Search results

To provide sufficient conditions for existence, uniqueness and finite element approximability of the solution of time‐harmonic electromagnetic boundary value problems involving metamaterials.

The objectives are achieved by analysing the most simple conditions under which radiation, scattering and cavity problems are well posed and can be reliably solved by the finite element method. The above “most simple conditions” refer to the hypotheses allowing the exploitation of the simplest mathematical tools dealing with the well posedness of variationally formulated problems, i.e. Lax‐Milgram and first Strang lemmas.

The results of interest are found to hold true whenever the effective dielectric permittivity is uniformly positive definite on the regions where no losses are modelled in it and, moreover, the effective magnetic permeability is uniformly negative definite on the regions where no losses are modelled in it. The same good features hold true if “positive” is replaced by “negative” and vice versa in the previous sentence.

It is a priori known that more sophisticated mathematical tools, like Fredholm alternative and compactness results, can provide more general results. However this would require a more complicated analysis and could be considered in a future research.

The design of practical devices involving metamaterials requires the use of reliable electromagnetic simulators. The finite element method is shown to be reliable even when metamaterials are involved, provided some simple conditions are satisfied.

For the first time to the best of authors' knowledge a numerical method is shown to be reliable in problems involving metamaterials.

Spurious modes often appear in the computed spectrum when an electromagnetic eigenproblem is solved by the finite element method. Demonstrates that the inclusion condition, often claimed as the theoretical reason for the absence of (non‐zero frequency) spurious modes, is a sufficient but not necessary condition for that. Does this by proving that edge elements, which are spectrally correct, do not satisfy the inclusion condition. As intermediate steps towards this result, proves the equivalence of the inclusion condition to a less cryptic one and gives two more easily‐checked necessary conditions for the latter. Concludes that from this investigation, the inclusion condition seems too strong to be useful as a sufficient condition. Works out the present analysis in the framework of spectral approximation theory for non‐compact operators, which emerges as a basic tool for a deeper understanding of the whole question of spurious modes.

The paper's purpose is to deduce additional information on the accuracy of finite element simulators for electromagnetic problems involving effective models of metamaterials.

The objective is achieved by solving, with a well known commercial simulator, many different configurations of two types of electromagnetic problems: a free‐space scattering by a sphere and a waveguide discontinuity problem. Such problems are known to be able to point out the difficulties of numerical simulators. On the other hand, they are representative of two important classes of problems and can provide indications on what can happen in other cases.

This analysis confirms that the numerical errors can be important just in close proximity of the interface between metamaterials and standard media. Small values of loss tangents can be sufficient to obtain very accurate results. Adaptive mesh generators should not be used in the presence of negligible values of the loss tangents. For more uniform meshes the results are satisfactory, with sufficiently fine meshes. When the magnitude of the real parts of the effective dielectric permittivity of a metamaterial and of the adjacent standard media are significantly different, the accuracy is satisfactory in any case.

The results are obtained by considering problems of two types. There is no guarantee that all the deductions apply to other models.

To design practical devices involving metamaterials reliable electromagnetic simulators are necessary. The reported results seem to indicate that it is possible to adopt some countermeasures against the possible lack of accuracy of finite element simulators in the presence of effective models of metamaterials.

For the first time, to the best of authors' knowledge, an extensive analysis on the accuracy of finite element simulators for critical problems involving metamaterials has been carried out. Some simple suggestions to improve their reliability in these cases are provided.

From a theoretical point of view the question of spurious modes has been regarded as a closed problem. However, in this paper we show that even a precise definition of spurious‐free approximation was lacking. Hence, a sound definition of spurious‐free finite element method is given and a set of necessary and sufficient conditions ensuring that a finite element method is spurious‐free in the defined sense is stated. A critical comparison between the proposed theory and the currently accepted one is then carried out and existing counterexamples to the latter are pointed out. Comparison with an older theory leads to another set of necessary and sufficient conditions providing a better grasp of the key feature a finite element space must have to rule out spurious modes. The impact of the proposed theory is stressed, showing that Nedelec's tetrahedral edge elements of all orders provide spurious‐free approximations in all conditions of practical interest. Finally, it is shown, for the first time to the best of authors’ knowledge, that also many high‐order edge elements, recently proposed in the engineering literature for the analysis of electromagnetic problems, provide the same kind of reliable approximation.

Metamaterials have been utilised in several exciting configurations such as tuneable reflectors, reconfigurable absorbers, and programmable modulators, triggering intense research efforts. Among them, the ability to steer the radiation pattern of a single antenna component by employing a metamaterial-based superstrate is considered crucial for the development of advanced beam forming applications. The purpose of this paper is to introduce an adjustable omega-inspired metamaterial module to facilitate the design of beam steering implementations, involving beam forming capabilities, as well.

A variable capacitive diode is properly positioned at the novel omega element, hence advancing the controllability of its electromagnetic performance and circumventing the requirement of extra bias networks. When an array of these particles is placed in front of an antenna, several negative refractive index profiles can be realised, allowing the manipulation of the beam direction. Furthermore, a pyramidal horn antenna, loaded with this complex medium superstrate, is thoroughly investigated in terms of programmable beam steering and beam forming attributes. Several numerical data derived via the finite element method unveil the merits of the featured configuration.

The proposed structure allows programmability of the electromagnetic behaviour, but also circumvents the necessity of complicated bias networks, while minimising interference. The numerical assessment of a standard gain pyramidal horn antenna, associated to the featured metamaterial superstrate, sufficiently proves the controllable beam steering and beam forming attributes. Several parametric studies clarify the principal characteristics of the proposed setup, facilitating the design of high-end systems.

Development of tuneable metamaterial, which utilises variable capacitive diodes to enable controllability. Incorporation of reconfigurable metamaterials into antenna technology. Design of a pyramidal horn antenna, loaded with a complex medium superstrate exhibiting programmable beam steering and beam forming attributes. The proposed device circumvents the necessity of complicated bias networks, while minimising interference.

Wireless power transfer (WPT) is deemed as an emerging technology with exciting applications, like wireless charging devices, and electric vehicles, whereas metamaterials exhibit exceptional properties. For every WPT system that occupies coupled magnetic resonances, it is also mandatory to involve resonators. The purpose of this paper is to introduce a new interdigitated split-ring resonator (I-SRR) as the basic part of a WPT system, pursuing advanced levels of efficiency.

A novel WPT system, which exploits I-SRRs as its elementary blocks, is comprehensively examined. The analysis investigates the distance between the modules, the distance between transmitting and receiving components as well as the geometrical features of the structure. Several numerical data derived via the finite element method unveil the merits of the featured configuration.

The proposed arrangement reveals a noteworthy enhancement of the power delivered to the load and a promising tuning of the operational frequency via the interdigitated topology. Several parametric studies clarify the principal characteristics of the proposed setup, facilitating the design of high-end systems. In particular, the distance between the resonators and the port loops affect the matching of the input and output ports, allowing optimisation of power efficiency, while the length of the I-SRR gap can determine the operational frequency.

Development of a WPT system, which utilises I-SRRs as its key elements. Incorporation of metamaterials into WPT technology. Efficiency enhancement of WPT systems and alternative design via geometrical modifications. The necessity of lumped elements to implement the WPT resonators is eliminated by utilising split-ring resonators components, enabling compactness in several implementations.