The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China.
Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea.
Phys Rev Lett. 2018 Dec 28;121(26):263902. doi: 10.1103/PhysRevLett.121.263902.
Flatband systems typically host "compact localized states" (CLS) due to destructive interference and macroscopic degeneracy of Bloch wave functions associated with a dispersionless energy band. Using a photonic Lieb lattice (LL), such conventional localized flatband states are found to be inherently incomplete, with the missing modes manifested as extended line states that form noncontractible loops winding around the entire lattice. Experimentally, we develop a continuous-wave laser writing technique to establish a finite-sized photonic LL with specially tailored boundaries and, thereby, directly observe the unusually extended flatband line states. Such unconventional line states cannot be expressed as a linear combination of the previously observed boundary-independent bulk CLS but rather arise from the nontrivial real-space topology. The robustness of the line states to imperfect excitation conditions is discussed, and their potential applications are illustrated.
平面带系统通常由于与无弥散能带相关的布洛赫波函数的相消干涉和宏观简并而承载“紧凑局域态”（CLS）。使用光子李代数（LL），发现这种传统的局域平面带态本质上是不完整的，缺失的模式表现为扩展的线态，这些线态形成不可约的环绕整个晶格的环。在实验中，我们开发了一种连续波激光写入技术来建立具有特殊边界的有限尺寸光子 LL，并直接观察到异常扩展的平面带线态。这种非常规的线态不能表示为以前观察到的与边界无关的体 CLS 的线性组合，而是源于非平凡的实空间拓扑。讨论了线态对不完美激发条件的鲁棒性，并说明了它们的潜在应用。
