Understanding how bound states in the continuum (BICs) emerge in periodic metasurfaces is essential for the controlled design of high-Q resonances and their systematic manipulation. Here, we investigate the singular value decomposition (SVD) of the effective transition matrix and the scattering matrix of periodic metasurfaces within a parameter range where the metasurface sustains a BIC. Our analysis yields general and practically applicable conditions on the singular values and singular vectors that enable BIC formation. At the BIC eigenfrequency, the inverse of the largest singular value of both matrices vanishes, and the corresponding left (right) singular vector is orthogonal to outgoing (incoming) plane waves that propagate in the directions of open diffraction orders. Our SVD-based approach predicts the spectral position of the BIC and provides detailed information about its properties, including the expansion coefficients in the multipole and plane-wave bases, as well as its behavior under perturbations that transform the BIC into a quasi-BIC. The approach is numerically validated by considering both symmetry-protected and accidental BICs in arrays of scatterers supporting electromagnetic or acoustic multipole resonances. The presented SVD framework offers a broadly applicable foundation for engineering BICs and quasi-BICs in complex metasurfaces, potentially enabling new routes for wave-based devices with tailored radiative properties.
Introducing a Symmetry-Breaking Coupler into a Dielectric Metasurface Enables Robust High-Q Quasibound States in the Continuum and Efficient Nonlinear Frequency Conversion
介电超颖表面支持准束缚态的连续（准BIC）表现出非常高的品质因数共振和电场限制。然而，访问准BIC制度的高Q端通常需要从BIC条件略微扭曲超颖表面设计，将所需的纳米级制造精度推向极限。这项工作介绍了一种新的概念，用于产生高Q准BIC，它强烈放宽了这一要求，通过将一个相对较大的微扰元素接近高对称点的一个未失真的BIC元表面，作为耦合器的辐射连续。我们通过在椭圆形圆盘超颖表面单元格中由300 nm间隙分离的两个反射对称点之间添加直径为$\sim$ 100 nm的圆柱体来验证这种方法，使用磷化镓作为电介质。我们发现，高Q共振出现时，圆柱形耦合器被放置在任何位置之间的对称点。我们进一步探讨这种超颖表面的二次谐波产生能力在光学范围内。将耦合器从BIC条件下位移全直径，产生破纪录的归一化转换效率>10 $^{2}$ W $^{-1}$。在BIC元表面中的多个高对称点之间包围破坏性元素的策略可以应用于在许多几何设计中构造鲁棒的高Q准BIC。
Sensitive biodetection in flow using metasurface hosting quasi-bound state in the continuum resonances
Griffith University（格里菲斯大学）；Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学）；Fraunhofer Institute for Applied Optics and Precision Engineering（弗劳恩霍夫应用光学和精密工程研究所）
Continuous wave second harmonic generation enabled by quasi-bound-states in the continuum on gallium phosphide metasurfaces
共振超颖表面是一个有吸引力的平台，用于增强非线性光学过程，如二次谐波产生（SHG），因为它们可以产生非常大的局部电磁场，同时放松相位匹配的要求。在这里，我们通过演示可见范围的连续波（CW）SHG，使该平台更接近实际应用。我们这样做是通过结合有吸引力的材料特性的磷化镓工程，高品质因数的光子模式，使在连续的束缚态。对于最佳情况，当泵浦波长为1200 nm，连续光强为1 kW/cm $^2$时，系统的效率约为5e-5% W $^{-1}$.此外，我们测量的外部效率高达0.1% W $^{-1}$与泵的强度只有10 MW/cm $^2$的脉冲照射。该效率高于先前报道的电介质超颖表面的值，但在这里实现的泵浦强度低两个数量级。
Chiral lasing via broken parity-time symmetry in bound-state-in-the-continuum metasurfaces
ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), Department of Electronic Materials Engineering, Research School of Physics, Australian National University（澳大利亚国立大学变革性超光学系统卓越中心）
Robust enhancement of high-harmonic generation from all-dielectric metasurfaces enabled by polarization-insensitive bound states in the continuum
新兴的全电介质平台表现出高质量（$Q$）共振，其由驱动高效非线性光学过程的连续体（BIC）中的束缚态物理所支配。在这里，我们展示了强大的增强三次谐波（THG）和五次谐波产生（FHG）从由四个硅纳米盘组成的全介电超颖表面。通过对称性破缺，真正的BIC转变为具有紧密场约束的高$Q$准BIC共振，以使用1 GW/cm $^{2}$的中等泵浦强度来实现$3.9\times10^{-4}$ W $^{-2}$的创纪录的高THG效率和$4.8\times10^{-10}$ W $^{-4}$的FHG效率。此外，准BIC和共振增强谐波表现出偏振不敏感的特性，由于特殊的$C_{4}$排列的元原子。我们的研究结果为智能设计高效、鲁棒的非线性纳米光子器件提供了思路。
Substrate-engineered tunable bound states in the continuum and directional radiation in dielectric metasurfaces
Neijiang Normal University（内江师范学院）；Neijiang Optoelectronic Devices Engineering Research Center（内江光电器件工程研究中心）；Shenzhen University（深圳大学）；Great Bay University（大湾区大学）；Chongqing University（重庆大学）
Electro-optically tunable second-harmonic generation in lithium niobate metasurfaces boosted by Brillouin zone folding induced bound states in the continuum
Polarization-controlled dynamically switchable high-harmonic generation from all-dielectric metasurfaces governed by dual bound states in the continuum
Enhanced third-harmonic generation and degenerate four-wave mixing in an all-dielectric metasurfaces via Brillouin zone folding-induced bound states in the continuum
Rewritable Chirality of Metasurfaces with Permittivity-Asymmetric Flatband Quasi-Bound States in the Continuum
Hamburg University of Technology（汉堡工业大学）；Ludwig- Maximilians-Universität München（慕尼黑大学）；Universidade Federal de Pernambuco（伯南布哥联邦大学）；National University of Science and Technology ‘MISIS’（国立科技大学 MISIS）；National Research Nuclear University ‘MEPhI’ (Moscow Engineering Physics Institute)（国立核研究大学 MEPhI（莫斯科工程物理学院））
Strong Mode Coupling via Quasi-Bound States in the Continuum in Bianisotropic Metasurfaces
Nanophotonics Technology Center, Universitat Politècnica de València（纳米光子技术中心，瓦伦西亚理工大学）；Department of Electronics and Nanoengineering, Aalto University（电子与纳米工程系，阿尔托大学）
Fano resonances induced by symmetry protected bound states in the continuum in dielectric metasurfaces: line-shape prediction by machine learning method
