Comparison of integral equations for the Maxwell transmission problem with general permittivities

Improving accuracy of the numerical solution of Maxwell's equations by processing edge singularities of the electromagnetic field

In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior of the electromagnetic field near the geometric edges of wedge-shaped structures. Several algorithms for incorporating treatment of singularities into methods for solving Maxwell's equations in two-dimensional structures by the examples of the analytical modal method and the spectral element method are discussed. In test calculations, for which we use diffraction gratings, the si…

将Maxwell方程的传输问题嵌入椭圆理论

Embedding transmission problems for Maxwell's equations into elliptic theory

将时谐Maxwell方程的边界值问题嵌入椭圆理论，通过引入两个新标量函数和额外边界条件使问题变为椭圆型，建立Maxwell问题与椭圆边界值问题的一一对应关系。

Dirac integral equations for dielectric and plasmonic scattering

A new integral equation formulation is presented for the Maxwell transmission problem in Lipschitz domains. It builds on the Cauchy integral for the Dirac equation, is free from false eigenwavenumbers for a wider range of permittivities than other known formulations, can be used for magnetic materials, is applicable in both two and three dimensions, and does not suffer from any low-frequency breakdown. Numerical results for the two-dimensional version of the formulation, including examples featuring surface plasmon waves, demonstrate competitiveness relative to state-of-the-art integral formul…

使用基于 Chebyshev 的 Nyström 边界积分方程方法的 H-Matrix 加速 Maxwell 方程直接矩阵求解器

H-Matrix Accelerated Direct Matrix Solver for Maxwell's Equations using the Chebyshev-based Nyström Boundary Integral Equation Method

本文提出一种基于 Chebyshev 边界积分方程（CBIE）的 H-Matrix 加速直接矩阵求解器，通过全局变量替换处理奇异性，并利用 H-Matrix 框架解决电大尺寸散射问题中矩阵填充与分解耗时的挑战，有效求解病态矩阵方程。

纳米结构材料中电磁俘获模在超常透射中的作用

The role of electromagnetic trapped modes in extraordinary transmission in nanostructured materials

我们断言，纳米结构材料中的异常光透射（反射）的物理基础可以从基于量子力学中发展的正式散射理论的相当普遍的原理来理解。无源（色散和吸收）线性介质中的麦克斯韦方程组被写成薛定谔方程的形式，其中应用了量子力学共振散射理论（李普曼-施温格形式）。它表明，长寿命的准稳态本征态的有效哈密顿麦克斯韦理论的存在自然解释了在各种纳米结构材料中观察到的非凡的传输特性。这样的状态对应于被捕获在散射结构中的准稳态电磁模式。我们的一般方法也说明了一个例子的TE-偏振光通过金属介质光栅结构的零级传输。这里，依赖于时间的麦克斯韦方程组的直接网格解证明了共振（或捕获模式）对于非常光传输的重要性。

An extended charge-current formulation of the electromagnetic transmission problem

A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all combinations of wavenumbers in the closed upper half-plane for which Maxwell's equations have a unique solution. This includes the challenging combination of a real positive wavenumber in the outer region and an imaginary wavenumber inside the object. The formulation, or variants thereof, is particularly suitable for numerical field evaluations as confirmed by ex…