In this study, we derived analytical relations for designing a step index optical fiber that operates in the linear mode and remains insensitive to external thermal and electrical fluctuations. These relations are based on the fragments of cloaking theory previously developed for two-dimensional structures using the approaches of transformation optics. We obtained and analyzed the radial dependence of the refractive index in both the cladding and core regions under thermal disturbances. An expression for the nonlinear thermal coefficient of the materials of the both regions was also derived, ensuring opacity to thermal fluctuations for a given fiber geometry. The analytical results were validated using MATLAB simulations. The results show that, in steady-state mode, both thermal and electric fields bypass the fiber smoothly, without disturbing the surrounding medium.

In this work, a novel physical transformation-based approach has been employed to realize the cloak effect. The transformation mapping is derived for the first time by minimizing the energy functional subject to specified geometric constraints on the scatterer's boundaries. This variational problem has been solved using a physics-informed neural network to solve the boundary-value problem for the Laplace equation. Numerical analysis and graphical visualization of the obtained results clearly demonstrate weak scattering and distortion, as well as negligible perturbation to exterior fields. Furthermore, we show that the proposed mapping achieves considerably improved performance compared with conventional transformation-based cloaking methods, which can be used to mask compact radiating devices, particularly patch antennas.

This work explores the connection between neural networks and cloaking systems. Specifically, it focuses on achieving bifunctional cloaking of thermal and electric fields using the wave equation and heat conduction equation. The parameters of neural networks, including the activation function, the bias function, and the weight functions, are incorporated to enhance the design of the bifunctional cloaking mechanism. The primary aim is to address various practical challenges, such as cloaking and shielding, by offering a novel approach to simplify and optimize bifunctional cloaking. A significant advantage of this principle is its ability to elucidate bifunctional cloaking for thermal and electric fields more effectively and efficiently than existing methods. To the best of our knowledge, this is the first approach to comprehensively address these challenges.

We present a theory for determining the linear dimensions of compact rectangular microwave patch antennas on metamaterial substrates with a high real part of the effective relative permittivity. This theory demonstrates that significant miniaturization of the volume profile of such antennas is achievable with enhanced performance using a metamaterial substrate instead of a dielectric substrate. It is assumed that the metamaterial substrate is a host dielectric medium with periodically embedded metallic inclusions. The proposed theory is based on a simple analytical algorithm design to minimize the volume profile of the antenna patch. It establishes a relationship between the effective relative permittivity of the substrate, the resonant frequency, and the substrate thickness. The proposed approach achieves up to 80

This study investigates a bifunctional cloak composed of concentric metamaterials arranged in 4N thin layers, where N denotes the number of periodic layer pairs within the structure. The structure includes an inner circular domain, an outer domain, and alternating sequences of 2N layers between them. We explore two models: one using isotropic materials and another one using anisotropic materials. The anisotropic model demonstrates superior cloaking performance for both electrical and thermal fields. Analytical solutions based on the Effective Medium Theory and boundary-value problems reveal the structure’s response under quasi-static conditions. Numerical simulations using COMSOL validate these findings, highlighting the cloak’s and concentration’s ability to manipulate external thermal and electric fields efficiently.

This study investigates the design of electromagnetic devices, specifically wave rotators and cloaks, utilizing a polar rose-shaped structure. By applying the principles of transformation optics, the constitutive parameters - permittivity and permeability tensors - are analytically derived for transforming virtual space in cylindrical coordinates to physical space in Cartesian coordinates. Both integer and fractional indices of the rose configurations are considered, each yielding distinct electromagnetic properties. The analytical findings are validated and supported by numerical simulations conducted using COMSOL Multiphysics. The results highlight the tunability and adaptability of the proposed structures in controlling electromagnetic wave propagation, exhibiting rotational dynamics, cloaking, and absorption phenomena. Potential applications of these rose-shaped structures are briefly discussed.

In this study, a two-dimensional scattering problem is considered for a TM-polarized harmonic electromagnetic wave incident obliquely from a free space onto a cylinder with a rectangular cross section. An approximate solution to the appropriate boundary-value problem was obtained using the method of fictitious sources. Specifically, a modified version of this method was employed, incorporating the solution of the Laplace equation. The accuracy of the solution was validated by comparing it with results from numerical simulations performed using commercial finite difference software, as well as with the solution obtained from a numerical solver previously developed by the authors of the present study.

