Effective parameters of metamaterials: a rigorous homogenization theory via Whitney interpolation
Effective parameters of metamaterials: a rigorous homogenization theory via Whitney interpolation
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DOI：
10.1364/josab.28.000577
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发表时间：
2011-03
影响因子：
1.9
通讯作者：
I. Tsukerman
中科院分区：
文献类型：
--
作者：
I. Tsukerman
发展了一种严格的超材料均匀化理论--精心设计的人造周期结构来控制电磁波的传播。该理论是两个概念的融合：史密斯和彭德里对域平均的物理见解和惠特尼式内插的数学框架。所有粗粒度场都是明确定义的，并且完全满足麦克斯韦方程。具有切向和法向跨边界连续性的场与两种不同的插值法相关联，这揭示了“人造磁性”的物理和数学起源。新方法用几个例子进行了说明，并在后者的适用范围内与已有的结果(如Maxwell-Garnett公式和零胞大小限制)很好地吻合。清楚地确定了近似误差的来源和各自合适的误差指标，以及进一步提高精度的系统路线。建议的方法应适用于超材料和电磁波以外的领域(例如，声学和弹性)。
A rigorous homogenization theory of metamaterials—artificial periodic structures judiciously designed to control the propagation of electromagnetic (EM) waves—is developed. The theory is an amalgamation of two concepts: Smith and Pendry’s physical insight into field averaging and the mathematical framework of Whitney-like interpolation. All coarse-grained fields are unambiguously defined and satisfy Maxwell’s equations exactly. Fields with tangential and normal continuity across boundaries are associated with two different kinds of interpolation, which reveals the physical and mathematical origin of “artificial magnetism.” The new approach is illustrated with several examples and agrees well with the established results (e.g., the Maxwell–Garnett formula and the zero cell-size limit) within the range of applicability of the latter. The sources of approximation error and the respective suitable error indicators are clearly identified, along with systematic routes for improving the accuracy further. The proposed methodology should be applicable in areas beyond metamaterials and EM waves (e.g., in acoustics and elasticity).