We propose a simple and rapid way of optimising directivity in metamaterial-inspired endfire antenna arrays with strong inter-element coupling. We introduce, in addition to the traditional 3D directivity, also its planar equivalents defined as the ratio of the power density in the desired endfire direction to the average power density calculated either in the horizontal (azimuthal) or vertical (elevation) plane. Using dimers of magnetically coupled split-ring resonators with only one element driven by an external source, we derive conditions that must be satisfied in order to realise superdirective current distributions. The superdirective conditions link the quality factor of the resonators and their coupling constant to the array size and the operating frequency. We demonstrate that a rapid measurement in the azimuthal plane can be used as a reliable indicator for whether the superdirective conditions for the 3D directivity are satisfied. Analytical calculations are verified by CST simulations in the MHz frequency range for meta-atoms of circular and square shape. Our method can be extended to arrays comprising larger number of meta-atoms of various shape and would enable rapid prototyping of 3D-printed meta-atoms with desired radiation properties.

中文翻译：

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一种通过平面方向性评估优化耦合元原子超方向性的方法


我们提出了一种简单快速的方法来优化具有强元件间耦合的超材料端射天线阵列的方向性。除了传统的 3D 方向性之外，我们还介绍了其平面当量，定义为所需端射方向上的功率密度与水平（方位角）或垂直（仰角）平面中计算的平均功率密度之比。使用仅由外部源驱动的一个元件的磁耦合开环谐振器的二聚体，我们得出了实现超方向电流分布必须满足的条件。超方向条件将谐振器的品质因数及其耦合常数与阵列尺寸和工作频率联系起来。我们证明，方位角平面中的快速测量可以用作是否满足 3D 方向性的超方向条件的可靠指标。对于圆形和方形元原子，分析计算通过 MHz 频率范围内的 CST 模拟进行了验证。我们的方法可以扩展到包含大量不同形状的元原子的阵列，并且能够快速制作具有所需辐射特性的 3D 打印元原子原型。