Analytic expressions for the constitutive parameters of magnetoelectric metamaterials
Analytic expressions for the constitutive parameters of magnetoelectric metamaterials
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DOI：
10.1103/physreve.81.036605
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发表时间：
2010-03-01
影响因子：
2.4
通讯作者：
Smith, D. R.
中科院分区：
文献类型：
--
作者：
Smith, D. R.
电磁超材料是人工结构化介质，通常由谐振电磁电路阵列组成，其尺寸和间距远小于自由空间工作波长。超材料的本构参数，这可以得到使用全波模拟结合数值检索算法，表现出文物的超材料细胞相对于波长的有限大小。Liu等[R. Liu，T. J. Cui，D.黄，B。Zhao和D. R. Smith，Phys.Rev.E76，026606（2007）]表明，本构参数的复杂的频率依赖形式可以通过一组相对简单的解析表达式来描述。这些表达式提供了有用的见解，可以作为更智能的插值或优化方案的基础。在这里，我们表明，相同的解析表达式可以得到使用传输矩阵形式主义适用于一个一维的周期性阵列薄，谐振，电介质，或磁性片材。然而，当电响应和磁响应都存在于同一个晶胞中时，转移矩阵形式主义就崩溃了，因为它忽略了晶胞之间的磁电耦合[C. R. Simovski，Metamaterials 1，62（2007）]。我们表明，一种替代的分析方法，基于相同的物理模型，必须适用于这样的结构。此外，除了单元间耦合之外，单元内的电和磁谐振器也可以表现出磁电耦合。对于这样的细胞，我们找到了一个有效的折射率，它显示了显着的特征色散特性，依赖于耦合系数的强度的解析表达式。我们说明推导出的表达式的适用性，通过比较磁电单位电池的全波模拟。我们的结论是，设计的超材料与定制的同时电和磁响应，如负折射率材料，通常会复杂的潜在不必要的磁电耦合。
Electromagnetic metamaterials are artificially structured media typically composed of arrays of resonant electromagnetic circuits, the dimension and spacing of which are considerably smaller than the free-space wavelengths of operation. The constitutive parameters for metamaterials, which can be obtained using full-wave simulations in conjunction with numerical retrieval algorithms, exhibit artifacts related to the finite size of the metamaterial cell relative to the wavelength. Liu et al. [R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, Phys. Rev. E 76, 026606 (2007)] showed that the complicated, frequency-dependent forms of the constitutive parameters can be described by a set of relatively simple analytical expressions. These expressions provide useful insight and can serve as the basis for more intelligent interpolation or optimization schemes. Here, we show that the same analytical expressions can be obtained using a transfer-matrix formalism applied to a one-dimensional periodic array of thin, resonant, dielectric, or magnetic sheets. The transfer-matrix formalism breaks down, however, when both electric and magnetic responses are present in the same unit cell, as it neglects the magnetoelectric coupling between unit cells [C. R. Simovski, Metamaterials 1, 62 (2007)]. We show that an alternative analytical approach based on the same physical model must be applied for such structures. Furthermore, in addition to the intercell coupling, electric and magnetic resonators within a unit cell may also exhibit magnetoelectric coupling. For such cells, we find an analytical expression for the effective index, which displays markedly characteristic dispersion features that depend on the strength of the coupling coefficient. We illustrate the applicability of the derived expressions by comparing to full-wave simulations on magnetoelectric unit cells. We conclude that the design of metamaterials with tailored simultaneous electric and magnetic response-such as negative index materials-will generally be complicated by potentially unwanted magnetoelectric coupling.