AI 中文总结
本文针对具有单一周期方向的二维介质结构，提出连续介质中传播束缚态（BIC）鲁棒性的严格理论，分析可解性、给出摄动级数估计并证明其收敛性。
AI 中文摘要
连续介质中的束缚态（BICs）是频率处于散射态辐射连续介质中的局域本征模，BIC的存在意味着给定入射波下散射问题的唯一性丧失。接近理想BIC的受扰波系统会展现出强共振效应，这对诸多实际应用至关重要。一个基础重要问题是BIC是否鲁棒，即结构微扰时其能否继续存在。早期工作[Yuan和Lu，《光学快报》，第42卷，第4490-4493页，2017年]中，针对一类由二维（2D）亥姆霍兹方程支配、非平凡受对称性保护的BIC，我们揭示了确保鲁棒性的条件，并利用摄动方法在受扰系统中形式构造了该BIC。本文中，我们针对具有单一周期方向的二维介质结构中的BIC鲁棒性提出了严格理论，具体分析了可解性，给出了摄动级数各阶的估计，并证明了该级数的收敛性。
英文摘要
Bound states in the continuum (BICs) are localized eigenmodes with their frequencies in the radiation continuum of scattering states. The existence of a BIC implies the loss of uniqueness for scattering problems with given incident waves. Perturbed wave systems close to the ideal ones with a BIC exhibit strong resonance effects that are essential to numerous practical applications. A question of fundamental importance is whether a BIC is robust, i.e., whether it can continue its existence when the structure is slightly perturbed. In an earlier work [Yuan and Lu, Optics Letters, Vol.~42, pp.~4490-4493, 2017], for a class of BICs governed by the two-dimensional (2D) Helmholtz equation, which are not trivially protected by symmetry, we uncovered the conditions that ensure robustness and formally constructed the BIC in perturbed systems using a perturbation method. In this paper, we present a rigorous theory on the robustness of BICs in 2D dielectric structures with a single periodic direction. Specifically, we analyze the solvability and provide estimates for each order in the perturbation series, and prove the convergence of the series.
Comments24 pages, 1 figure