An analytical solution is derived for the problem of scattering of a plane E-polarized electromagnetic wave obliquely incident on a metagrating-like structure. The structure consists of a finite array of identical, thin, infinitely long, unloaded metallic cylindrical wires with circular cross-sections, in-plane-periodically arranged on the surface of a dielectric/ferrite layer backed by a conducting half-space. The ferrite layer is magnetized to saturation perpendicular to the direction of wave propagation. The solution is based on J.R. Wait’s earlier work on the problem of scattering of a plane E-polarized wave by a finite thin wire grating placed on a conducting half-space. Using long-wave approximations, expressions for the scattered electric field, total reflection coefficient, and far-field pattern are derived. The analysis of dependence of the reflection coefficient and far-field pattern depend on the angle of incidence and the strength of the DC bias magnetic field is also carried out in the study. It has been shown that a change in the layer magnetization results in a rearrangement of the scattered field pattern. The behavior of this rearrangement has been analyzed and discussed. The analytical results are validated at microwave frequencies through numerical simulations performed using electromagnetic software, confirming the accuracy of the proposed approach.

The principle for designing a two-dimensional concentric semiconductor two-layer structure bifunctionally invisibility in terms of its thermal and electrical properties is proposed in this study. The structure consists of an inner circular isotropic region, a background isotropic one, and two anisotropic concentric circular layers in between. The principle is based on the appropriate effective medium approach created by using the Wiedemann-Franz law and Schulgasser's formula. The proposed principle shows off a perfect cloaking performance for electrical and thermal properties of the structure. The effective response of the structure in the form of electric and thermal fields are calculated analytically using the obtained effective medium approach. To validate the principle and analyze the evolution of the above response of the considered structure, numerical simulations were carried out using COMSOL software.

In this study, a hybrid solution of the problem of scattering of a plane electromagnetic wave oblique incident on a wire metagrating located on infinite dielectric layer backed by a conducting background is obtained. The metagrating is an infinite set of identical thin infinitely long metal cylindrical wires of circular cross section periodically located on the interface between free space and top of the dielectric layer. The solution of the above problem has obtained basing on the approaches proposed by J.R. Wait and D. Hill for structures containing thin wire gratings. Microwave approximations for amplitudes of the scattered electric field component and total reflection coefficient from the surface of the structure under consideration have obtained. The dependence of the magnitude and phase of the reflection coefficient on the angles of incidence have analyzed. The analytical approximations have been verified by numerical simulations using a commercial electromagnetic software at microwave frequencies.

In this study, we theoretically propose cloaking and concentration devices allowing simultaneous control of electric and thermal fields in spherically inhomogeneous layered medium with isotropic and anisotropic layers. The above combination of layers (isotropic and anisotropic ones) is obtained by the transformation coordinate approach applied to a spherically inhomogeneous layered medium which contains isotropic and anisotropic layers. It is shown that in steady-state conditions, both thermal and electric fields can pass smoothly around the targeted area while preventing any disturbance in the surrounding medium. The constitutive parameters of both fields have been determined analytically. In this work, we have combined two different methodologies to achieve cloaking in ideal state and in homogenized structure for cylindrical and spherical cases. Numerical validation of the obtained solutions using COMSOL software is performed in this study.

In this paper, the problem of scattering of a plane harmonic electromagnetic wave on a double wire array is solved accurately. The array consists of two identical infinite wire gratings arranged in a free space. Each of the grids consists of parallel thin, infinitely long metal cylinders of circular cross section. The study considers the case when the electric vector of the incident wave is parallel to the wires. The expression for the total reflection coefficient is obtained in the dipole approximation for the case of s -polarization. Analysis of the spectrum of the total reflection coefficient in the subwavelength part of the microwave frequency range was carried out. The paper proposes a new approach for determining the effective relative permittivity and permeability, as well as the effective refractive index of the grating. The approach does not depend on the number of grating layers and allows to taking into account near-field couplings in homogenizing the grating. This approach also allowed us to describe the behavior of the reflectivity and obtain expressions for the effective parameters of the grating at and near the resonant frequency. The validation of all the approximations obtained in the study was carried out using a finite-difference time-domain electromagnetic simulator.

