A high–order spectral algorithm for the numerical simulation of layered media with uniaxial hyperbolic materials
A high–order spectral algorithm for the numerical simulation of layered media with uniaxial hyperbolic materials
复制标题
用于单轴双曲材料层状介质数值模拟的高阶谱算法
DOI：
10.1016/j.jcp.2022.110961
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发表时间：
2022
影响因子：
4.1
通讯作者：
Nicholls, David P.
中科院分区：
文献类型：
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作者：
Nicholls, David P.
电磁超材料是由尺寸远小于照明辐射波长的部件组装而成的人工介质。已经证明，这些介质可以具有超出传统材料的特性，在许多科学和工程领域具有重要应用。在这些材料的集合中，目前获得了极大的关注，是双曲超材料。这些是高度各向异性的结构，由于相对介电常数或磁导率张量的一个主分量具有与其他两个相反的符号，因此具有双曲色散关系。对于这样的材料，所有尺度的散射波信息都被传输到很远的地方，这意味着许多重要的应用，其中最直接的是成像低于衍射极限的物体（超透镜）。很明显，对这些迷人的材料具有数值模拟能力是当前的一大兴趣。由于双曲线响应是相当强的，其性质是非常敏感的，这些配置的数值模拟应该是强大的和高精度的。出于这个原因，我们专注于高阶谱算法，有效地产生高保真度的解决方案。更具体地说，我们描述了一个高阶扰动的表面的方法，它享有大大减少操作计数和节省内存的界面方法，同时避免了复杂性和不确定的线性系统所面临的积分方程算法。我们给出了充分的讨论，我们的配方在阻抗阻抗算子（这避免了其他配方的虚假奇异性）和实施细节，随后出现在工程文献中的结果的数值验证和模拟。
Electromagnetic metamaterials are artificial media assembled from components which have dimensions much smaller than the wavelength of the illuminating radiation. It has been demonstrated that these media can have properties beyond those found in conventional materials with important applications to many areas of science and engineering. Among the collection of such materials currently garnering significant attention are the Hyperbolic Metamaterials. These are highly anisotropic structures which have a hyperbolic dispersion relation due to the fact that one principal component of the relative permittivity or permeability tensor has the opposite sign of the other two. For such materials scattered wave information at all scales is transmitted far away which suggests a number of important applications, the most immediate of which is imaging objects below the diffraction limit (superlensing). Clearly it is of great current interest to have numerical simulation capabilities for these fascinating materials. As the hyperbolic response is quite strong and its nature is very sensitive, numerical simulations of these configurations should be robust and highly accurate. For this reason we focus on High–Order Spectral algorithms which efficiently produce high fidelity solutions. More specifically, we describe a High–Order Perturbation of Surfaces approach which enjoys the greatly reduced operation counts and memory savings of interfacial methods while avoiding the complexities and indefinite linear systems faced by Integral Equation algorithms. We give a full discussion of our formulation in terms of Impedance–Impedance Operators (which avoids spurious singularities of other formulations) and implementation details, followed by numerical validation and simulation of results which appear in the engineering literature.