Metamaterials from the Greek word "meta-", μετά- meaning to go beyond, are smart materials engineered to have properties that have not yet been found in nature. They are made from assemblies of multiple elements fashioned from composite materials such as metals or plastics. The materials are usually arranged in repeating patterns, at scales that are smaller than the wavelengths of the phenomena they influence. Metamaterials derive their properties not from the properties of the base materials, but from their newly designed structures. Their precise shape, geometry, size, orientation and arrangement gives them their smart properties capable to manipulate electromagnetic waves: by blocking, absorbing, enhancing, bending waves, to achieve benefits that go beyond what is possible with conventional materials. They are in essence the materials of the future.
Reflection and Refraction of Magneto-Inductive Waves
Richard Syms, Laszlo Solymar, Ekaterina Shamonina (Osnabrück University)
We have extended previous studies of magnetoinductive waves in homogeneous media based on resonant elements consisting of capacitively loaded metallic loops to the case when a wave is incident from one medium upon another one. The relationship between the input and output angles and the reflection and transmission coefficients have been determined with the aid of the dispersion equation for different scenarios. An expression has been obtained for the power density vector, and it has been shown that its component perpendicular to the boundary is conserved across the boundary. Using different configurations of the elements both positive and negative refraction may occur.
|Boundary between two different MI wave media|
|Matching of wave vectors across the boundary leading to negative refraction|
Magneto-Inductive Waveguide Devices
Richard Syms, Laszlo Solymar, Ekaterina Shamonina (Osnabrück University)
We have considered evices formed from magneto-inductive waveguides based on coupled loop resonators using simple analytic theory, initially assuming lossless propagation and nearest-neighbour coupling. Two-port devices considered include mirrors, Fabry-Perot resonators, Bragg gratings and tapers, while more general N-port devices include power splitters and directional couplers. Conditions for multiple-beam resonance and Bragg reflection in two-port devices have been identified, and it has been shown that quasi-optical filters may be constructed by simple layout variations. Conditions for low reflection have been identified in splitters, and it is shown that matched three-port splitters with arbitrary power division ratios may be achieved for a particular input port. However, matching is not possible for all ports simultaneously. Directional couplers have been shown to operate well only at mid-band and with weak coupling. The effect of loss has been examined and it is shown that idealised performance is obtained using resonators with high Q-factors.
Magneto-Inductive Waveguides with Next Nearest Neighbour Coupling
We have examined the properties of periodic chains of magnetically coupled L-C resonators supporting magneto-inductive (MI) waves in the case when non-nearest neighbour interactions are significant. The variation of the coupling coefficient with separation has been measured using resonant elements based on printed circuit board inductors and surface mount capacitors, and used to predict the S-parameters and dispersion characteristics of magnetoinductive waveguides. Good agreement with experimental measurements is obtained when higher order interactions are included. The significance of non-nearest neighbour interactions in more general MI wave devices has then been highlighted in an example problem involving reflection from a waveguide discontinuity, and the influence of higher order evanescent waves is discussed.
|MI waveguide with next-nearest neighbour coupling|
|Variation of coupling coefficient with axial separation|
Low-loss Magneto-Inductive Waveguides
We have developed low-loss magneto-inductive (MI) waveguides based on magnetically coupled chains of L-C resonators. The waveguides are constructed using printed circuit board inductors and external capacitors. Methods for increasing the nearest-neighbour coupling and reducing the non-nearest neighbour coupling using double-sided PCBs have been demonstrated. Conditions for low propagation loss have been determined, and a method of approximate matching to 50 Ω transmission lines has been developed. Propagation losses as low as 0.12 dB per element and coupling losses of 0.4 dBhave been achieved, using elements with Q-factors of 110 at ≈150 MHz frequency. Simple recursive Fabry-Perot filters have been demonstrated by inserting reflectors into the waveguide.
|MI waveguide based on PCB elements|
|Transfer characteristic of MI waveguides with different axial spacing.|
Thin-film Magneto-Inductive Cables
Richard Syms, Laszlo Solymar, Ian Young and Timmy Floume
Array of thin-film magneto-inductive cables with different unit cells
Magneto-inductive cables for low (ca 100 MHz) radio frequencies have been demonstrated in thin-film form. 20 cm long resonant elements have been formed using double-sided patterning of copper-clad polyimide, based on single-turn inductors and parallel plate capacitors that use the substrate as an interlayer dielectric. Continuous cables in two-metre lengths have been formed by overlaying elements, in an arrangement that allows a high, positive coupling coefficient ( > 0.6) to be achieved despite the use of a planar geometry. Equivalent circuit parameters have been extracted from experiments on integrated coupling transducers, and propagation characteristics are compared with simple theory. Low propagation loss (4 dB/m at 55 MHz, falling to 2.3 dB/m at 130 MHz) has been demonstrated near the operating frequencies of magnetic resonance imaging, for a potential application as patient-safe cable in internal imaging.
