Isotropic Dielectrics Research Articles

A Coordinate Transformation-Based Broadband Flat Lens via Microstrip Array

A conventional convex lens is compressed into a flat one based on a so-called discrete coordinate transformation technique. While maintaining a good performance of the original lens, such a transformed flat lens only requires a few blocks of isotropic dielectrics. Physical realization via multiple transmission lines is then demonstrated, and it shows an alternative approach to achieve the desired spatially varying dielectric constant across the lens aperture. The full-wave simulation shows that the proposed microstrip array mimics the original convex lens nicely and can function well over a broad frequency band while possessing the merits of a flat profile and small volume.

Simplified ground plane invisibility cloak by multilayer dielectrics

Most implementations of the ground plane invisibility cloak are based on the isotropic design through the quasi-conformal transformation. However recent theoretical analysis predicts the unavoidable lateral shift of the scattering fields associated with these cloaks making them detectable. In this paper, we propose an alternative method to design the ground plane invisibility clock with electromagnetic beam modulation blocks through simple coordinate transformation discussed in our previous work. The ground plane cloak obtained with the rigorous transformation optics possesses moderate anisotropic distributions of material parameters, but results in no lateral shift of the scattering fields. To realize the design, a possible scheme is suggested by discretizing the ground plane cloak to several homogeneous sub-blocks. These sub-blocks can be realized with multilayer isotropic dielectrics with alignment angles that are determined by the effective medium theory. Thus the non-magnetic ground plane invisibility cloak can be constructed by several multilayered normal dielectrics aligned in different angles. The performance of the proposed cloak and its practical implementation is validated by full-wave electromagnetic simulations with both near field distributions and far field scattering patterns under different EM wave incident angles. The proposed cloak is composed of normal dielectric multilayers, thus can leads to easy experimental demonstration of non-magnetic ground plane cloak in the frequency range from microwave to optical.

Instabilities in multilayered soft dielectrics

Experimental observations clearly show that the performance of dielectric elastomeric-based devices can be considerably improved using composite materials. A critical issue in the development of composite dielectric materials toward applications is the prediction of their failure mechanisms due to the applied electromechanical loads. In this paper we investigate analytically the influence of electromechanical finite deformations on the stability of multilayered soft dielectrics under plane-strain conditions. Four different criteria are considered: (i) loss of positive definiteness of the tangent electroelastic constitutive operator, (ii) existence of diffuse modes of bifurcation ( microscopic modes), (iii) loss of strong ellipticity of the homogenized continuum (localized or macroscopic modes), and (iv) electric breakdown. While the formulation is developed for generic isotropic hyperelastic dielectrics, results are presented for the special class of ideal dielectrics incorporating a neo-Hookean elastic response. The effect of material properties and loading conditions is investigated, providing a detailed picture of the different possible failure modes.

Broadband cloaking and mirages with flying carpets

This paper extends the proposal of Li and Pendry [Phys. Rev. Lett. 101, 203901-4 (2008)] to invisibility carpets for infinite conducting planes and cylinders (or rigid planes and cylinders in the context of acoustic waves propagating in a compressible fluid). Carpets under consideration here do not touch the ground: they levitate in mid-air (or float in mid-water), which leads to approximate cloaking for an object hidden underneath, or touch either sides of a square cylinder on, or over, the ground. The tentlike carpets attached to the sides of a square cylinder illustrate how the notion of a carpet on a wall naturally generalizes to sides of other small compact objects. We then extend the concept of flying carpets to circular cylinders and show that one can hide any type of defects under such circular carpets, and yet they still scatter waves just like a smaller cylinder on its own. Interestingly, all these carpets are described by non-singular parameters. To exemplify this important aspect, we propose a multi-layered carpet consisting of isotropic homogeneous dielectrics rings (or fluids with constant bulk modulus and varying density) which works over a finite range of wavelengths.

