Abstract
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.
Highlights
T HE CONCEPT of superdirectivity implies that an arbitrarily sharp radiation beam can be produced by a finite size system
Uzsoky and Solymar [5] introduced the concept of tolerance sensitivity, T, and quality factor, Q, to point out the limitations on superdirectivity, and found a closed-form solution for maximum directivity taking into account T and Q
Equating the real parts of Eqns. (6) and (8) we find the superdirective condition 1 which prescribes at what frequency the dimer can be superdirective: κ = 1 − ν2 2 (SD1 condition)
Summary
T HE CONCEPT of superdirectivity implies that an arbitrarily sharp radiation beam can be produced by a finite size system. We can conclude that in order to achieve the optimum directivity (3D, H-plane and V-plane) the operating frequency has to be tuned to the resonance frequency of the antisymmetric mode for two coupled meta-atoms [37] at which both currents are nearly in anti-phase, just as required for the destructive interference mechanism of superdirectivity. It is an important result that the SD1 condition is the same for all three types of directivity, verifying that by choosing the operating frequency optimising planar directivity we are simultaneously optimising the 3D directivity as well This condition is necessary but not sufficient for realising superdirectivity with a dimer of two coupled meta-atoms. Our findings confirm our conclusions that it would be feasible in a lab environment to resort to a simplified procedure of measuring planar directivities and optimising the setup without the need of capturing the 3D radiation pattern
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