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而又快速的方法，可以在元素间强耦合的超材料启发的端射天线阵列中优化方向性。除了传统的3D方向性之外，我们还介绍了其平面等效项，即定义为所需端火方向上的功率密度与在水平（方位角）或垂直（仰角）平面中计算的平均功率密度之比。使用仅由一个外部电源驱动的一个元件的磁耦合开口环谐振器的二聚体，就可以得出实现超指向电流分布所必须满足的条件。超指令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。我们证明了在方位平面中的快速测量可以用作3D方向性超指令条件是否得到满足的可靠指标。分析计算通过CST模拟在MHz频率范围内验证了圆形和方形的偏原子。我们的方法可以扩展到包含大量具有各种形状的亚原子的阵列，并将能够快速制作具有所需辐射特性的3D打印的亚原子原型。