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Random media uncertainties exhibit a significant impact on the properties of electromagnetic fields that usually deterministic models tend to neglect. As a result, these models fail to quantify the variation in the calculated electromagnetic fields, leading to inaccurate outcomes. This paper aims to introduce an unconditionally stable finite-difference time-domain (FDTD) method for assessing two-dimensional random media uncertainties in one simulation.

The proposed technique is an extension of the stochastic FDTD (S-FDTD) scheme, which approximates the variance of a given field component using the Delta method. Specifically in this paper, the Delta method is applied to the locally one-dimensional (LOD) FDTD scheme (hence named S-LOD-FDTD), to achieve unconditional stability. The validity of this algorithm is tested by solving two-dimensional random media problems and comparing the results with other methods, such as the Monte-Carlo (MC) and the S-FDTD techniques.

This paper provides numerical results that prove the unconditional stability of the S-LOD-FDTD technique. Also, the comparison with the MC and the S-FDTD methods shows that reliable outcomes can be extracted even with larger time steps, thus making this technique more efficient than the other two aforementioned schemes.

The S-LOD-FDTD method requires the proper quantification of various correlation coefficients between the calculated fields and the electrical parameters, to achieve reliable results. This cannot be known beforehand and the only known way to calculate them is to run a fraction of MC simulations.

This paper introduces a new unconditional stable technique for measuring material uncertainties in one realization.

The purpose of this paper is to present a family of robust metasurface-oriented wireless power transfer systems with improved efficiency and size compactness. The effect of geometric and structural features on the overall efficiency and miniaturisation is elaborately studied, while the presence of substrate losses is, also, considered. Moreover, to further enhance the performance, possible means for reducing the operating frequency, without comprising the unit-cell size, are proposed.

The key element of the design technique is the edge-coupled split-ring resonators patterned in various metasurface configurations and optimally placed to increase the total efficiency. To this goal, a rigorous three-dimensional algorithm, launching a new high-order prism macroelement, is developed in this paper for the fast evaluation of the required quantities. The featured scheme can host diverse approximation orders, while it is drastically more economical than existing methods. Hence, the demanding wireless power transfer systems are precisely modelled via reduced degrees of freedom, without the need to conduct large-scale simulations.

Numerical results, compared with measured data from fabricated prototypes, validate the design methodology and prove its competence to provide enhanced metasurface wireless power transfer systems. An assortment of optimized 3 x 3 and 5 x 5 metamaterial setups is investigated, and interesting deductions, regarding the impact of the inter-element gaps, the distance between the transmitting and receiving components and the substrate losses, are derived. Also, the proposed vector macroelement technique overwhelms typical implementations in terms of computational burden, particularly when combined with the relevant commercial software packages.

Systematic design of advanced real-world wireless power transfer structures through optimally selected metasurfaces with fully controllable electromagnetic properties is presented. The analysis is performed by means of a rapid prism macroelement methodology, which leads to very confined meshes, accurate results and significantly reduced overhead. The selected metamaterial resonators are found to be very flexible and reconfigurable, even in the case of large substrate conductivity losses, whereas their contribution to the system’s total efficiency is decisive.

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.

Important statistical variations are likely to appear in the propagation of surface plasmon polariton waves atop the surface of graphene sheets, degrading the expected performance of real-life THz applications. This paper aims to introduce an efficient numerical algorithm that is able to accurately and rapidly predict the influence of material-based uncertainties for diverse graphene configurations.

Initially, the surface conductivity of graphene is described at the far infrared spectrum and the uncertainties of its main parameters, namely, the chemical potential and the relaxation time, on the propagation properties of the surface waves are investigated, unveiling a considerable impact. Furthermore, the demanding two-dimensional material is numerically modeled as a surface boundary through a frequency-dependent finite-difference time-domain scheme, while a robust stochastic realization is accordingly developed.

The mean value and standard deviation of the propagating surface waves are extracted through a single-pass simulation in contrast to the laborious Monte Carlo technique, proving the accomplished high efficiency. Moreover, numerical results, including graphene’s surface current density and electric field distribution, indicate the notable precision, stability and convergence of the new graphene-based stochastic time-domain method in terms of the mean value and the order of magnitude of the standard deviation.

The combined uncertainties of the main parameters in graphene layers are modeled through a high-performance stochastic numerical algorithm, based on the finite-difference time-domain method. The significant accuracy of the numerical results, compared to the cumbersome Monte Carlo analysis, renders the featured technique a flexible computational tool that is able to enhance the design of graphene THz devices due to the uncertainty prediction.