Equivalent circuit, physical arrangement and unit cell of thin-film magneto-inductive cable.
Frequency variation of S-parameters for two-metre lengths of thin-film magneto-inductive cable with different parameters.
Broad-band Coupling Transducers for Magneto-inductive Cable
We have developed a broadband resonant transducer capable of low-loss coupling between magneto-inductive waveguides and a conventional RF system with real impedance. The transducer is an L-C circuit resonating at the resonant frequency of the elements forming the guide. However, the values of the components in the transducer are different, and chosen to obtain two separate nulls in reflection so that low reflection is obtained over a wide spectral range. The transducer can be incorporated into the MI waveguide itself, allowing a connection between a magneto-inductive cable and a conventional system to be made as a simple splice. The design has been confirmed using two metre lengths of low-loss thin-film magneto-inductive cables formed using copper-clad polyimide and operating near 100 MHz frequency.
|Broad-band transducer constructed from half a resonant element in a magneto-inductive cable.|
|Experimental realisation of a broad-band transducer for magneto-inductive cable.|
|Comparison between experimental and theoretical performance of a broad-band transducer. Low reflectivity is obtained over most of the magneto-inductive band.|
Bends in Magneto-inductive Cable
We have investigated the effect of waveguide bending on the propagation of MI waves, and have shown that discontinuities in axis curvature will typically generate reflections.
Changes in the equivalent circuit parameters of two types of MI waveguides (formed from discrete elements and continuous cable, respectively) at abrupt bends have been identified, and simple formulae have been developed for the reflection and transmission coefficients in each case.
We have shown that thin-film MI cable can outperform MI waveguides formed using separate elements, due to the inherent stability of the mutual inductance, and can tolerate extremely tight bends. The theory has been confirmed using experiments carried out using thin-film cable operating at 100 MHz frequency.
Variation of normalised inductance with normalised bend radius for magneto-inductive cable. The self-inductance (and hence also the mutual inductance) is broadly constant until the bends become very tight.
Magneto-inductive cable in a spiral winding around cylindrical formers of radii as small as 5 mm.
Frequency variation of S-parameters in two-metre lengths of straight cable (black line) and spiral-wound cable with 5 mm radius (blue line).
Crosstalk in Magneto-inductive Cable
We have investigated the properties of cable arrays formed from a set of parallel magneto-inductive lines, which might be expected to suffer from crosstalk due to the spread of magnetic fields between adjacent cables. We have calculated the mutual inductance numerically for typical arrangements. We have developed analytic methods for estimating the coupling between elements in neighbouring cables and the frequency dependence of cross-talk. Theoretical confirmation has provided by experimental results for cables operating at ≈ 100 MHz. Strategies for reducing cross-talk using alternative element designs that achieve low mutual inductance by cancellation of induced currents have been explored.
|Broadside-coupled magneto-inductive cables.|
|Experimental arrangement for measurement of crosstalk in magneto-inductive cable.|
|Frequency-variation of cross-coupled power and normalised cross-talk between paired cables|
Magneto-inductive Phase-shifters and Interferometers
We have demonstrated controllable phase shifting of magneto-inductive waves by ferrite loading of magneto-inductive waveguides. Ferrite loading reduces the resonant frequency in isolated resonators and lowers the pass-band in waveguides. We have developed simple theory to estimate the dependence of the phase shift on the perturbed waveguide parameters and wavelength, and confirmed its predictions using experiments carried out using thin film L-C resonators and thin-film magneto-inductive cable operating near 100 MHz frequency. Phase shifts are converted into amplitude changes by interference of magneto-inductive waves in Mach-Zehnder interferometer structures analogous to those used in guided wave optics, using conventional RF components for beam splitting and recombination. We have demonstrated modulation and space switching, and shown that in each case the variation of output power with phase shift follows the conventional sinusoidal characteristic.
