连续域束缚态（BIC）是位于系统辐射连续域内的束缚态。在太赫兹波段，BIC为超高品质因数（Q）的功能器件的研发提供了新思路。基于超晶格模式的对称性保护原理，设计并数值研究了由经典金属裂环谐振器（SRR）组成的太赫兹BIC超表面。在BIC向远场泄漏的过程中，通过改变SRR的间隙宽度，系统形成了可观测的准BIC（QBIC）模式。通过采用Drude模型，研究了金属材料的欧姆损耗对QBIC模式Q值的影响。提出的BIC和QBIC模式对入射角度也具有独特的响应特征。所提出的SRR基BIC超表面不仅为开发高 Q 太赫兹功能器件提供了一个机制清晰且易于实现的框架，而且从损耗和角度依赖特性等方面为后续太赫兹波段BIC超表面的研究提供了思路。

Bound states in the continuum (BIC) refers to the non-radiative state located in the radiative continuum. BIC provides a novel method for the research and development of functional devices with ultra-high quality factor (Q) in the terahertz band. It has the potential to be used in several applications, including narrow linewidth filtering, terahertz slow light devices, and the enhanced interaction between terahertz waves and matter. In this study, terahertz BIC metasurfaces composed of classical metallic split ring resonators (SRRs) are proposed and numerically studied based on the symmetry protection principle of the structure. The leakage of BIC to the far field can be observed in the spectrum by changing the gap width of SRR to form an observable quasi BIC (QBIC) mode. Moreover, the influence of ohmic loss on the Q of QBIC is systematically studied by applying the Drude model. The proposed BIC and QBIC also have unique responses to the incident angle. The BIC based on SRR metasurface proposed in this study not only provides a new framework with clear mechanism and easy implementation for the development of high-Q terahertz functional devices, but also provides research ideas for subsequent studies on the terahertz BIC metasurface from the aspects of loss and tilted incidence.

The metasurfaces are composed of different superlattices based on classical metallic SRRs. A single unit cell is composed of either 2 or 4 SRRs. For the superlattices with two SRRs in the lattice, two adjacent SRRs with different orientations are arranged vertically [superlattice ① in Fig. 1(b)] or horizontally [superlattice ② in Fig. 1(c)] to form two types of superlattices. For the superlattices composed of four lattices, each SRR orients in a clockwise direction (superlattice ③ in Fig. 4). All metasurfaces have 2-μm-thick high resistivity silicon wafer as substrate. The refractive index of silicon is set as 3.4 and the SRR is set as perfect electric conductor (PEC). The structure is simulated in CST microwave Studio.

First, the BICs in superlattices ①, ②, and ③ are numerically investigated using the eigen-mode solver. Subsequently, the frequency solver is applied to calculate the transmission of the corresponding QBIC metasurfaces by breaking the structural symmetry of the BICs. The field monitor is used to observe the field distribution to clarify the relationship between a BIC and its derivative QBIC. The evolution from BIC to QBIC is effectively presented by changing the gap widths of the SRRs, and the Fano coupling mode is used to calculate the Q of the QBICs. The influence of ohmic loss on the QBICs is investigated by applying the Drude model to the SRRs. Tilted incidence is realized by changing the input and output directions of the ports in the frequency solver, and the unique dependence of the QBICs in superlattices ① and ② is obtained.

Only one BIC exists in superlattices ① and ②. For superlattice ③, which is composed of 4 SRRs, there are two different BICs existing in the metasurface. QBICs with Fano line shape appear in the transmission spectra when the symmetry of the superlattices is broken. The Q of QBIC exhibits an inverse quadratic correlation with the asymmetric parameter. The residual ohmic loss in the SRRs deteriorates the Q of the QBICs, in which the Q of the metasurface calculated using the Drude model drops to half compared to the result with PEC. Regarding the incidence dependence, a tilted incidence with transverse electric (TE) polarization induces a leakage of the BICs in superlattices ① and ②, in which the linewidth of the derivative QBICs is proportional to the oblique angle. However, the tilted incidence with transverse magnetic (TM) polarization will not perturb the BICs in the superlattices.

In this study, we construct symmetry-protected BICs in three superlattices based on SRRs. Subsequently, the bound states at Γ point in these superlattices are investigated via numerical simulation. When the structural symmetry is broken, BICs are converted to the corresponding QBICs, and the Q of the QBICs decreases with the increase in structural asymmetry. The Q of the QBIC is also strongly correlated to the ohmic loss in the SRRs, which was generally neglected in previous studies related to terahertz metasurfaces developed by SRRs. In addition, the superlattices ① and ② have a certain pitch angle dependence. Oblique incidence of TE polarization with an electric vector parallel to the gap can lead to the leakage of BIC. The Q of the formed QBIC decreases with the increase in incident angle, while the TM wave does not have a similar effect. The metasurface designed in this study has a clear mechanism and is conveniently fabricated, which provides a novel direction for the design of high-Q terahertz devices.