A class of robust and efficient beamforming methods is developed in this paper for the optimised design of realistic microstrip antennas on arbitrarily curved substrates. More specifically, this paper aims to focus on the formulation of an effective and computationally light beamforming algorithm and its implementation on a novel realistic cylindrical-substrate microstrip array antenna with significantly decreased size, wideband operation and enhanced radiation characteristics.

The proposed multi-parametric schemes introduce an efficient null-steering concept, which drastically annihilates the undesired beamformer waveform artefacts, while retaining the real output signal undistorted. In particular, the key objective is the accurate calculation of the appropriate complex feeding weights, required to set nulls along the propagation directions of the unwanted signals and a maximum towards the propagation direction of the desired incoming signal. The featured technique, combined with a modified finite element method, is applied to the design of a new family of cylindrical-substrate microstrip array antennas.

Numerical results, mainly concerning customisable three-dimensional radiation patterns and attributes, certify the merits of the algorithm and its limited system demands. The introduced beamforming algorithms are applied to a variety of different inputs (desired radiation patterns), which indicate that the designed cylindrical-substrate antenna overwhelms existing designs in terms of computational cost for the beamforming algorithm, while retaining acceptable values for radiation characteristics, such as gain, directivity and side-lobe suppression. In this manner, the effectiveness of the prior methodology and the benefits of this newly shaped array antenna are comprehensively revealed and substantiated.

Rigorous beamforming techniques in conjunction with a class of contemporary array antennas are developed for potential use in high-end communication systems, such as 5G configurations. The proposed cylindrical-shaped structures are systematically designed, with an emphasis on space efficiency and wideband radiation effectiveness to offer fully adjustable setups. To this aim, the cylindrical-substrate microstrip antenna, because of its inherent azimuthal symmetry and confined overall dimensions, provides reliable operation and promising performance.

The majority of first-principle, homogenisation techniques makes use of the dipole terms of a small particle radiation, and, consequently, the respective dipole polarisabilities. This paper aims to take the next step and propose a new systematic technique for extracting the quadrupolarisability of planar metamaterial scatterers.

Firstly, it is assumed that the particle, under study, can be modelled as a set of dipole and quadrupole moments, and by utilising the respective polarisabilities, the far-field response of the scatterer is calculated. Then, the far-field scattering field of the particle is constructed in terms of the dipole and quadrupole moments, which, in turn, are expressed as a function of the unknown polarisabilities. Finally, the desired polarisabilities are retrieved by a system of equations, which involves numerically derived electric field values at specific positions around the scatterer.

The quadrupolarisability of planar metamaterial particles is extracted, through an easy to use, yet very accurate and efficient methodology. Moreover, the proposed technique is verified via comprehensive comparisons of consequently computed and simulated total radiated power values, which reveal its advantages and applicability limits. Finally, the total radiation power contribution of each calculated, individual multipole is provided, to further investigate the radiation mechanism of all nano-particles under study.

The initial and most important step of extracting a single quadrupolarisability of a planar realistic nano-particle has been performed, herein, for the first time. The addition of the respective quadrupole in the scattering model, shifts the multipole approximation limit upwards in terms of frequency, and, therefore, nano-particles with quadrupole resonances can, now, be precisely represented via polarisabilities for various metamaterial or metasurface applications.

The computational accuracy and performance of finite-difference time-domain (FDTD) methods are affected by the implementation of approximating derivative formulae in diverse ways. This study aims to focus on FDTD models featuring material dispersion with negligible losses and investigates two specific aspects that, until today, are usually examined in the context of non-dispersive media only. These aspects pertain to certain abnormal characteristics of coarsely resolved electromagnetic waves and the selection of the proper time-step size, in the case of a high-order discretization scheme.

Considering a Lorentz medium with negligible losses, the propagation characteristics of coarsely resolved waves is examined first, by investigating thoroughly the numerical dispersion relation of a typical discretization scheme. The second part of the study is related to the unbalanced space-time errors in FDTD schemes with dissimilar space-time approximation orders. The authors propose a remedy via the suitable choice of the time-step size, based on the single-frequency minimization of an error expression extracted, again, from the scheme’s numerical dispersion formula.

Unlike wave propagation in free space, there exist two parts of the frequency spectrum where waves in a Lorentz medium experience non-physical attenuation and display non-changing propagation constants, due to coarse discretization. The authors also show that an optimum time-step size can be determined, in the case of the (2,4) FDTD scheme, which minimizes the selected error formula at a specific frequency point, promoting more efficient implementations.

