Bound states in the continuum (BICs) enable unique features in tailoring light-matter interaction on nanoscale. These radiationless localized states drive theoretically infinite quality factors and lifetimes for modern nanophotonics, making room for a variety of emerging applications. Here we use the peculiar properties possessed by the so-called $\mathcal{PT}$-symmetric optical structures to propose the novel mechanism for the quasi-BIC manifestation governed by the $\mathcal{PT}$-symmetry breaking. In particular, we study regularities of the spontaneous $\mathcal{PT}$-symmetry breaking in trilayer structures with the outer loss and gain layers consisting of materials with permittivity close to zero. We reveal singular points on the curves separating $\mathcal{PT}$-symmetric and broken-$\mathcal{PT}$-symmetry states in the parametric space of the light frequency and the angle of incidence. These singularities remarkably coincide with the BIC positions at the frequency of volume plasmon excitation, where the dielectric permittivity vanishes. The loss and gain value acts as an asymmetry parameter that disturbs conditions of the ideal BIC inducing the quasi-BIC. Fascinating properties of these quasi-BICs having ultrahigh quality factors and almost perfect transmission can be utilized in sensing, nonlinear optics, and other applications.
PT-symmetry breaking with divergent potentials: lattice and continuum cases
研究了在连续极限下，长程、非厄米、$\mathcal{PT}$对称势保持有限或发散时，格点模型中的宇称和时间反演（$\mathcal{PT}$）对称性破缺.通过对开放有限格点的脆弱$\mathcal{PT}$阈值的标度分析，我们证明了连续损失-增益势$V_α(x)\propto i |x|^α\mathrm{sign}(x)$对$α>-2$有正的$\mathcal{PT}$ -破缺阈值，对$α\leq -2$有零阈值.当$α<0$局域态具有复杂的（共轭）能量的连续带中出现在较高的损失增益强度。我们研究了耦合波导中$\mathcal{PT}$对称性破缺的特征，发现局域态的出现大大缩短了$\mathcal{PT}$对称性破缺区域的时间尺度.
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。
Robustness of Bound States in the Continuum in Bilayer Structures against Symmetry Breaking
Qingdao Innovation and Development Center of Harbin Engineering University（哈尔滨工程大学青岛创新发展基地）；School of Physics and Engineering, ITMO University（ITMO大学物理与工程学院）；Ioffe Institute（约费研究所）
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）
