Superdirectivity from arrays of strongly coupled meta-atoms

This is the final version of the article. Available from AIP Publishing via the DOI in this record.We explore the possibility of achieving superdirectivity in metamaterial-inspired endfire antenna arrays relying on the good services of magnetoinductive waves. These are short-wavelength slow waves propagating by virtue of coupling between resonant meta-atoms. Magnetoinductive waves are capable of providing a rapidly varying current distribution on the scale of the free space wavelength. Using dimers and trimers of magnetically coupled split ring resonators with only one element driven by an external source, we introduce an analytical condition for realising superdirective current distributions. Although those current distributions have been known theoretically for a good 60 years, this is the first time that a recipe is given to realise them in practice. Our key parameters are the size of the array, the resonant frequency and quality factor of the elements, and their coupling constant. We compare our analytical results for coupled magnetic dipoles with numerical results from CST simulations for meta-atoms of various shapes. The calculated bandwidth of 5 MHz for a dimer operating at 150 MHz indicates that, contrary to popular belief, superdirective antennas exist not only in theory but may have practical applications.Financial support by the John Fell Fund (University of Oxford) and by the EPSRC UK (SYMETA, EP/N010493/1) is gratefully acknowledged

Superdirective dimers of coupled self-resonant split ring resonators: Analytical modelling and numerical and experimental validation

Superdirective antennas developed over the last century have received renewed interest in recent years from the development of metamaterials. These arrays of electromagnetic resonators (or meta-atoms) carrying short wavelength electro- and/or magneto-inductive waves support current distributions with very high spatial frequency as required by the classical conditions for superdirectivity. As meta-atoms can have both electric and magnetic dipole characteristics (and hence radiation properties), developing antennas exploiting these distributions can challenge conventional intuitions regarding the optimal configurations required. In this work we are reporting the development of a genuinely superdirective array using split ring resonators (SRRs). We provide a comprehensive analytical model characterizing the radiation from SRR dimers in which excitation of only one split ring leads to superdirective radiation via mutually coupled modes. Our model exploits simple circuit descriptions of coupled resonant circuits, combined with standard radiation formulae for curvilinear current distributions. Using this simple model we are able to map directivity against possible SRR locations and orientations in two dimensions and identify the unique optimal configuration which meets the requirements for superdirective emission. We validate the theoretical findings by comparison to both full wave simulations and experiments showing that our SRR dimer achieves endfire directivity very close to the maximum theoretical value

Superdirective dimers of coupled self-resonant split ring resonators: Analytical modelling and numerical and experimental validation

Superdirective antennas developed over the last century have received renewed interest in recent years from the development of metamaterials. These arrays of electromagnetic resonators (or meta-atoms) carrying short wavelength electro- and/or magneto-inductive waves support current distributions with very high spatial frequency as required by the classical conditions for superdirectivity. As meta-atoms can have both electric and magnetic dipole characteristics (and hence radiation properties), developing antennas exploiting these distributions can challenge conventional intuitions regarding the optimal configurations required. In this work we are reporting the development of a genuinely superdirective array using split ring resonators (SRRs). We provide a comprehensive analytical model characterizing the radiation from SRR dimers in which excitation of only one split ring leads to superdirective radiation via mutually coupled modes. Our model exploits simple circuit descriptions of coupled resonant circuits, combined with standard radiation formulae for curvilinear current distributions. Using this simple model we are able to map directivity against possible SRR locations and orientations in two dimensions and identify the unique optimal configuration which meets the requirements for superdirective emission. We validate the theoretical findings by comparison to both full wave simulations and experiments showing that our SRR dimer achieves endfire directivity very close to the maximum theoretical value

Mapping inter-element coupling in metamaterials: Scaling down to infrared

The coupling between arbitrarily positioned and oriented split ring resonators is investigated up to THz frequencies. Two different analytical approaches are used, one based on circuits and the other on field quantities that includes retardation. These are supplemented by numerical simulations and experiments in the GHz range, and by simulations in the THz range. The field approach makes it possible to determine separately the electric and magnetic coupling coefficients which, depending on orientation, may reinforce or may cancel each other. Maps of coupling are produced for arbitrary orientations of two co-planar split rings resonant at around 2 GHz and then with the geometry scaled down to be resonant at around 100 THz. We prove that the inertia of electrons at high frequencies results in a dramatic change in the maps of coupling, due to reduction of the magnetic contribution. Our approach could facilitate the design of metamaterials in a wide frequency range up to the saturation of the resonant frequency

Switchable unidirectional waves on mono- and diatomic metamaterials.

We demonstrate switchable unidirectional propagation of slow waves of coupling within a metamaterial array of strongly coupled elements. We predict theoretically and verify experimentally that the direction of propagation of magnetoinductive waves for any chosen excitation pattern is dictated by the dispersion relations, with forward and backward waves propagating in opposite directions along a chain of meta-atoms. We further prove that the same fundamental phenomenon of direction selectivity due to the forward/backward wave nature is not limited to magnetoinductive waves: we predict analytically and verify numerically the same selective unidirectional signal propagation occurring in nanostructured metamaterial arrays with purely electric coupling. Generalising our method of unidirectional waveguiding to a diatomic magnetoinductive array featuring both forward-wave and backward-wave dispersion branches, switchable unidirectional signal propagation is achieved with distinct frequency bands with opposite directions of signal propagation. Finally, by expanding our technique of selective unidirectional waveguiding to a 2D metasurface, a selective directional control of waves in two dimensions is demonstrated opening up possibilities for directional wireless signal transfer via magnetoinductive surfaces. The observed phenomenon is analogous to polarisation-controlled near-field interference for unidirectional guiding of surface plasmon-polaritons

Resonant frequencies of a combination of split rings: Experimental, analytical and numerical study

The resonant frequencies of five different ring resonators are measured with the aid of a network analyser within the frequency range of about 1.5 to 2.8 GHz. The resonant frequencies for those configurations are also determined from numerical calculations using the commercially available MICRO-STRIPES package. The experimental and numerical results are shown to be very close to each other. Analytical results from various authors, available for three of the configurations, are also compared with the experimental results; one of them leads to a large discrepancy, but the other analytical approximations are shown to be not too far off. © 2005 Wiley Periodicals, Inc

Dimer and polymer metamaterials with alternating electric and magnetic coupling

Diatomic metamaterials, whose properties can be easily tailored, are studied with the aid of split ring resonator elements. Two different types are shown to exist depending on the coupling within a unit cell being larger or smaller than that between the unit cells. The freedom to adjust the coupling coefficients is used to construct a chain in which coupling alternates between electric and magnetic, between positive and negative. The resulting dispersion characteristics are shown to be radically different from the classical acoustic and optical branches: the upper branch is a forward wave and the lower branch is a backward wave, and even the gap between the two pass bands may disappear yielding infinite phase, finite group-velocity wave. The theory is confirmed both by simulations and experiments. © 2011 American Physical Society

An experimental study of the properties of magnetoinductive waves in the presence of retardation

Magnetoinductive (MI) waves owe their existence to the magnetic coupling between metamaterial elements. First experiments confirming the existence of MI waves were carried out on capacitively loaded loops and Swiss Rolls about three orders of magnitude smaller than the operating wavelengths (5-15 m) so that the radiation effects did not play any significant role. In the present paper MI waves are studied experimentally on various types of split ring resonators of about 1 cm diameter operating in the microwave region between 1 and 2 GHz. Our results prove that retardation has a significant effect upon the propagation of MI waves. © 2005 Elsevier B.V. All rights reserved