|Magneto-inductive Mach-Zehnder interferometer.|
|Frequency variation of transmission with and without ferrite loading on one arm of a magneto-inductive Mach-Zehnder interferometer.|
|Variation of transmission from the two output ports of a Mach-Zehnder interferometer with the number of loaded elements. The full lines show best fits to cosinusoidal variations.|
Noise in Magneto-inductive Arrays
Metamaterials made up of resonant elements containing lossy metallic conductors will invariably give rise to Johnson noise. We have developed a model based on nearest neighbour interaction of magnetically coupled elements, which predicts the propagation of noise waves and the excitation of resonances in regular arrays. We have calculated the power spectral density (PSD) of the noise for rectangular arrays of different dimension, and have shown that the effect of coupling is to alter the PSD, spreading the noise over the whole magneto-inductive bandwidth. The implications for passive and active devices have been examined using the simple model of a lossy one-dimensional interconnect with distributed parametric amplification, and it has been shown that the improvements to the noise factor offered by amplification are limited.
|Magneto-inductive arrays of different dimension, with embedded Johnson noise sources.|
|Frequency variation of normalised power spectral density of noise in 1D arrays with different coupling coefficients between the elements.|
|Magneto-inductive link with embedded noise sources|
|Variation of noise factor F with number of elements N in the line, for noisy magneto-inductive waveguides with different loop resistances.|
Flexible Magnetoinductive Ring MRI Detector
Richard Syms, Timmy Floume, Ian Young, Laszlo Solymar and Marc Rea (St Mary's)
|Principle of flexible octagonal MRI detector|
We have developed a flexible birdcage-type resonant RF detector for magnetic resonance imaging, to allow an improved match to the human head. The circuit consists of a polygonal ring of magnetically coupled L-C resonators, a periodic structure supporting backward magneto-inductive waves. The elements are mechanically linked to allow relative rotation, and the pivot point is optimised to hold the nearest neighbour coupling coefficient invariant to small changes in the angle of an undistorted joint. Simple theory based on a parallel wire approximation to rectangular inductors has been developed to allow the variation of the coupling coefficient with angle and radius to be estimated, and hence determine the location of the pivot. The optimised pivot has been shown to reduce resonance splitting in octagonal rings. The theory has been verified experimentally using printed circuit board elements coupled by flexible hinges, and the invariance of the nearest neighbour coupling coefficient has been confirmed. Octagonal ring resonators have been constructed for operation at 63.8 MHz frequency and the mode spectra of regular and distorted rings have been measured. Imaging properties have been investigated using 1H MRI of simple objects in a1.5 T field.
|1H imaging of a pomelo fruit using the flexible coil at 1.5 T in a GE Signa Excite scanner|
|1H MR images of pomelo fruit with coil octagonal (LH) and distorted (RH)|
Parametrically-Amplified Magneto-Inductive Ring Resonators
Richard Syms, Laszlo Solymar, Ian Young
We have demonstrated parametric amplification of magneto-inductive waves in magnetically coupled chains of non-linear L-C resonators. Analysis has been developed for a three-frequency travelling wave scheme in which the signal, idler and pump all propagate as MI waves. The effect of de-coupling the idlers has been considered and it is shown that this configuration relaxes the standard phase matching condition. Confirmation of the theory has been provided using low-frequency PCB unit cells containing varactors, which are arranged as a 16-element ring. Frequency matching and selective amplification of the primary resonance has been demonstrated. The primary resonance can be excited using the field of a rotating magnetic dipole, and an application in MRI is being considered.
Parametrically amplified MI ring resonator
Transfer characteristics of ring, with and without pumping of the primary resonance
Parametric amplification of magnetic resonance images
Richard Syms, Timmy Floume, Ian Young, Laszlo Solymar
We have investigated parametric amplification as a method for detecting magnetic resonance imaging (MRI) signals. We have converted a three-frequency amplifier circuit into an amplified surface coil for operation at 63.85 MHz, inserting appropriate TX protection to allow 1H MRI at 1.5 T field. Electrical characterization has been carried out, and good agreement obtained with theory. The Q-factor is controllable and the amplifier is frequency-tunable. A linear gain of 100 (corresponding to 40 dB power gain) and a Q-factor of 18,000 have been demonstrated. Imaging of phantoms has been carried out, and frequency-domain filtering of images and controllable shifting of the field of view have been demonstrated.
|Experimental realisation of parametrically amplified detector|
|Frequency variation of amplifier response at different pump powers|
|Phantom images at different pump powers.|