论文标题
耦合Helmholtz方程建模梯度索引石墨烯波导的非线性特征值问题
Nonlinear eigenvalue problems for coupled Helmholtz equations modeling gradient-index graphene waveguides
论文作者
论文摘要
我们讨论在涉及原子较厚的2D材料的光学波动问题的背景下引起的四分之一特征值问题。我们认为的波导构型由配备有传导内部接口的梯度指数（空间依赖）（空间依赖）。这导致了与混合横向电气和横向磁模式以及强耦合的电场和磁场的四分之一特征值问题。我们得出了四分之一特征值问题的薄弱公式，并基于五倍化方法引入数值求解器，其中四分之一特征值问题被转换为频谱等效的伴随问题。我们针对原型几何形状的分析解决方案验证了数值框架。作为一个实际的例子，我们证明了如何获得具有内部导电接口的梯度指数宿主材料的家族，如何获得改进的质量因子（由真实和计算特征值的比率定义）。我们概述了这结果如何为解决相关形状优化问题奠定基础。
We discuss a quartic eigenvalue problem arising in the context of an optical waveguiding problem involving atomically thick 2D materials. The waveguide configuration we consider consists of a gradient-index (spatially dependent) dielectric equipped with conducting interior interfaces. This leads to a quartic eigenvalue problem with mixed transverse electric and transverse magnetic modes, and strongly coupled electric and magnetic fields. We derive a weak formulation of the quartic eigenvalue problem and introduce a numerical solver based on a quadratification approach in which the quartic eigenvalue problem is transformed to a spectrally equivalent companion problem. We verify our numerical framework against analytical solutions for prototypical geometries. As a practical example, we demonstrate how an improved quality factor (defined by the ratio of the real and the imaginary part of the computed eigenvalues) can be obtained for a family of gradient-index host materials with internal conducting interfaces. We outline how this result lays the groundwork for solving related shape optimization problems.
