Lee Dayeong, Park Hyungchul, Yu Sunkyu
Intelligent Wave Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea.
Nanophotonics. 2023 Mar 8;12(13):2593-2601. doi: 10.1515/nanoph-2022-0740. eCollection 2023 Jun.
Selective manipulation of energy levels plays an essential role in realizing multichannel wave devices. One of the representative examples is to utilize the concept of quasi-isospectrality: a family of wave systems with an almost identical spectrum except for a part of energy levels. Most approaches toward quasi-isospectrality have employed analytical methods based on symmetry or tridiagonalization, such as supersymmetry, Householder, or Lanczos transformations. Although such analytical approaches provide deterministic and stable designs based on operator factorizations, the mathematical strictness in the factorizations, at the same time, hinders isospectral engineering in a given multidimension. Here we develop the semi-analytical method for engineering isospectrality in multidimensional photonic systems. The method provides the systematic perturbation for the target energy level shifts by decomposing the allowed form of system changes into the perturbation basis. We demonstrate the isospectrality of lower-, higher-, and random-order states while imposing the designed shifts on the other states. The stability analysis shows that the accuracy of the method is determined by the ranges of isospectral state numbers and perturbation strength. The systematic, free-form, and multidimensional natures of the proposed method show great potential for the platform-transparent design of multichannel devices.
对能级进行选择性操控在实现多通道波器件方面起着至关重要的作用。其中一个具有代表性的例子是利用准等谱性的概念：一族波系统，除了一部分能级外，具有几乎相同的频谱。大多数实现准等谱性的方法都采用了基于对称性或三对角化的解析方法，如超对称性、豪斯霍尔德变换或兰索斯变换。尽管这些解析方法基于算子分解提供了确定性和稳定的设计，但分解中的数学严格性同时也阻碍了在给定多维空间中的等谱工程。在此，我们开发了一种用于多维光子系统中等谱性工程的半解析方法。该方法通过将系统变化的允许形式分解为微扰基，为目标能级移动提供系统微扰。我们在对其他状态施加设计好的移动时，展示了低阶、高阶和随机阶状态的等谱性。稳定性分析表明，该方法的精度由等谱状态数范围和微扰强度决定。所提出方法的系统性、自由形式和多维性质显示出在多通道器件的平台透明设计方面具有巨大潜力。
