Transition Function for Closed-Form Representation of Metasurface Reactance
Transition Function for Closed-Form Representation of Metasurface Reactance
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DOI：
10.1109/tap.2015.2500264
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发表时间：
2016
影响因子：
5.7
通讯作者：
M. Mencagli;E. Martini;S. Maci
中科院分区：
文献类型：
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作者：
M. Mencagli;E. Martini;S. Maci
超表面是用于操纵平面波和表面波（SW）传播的薄超材料。它们可以通过均匀边界条件来表征，在没有损耗的情况下，可以通过等效电抗来表示。在本文中，我们介绍了各向同性频率相关电抗的一般表示，该表示沿着相关 TM SW 的色散曲线有效。该表示是根据对三次代数方程的卡尔达诺公式进行操作而得出的转换函数来编写的。在色散曲线的很大一部分中，该过渡函数仅取决于一个参数，即等效准静态电容。接近 Floquet-Bloch 区域，其中许多高阶 Floquet 模式被激发，应从全波数据中提取两个附加参数，以完成电抗的过渡表示，直到布里渊区域的上边界。当传播方向沿晶胞单元的对称轴时，最终公式对于一般各向同性电抗和各向异性电抗有效。
Metasurfaces are thin metamaterials used for manipulating propagation of plane waves and surface-waves (SWs). They can be characterized by homogenized-boundary conditions, which, in absence of losses, can be represented through an equivalent reactance. In this paper, we introduce a general representation of isotropic frequency-dependent reactance which is valid along the dispersion curve of the relevant TM SW. This representation is written in terms of a transition function derived from a manipulation of the Cardano's formula for third-degree algebraic equations. Throughout a large portion of the dispersion curve, this transition function depends on one parameter only, which is an equivalent quasi-static capacitance. Approaching the Floquet-Bloch region, where many higher order Floquet modes are excited, two additional parameters should be extracted from the full-wave data to complete the transitional representation of the reactance until the upper boundary of the Brillouin region. The final formula is valid for a generic isotropic reactance and for an anisotropic reactance when the direction of propagation is along a symmetry axis of the unit cell element.