BZ of a monoatomic supercell are folded to X′ and M′ points in the BZ of a diatomic supercell, and Г(Г′) point is fixed. (d) Band diagrams of monoatomic (black circles) and diatomic (orange lines) supercells showing the folding behavior where all the modes of a monoatomic supercell in unshaded region are reflected into the shaded region representing modes of a diatomic supercell. (e) Radiative quality factors of monoatomic and diatomic supercells. The same folding behavior of Q is inherited from the eigenmodes. (f) Comparison of radiative Q versus k between monoatomic and diatomic supercells. Circles are simulated values and solid lines are fitting curves with Eq. (2) whose coefficient is 4-times larger in a diatomic supercell than that of a monoatomic supercell. Here, px is period of supercell along x direction. Perfect electric conductor (PEC) was used for DSRRs in simulations to calculate eigenvalues and quality factors.
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Figure 3.
Experimental demonstration of the high-Q hybrid BIC. (a, b) Microscopic images of U-qBIC and Hx-BIC metasurfaces. Supercells of U-qBIC and Hx-BIC metasurfaces are shown in the inset. Scale bar, 20 μm. (c) Simulated transmission amplitude spectra of U-qBIC (left) and Hx-BIC (right) metasurfaces at an asymmetry degree of 2.97% with excitation electric field polarized along y-axis. Band diagrams of U-qBIC and Hx-BIC supercells are shown in the middle. (d) Simulated radiative Q (circles) versus asymmetry degree (α) with inverse quadratic fitting curves (solid lines) of U-qBIC (black) and Hx-BIC (orange) supercells. Here, an additional constant of β is necessary to account for the nonuniform asymmetry in the hybrid lattice. (e) Experimental transmission amplitude spectra of U-qBIC and Hx-BIC metasurfaces at an asymmetry degree of 7.42% with excitation electric field polarized along y-axis. The linewidth of Fano resonances is larger than that of simulations due to Ohmic loss in metallic resonators (aluminum) and finite number of supercells.
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Figure 4.
Generalized high-order hybrid BICs. (a, b) Microscopic images of Ht-BIC and Hq-BIC metasurfaces with three and one asymmetric resonators out of four in a 2×2 supercell, respectively, and the period is 2a along both x and y axes. Scale bar, 20 μm. (c) Schematic diagram of band folding from U-qBIC lattice (black) to Ht-BIC/Hq-BIC (red) in the Brillouin zone. (d) Simulated transmission amplitude spectra of the Ht-BIC (left) and Hq-BIC (right) metasurfaces at an asymmetry degree of 2.97%. The band structure of Ht-BIC/Hq-BIC is shown in the middle, and the modes at the Г point marked with different colored circles are folded from X (red), Y (orange), and M (blue) points in the Brillouin zone of U-qBIC lattice, respectively. The highlighted resonances show the original modes inherited from U-qBIC lattice. (e) Experimental (orange) and simulated (black) transmission amplitude spectra of Ht-BIC and Hq-BIC metasurfaces at an asymmetry degree of 7.42%. The overall linewidth of Fano resonances is larger than that of simulations due to Ohmic loss in metallic resonators (aluminum) and finite number of supercells.
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Figure 5.
Significant Q improvement in hybrid BIC supercells and robustness against fabrication imperfections. (a) Evolution of radiative Q versus AD for U-qBIC, Ht-BIC, Hx-BIC, and Hq-BIC supercells. The overall quality factors are improved in hybrid supercells with a lower radiation density. (b) Influences of fabrication imperfection on quality factors in the four scenarios. Imperfection is introduced by adjusting the sharp right-angle of square in the resonators to rounded angles indicated by radius r. Q and Q' indicate radiative quality factors for lattices with right-angle and rounded-angle resonators, respectively.