In this study, a novel integral effective medium approach (IEMA) to obtain the complex effective permittivity and permeability tensors of 3-D metal-dielectric composite is developed. An infinite isotropic homogenous dielectric medium with periodically imbedded spherical inclusions with spherical inhomogeneity is considered here as an artificial dielectric in subwavelength. Within full-scattering theory, it is shown that such composite belongs to a general class of metamaterials with spherical inclusions. The obtained expressions for the elements of the effective tensors are valid in the entire subwavelength range. In order to test the proposed IEMA, the problem for metallic spherical particles coated by a layer of dielectric is solved analytically in greater detail by using the approach proposed earlier by the first author of the study. We were able to show that a metal-dielectric composite/metamaterial with spherical inhomogeneous inclusions can be considered as a quasi-periodic artificial crystal with a tunable band gap in the subwavelength range. In certain sub-ranges in subwavelength, such crystals can exhibit the properties of homogeneous ferrite material.

A long-wave generalization of the effective permittivity and permeability tensors for the Polder-van Santen approximation for a 3-D two-component composite are presented in this study in terms of electric and magnetic polarizabilities. The composite is a cubic array of spherical particles imbedded in homogenous dielectric host medium. A specific representation of the particle polarizabilities allow to take one into account the radiation loss. The case of fully magnetized material of particles is considered in the study. The obtained expressions for the effective electromagnetic response of composite under the consideration have shown to agree well with rigorous but complicate analytical theory obtained earlier for subwavelength ranges.

This paper presents a hybrid technique for obtaining a numerical solution to the problem of scattering of the harmonic electromagnetic waves on a two-dimensional inhomogeneous scatterer. The scatterer is an infinite rectangular magneto-dielectric cylinder with an inhomogeneous cross section. Using the integral equation approach, the boundary conditions of the problem are reformulated in the form of integral equation of Fredholm of the second kind. The appropriate fast numerical algorithm corresponding to the problem is obtained by using the finite difference method. The results of numerical simulations obtained by implementing the proposed algorithm have been compared with the results obtained by using two electromagnetic software based on the different numerical methods. Some physical analysis of the above numerical results has been made in this study with a viewpoint of possible application.

This chapter presents the principle of miniaturization of microwave patch antennas with improved performance. A considerable miniaturization of volume profile of a microwave patch antenna, with improving the power gain and efficiency, and with decreasing the intensity of near field, is possible by using the layered metal-dielectric metamaterial/composite for creating the substrates. It is assumed that the substrates have enhancement in the effective relative permittivity and/or permeability. It has been found that the larger the number of layers, the better the improvement in power gain and efficiency, if the volume profile is kept unchanged. The hybrid algorithm enabling to evaluate the basic relation between the resonant frequency and thickness of metamaterial/composite substrate is obtained in the chapter. The algorithm is created under assumption that maximum miniaturization of the volume profile is achieved for a microwave patch antenna with non-magnetic substrate with the enhancement in effective relative permittivity of substrate. It has also been shown that interchanging a high dielectric substrate with a metamaterial having the same values of effective relative permittivity or permeability enables to create compact multi-band and multi-directional patch antennas.

In this study, a 2-D mathematical model of a high-directive microwave antenna with a miniaturized volume profile is developed analytically. The antenna is a rectangular patch antenna on a metaferrite substrate. The substrate is a parallelepiped-shaped dielectric matrix with periodically embedded thin cylindrical ferromagnetic inclusions of a circular cross section. It is assumed that the inclusions are fully or partially magnetized by an external DC bias magnetic field. It has been shown that the use of such a metamaterial substrate, instead of a dielectric one with the same values of permittivity and permeability, leads to a miniaturization of the volume profile of the antenna and an increase in its efficiency and power gain. The commercial electromagnetic software is used in the study to validate the proposed antenna model.

The rigorous analytical model of broadband effective electromagnetic response of the two-component metaferrite is presented in this study in the range up to THz frequencies. The metaferrite is a square array of ferric or ferromagnetic infinitely long cylinders of circular cross section symmetrically imbedded into homogenous isotropic dielectric host medium. It is assumed that the cylinders are fully or partially magnetized by a dc biasing magnetic field directed along the cylinder axes. Expressions of the complex effective permeability and permittivity tensors are obtained in the study. Expressions of the complex effective relative permeability and permittivity transverse to the direction of magnetization are derived and analyzed as functions of the frequency of incident electromagnetic wave and constitutive parameters of the metaferrite. It is shown that tuning a dc biasing magnetic field enables to effectively change the transmittivity and reflectivity of the metaferrites in the considered frequency range. We were also able to show that a layer of the metaferrite can be used for exciting surface plasmons at GHz frequencies. Finally, we have discussed the principal possibility of usage of the considered metaferrite for fabricating the substrates of miniaturized patch antennas with improved performance. (C) 2021 Elsevier Ltd. All rights reserved.