Unique characteristics displayed by discretized waves, which have been known for non-dispersive media, are examined and verified for the first time in the case of dispersive materials, thus completing the comprehension of the space-time discretization impact on simulated quantities. In addition, the closed-form formula of the optimum time-step enables the efficient implementation of the (2,4) FDTD method, minimizing the detrimental influence of the low-order temporal integration.

This paper aims to introduce an efficient time-domain formulation of adjustable accuracy for a consistent and trustworthy computation of electromagnetic field characteristics in randomly varying configurations. The developed methodology is carefully certified via comprehensive comparisons with the corresponding outcomes obtained by the Monte Carlo approach.

The presented methodology uses higher-order approximations of Taylor series expansions of stochastic multivariable functions for the rapid estimation of the electromagnetic field component mean value and confidence intervals of their variance. Toward this objective, new time-update equations for the mean value and the variance of the involved electromagnetic field are elaborately derived.

The featured technique presents an efficient alternative to the excessively resource-consuming Monte Carlo finite-difference time-domain (MC–FDTD) implementation, which requires an unduly number of realizations to achieve a satisfying convergence. The higher-order stochastic algorithm retrieves accurately the statistical properties of all electromagnetic field in a single simulation, presenting promising accuracy, stability and convergence.

The adjustable-accuracy higher-order scheme introduces a new framework for the derivation of the stochastic explicit time-update equations and precisely computes the required confidence intervals for the electromagnetic field variance instead of the variance itself, which can be deemed a key advantage over existing schemes. This fully controllable formulation results in significantly more accurate calculations of the electromagnetic field variance, especially for larger fluctuations of the involved electromagnetic media parameters.

The reliable transcranial imaging of brain inner structures for diagnostic purposes is deemed crucial owing to the decisive importance and contribution of the brain in human life. The purpose of this paper is to investigate the potential application of medical ultrasounds to transcranial imaging using advanced techniques, such as the total focussing method.

Initially, the fundamental details of the total focussing method are presented, while the skull properties, such as the increased acoustic velocity and scattering, are thoroughly examined. Although, these skull characteristics constitute the main drawback of typical transcranial ultrasonic propagation algorithms, they are exploited to focus the acoustic waves towards the brain. To this goal, a virtual source is designed, considering the wave refraction, to efficiently correct the reconstructed brain image. Finally, the verification of the novel method is conducted through numerical simulations of various realistic setups.

The theoretically designed virtual source resembles a focussed sensor; therefore, the directivity increment, owing to the propagation through the skull, is confirmed. Moreover, numerical simulations of real-world scenarios indicate that the typical artifacts of the conventional total focussing method are fully overcome because of the increased directivity of the proposed technique, while the reconstructed image is efficiently corrected when the proposed virtual source is used.

A new systematic methodology along with the design of a flexible virtual source is developed in this paper for the reliable and precise transcranial ultrasonic image reconstruction of the brain. Despite the slight degradation owing to the skull scattering, the combined application of the total focussing method and the featured virtual source can successfully detect arbitrary anomalies in the brain that cannot be spotted by conventional techniques.

The extraordinary properties of graphene render it ideal for diverse contemporary and future applications. Aiming at the investigation of certain aspects commonly overlooked in pertinent works, the authors study wave-propagation phenomena supported by graphene layers within a stochastic framework, i.e. when uncertainty in various factors affects the graphene’s surface conductivity. Given that the consideration of an increasing number of graphene sheets may increase the stochastic dimensionality of the corresponding problem, efficient surrogates with reasonable computational cost need to be developed.

The authors exploit the potential of generalized Polynomial Chaos (PC) expansions and develop low-cost surrogates that enable the efficient extraction of the necessary statistical properties displayed by stochastic graphene-related quantities of interest (QoI). A key step is the incorporation of an initial variance estimation, which unveils the significance of each input parameter and facilitates the selection of the most appropriate basis functions, by favoring anisotropic formulae. In addition, the impact of controlling the allowable input interactions in the expansion terms is investigated, aiming at further PC-basis elimination.

The proposed stochastic methodology is assessed via comparisons with reference Monte-Carlo results, and the developed reduced basis models are shown to be sufficiently reliable, being at the same time computationally cheaper than standard PC expansions. In this context, different graphene configurations with varying numbers of random inputs are modeled, and interesting conclusions are drawn regarding their stochastic responses.

The statistical properties of surface-plasmon polaritons and other QoIs are predicted reliably in diverse graphene configurations, when the surface conductivity displays non-trivial uncertainty levels. The suggested PC methodology features simple implementation and low complexity, yet its performance is not compromised, compared to other standard approaches, and it is shown to be capable of delivering valid results.