Peculiarities of Tamm states formed in degenerate photonic band gaps

The structure of the Tamm state localized at the interface between anisotropic magnetophotonic crystal (anisotropic MPC) and a photonic crystal (PC) made of isotropic dielectrics is studied. It is shown that if the frequency of this state appears within the degenerate band gap then its structure qualitatively differs from the structure of a well-known Tamm state localized at the interface between two one-dimensional PC made of isotropic materials. Since inside the degenerate BG the real part of the Bloch wavenumber differs from the Brillouin value, two Bloch waves with different signs in the real part of the wavenumber and the same sign in the imaginary part have different input impedance values. Moreover, contrary to the case of a PC made of isotropic materials the impedance of each Bloch wave is a tensor. As a consequence to construct a surface state at least three evanescent Bloch waves are required. The conditions that determine the Tamm state frequency also change.

MODAL ANALYSIS OF MULTILAYER CONICAL DIELECTRIC WAVEGUIDES FOR AZIMUTHAL INVARIANT MODES

By using fleld expansion in terms of the Legendre polynomials and Schelkunofi functions, Maxwell's equations in the spherical coordinate system are cast into a matrix form which lends itself to the analysis of a multilayer conical waveguide. The matrix formulation is then used to obtain an eigen-value problem whose eigen-values are the allowable wave-numbers for propagation in the radial direction. To verify the proposed numerical approach, it is used to evaluate the resonance frequency of a partially fllled spherical resonator. The computed resonance frequencies are then compared with those obtained using commercial software based on the flnite- element method. The computation time is enormously reduced using the semi-analytical method of this work. Although results are shown for lossless isotropic dielectrics, the method is also applicable to conical waveguides made of lossy dielectrics even with negative permittivity.

Infrared carpet cloak designed with uniform silicon grating structure

Through a particularly chosen coordinate transformation, we propose an optical carpet cloak that only requires homogeneous anisotropic dielectric material. The proposed cloak could be easily imitated and realized by alternative layers of isotropic dielectrics. To demonstrate the cloaking performance, we have designed a two-dimensional version that a uniform silicon grating structure fabricated on a silicon-on-insulator wafer could work as an infrared carpet cloak. The cloak has been validated through full wave electromagnetic simulations, and the nonresonance feature also enables a broadband cloaking for wavelengths ranging from 1372 to 2000 nm.

Simplified theory of axial propagation through structurally chiral media

Simple design formulae are derived for the co-, contra- and cross-handed reflection and transmission coefficients for light incident axially to a structurally chiral medium surrounded by dissimilar isotropic dielectrics. The results obtained agree well with exact calculations over the full range of achieved experimental parameters of practically manufactured structurally chiral media. The formulae are used to illustrate a number of design strategies.

Spherical cloaking with homogeneous isotropic multilayered structures

We propose a practical realization of electromagnetic spherical cloaking by layered structure of homogeneous isotropic materials. By mimicking the classic anisotropic cloak by many alternating thin layers of isotropic dielectrics, the permittivity and permeability in each isotropic layer can be properly determined by effective medium theory in order to achieve invisibility. The model greatly facilitates modeling by Mie theory and realization by multilayer coating of dielectrics. Eigenmode analysis is also presented to provide insights of the discretization in multilayers.

Surface polaritons in a thin layer of an anisotropic superconductor

An expression for the permittivity tensor of a superconductor is derived within the framework of a two-fluid model of the electron subsystem. For the temperature range T ≪ T c , the dispersion relations for surface polaritons that propagate in the direction of the three principal crystallographic axes of a thin superconducting layer along its two interfaces with isotropic dielectrics are found. A significant effect of the superconductor anisotropy on the dispersion relations is revealed. The polarization structure of the wave field inside and outside the superconducting layer is determined.

Consequences of anisotropy in electrical charge storage: application to the characterization by the mirror method of TiO2 rutile

This paper is devoted first, to anisotropic distributions of stored electric charges in isotropic materials and second, to charge trapping and induced electrostatic potential in anisotropic dielectrics.On the one hand, we examine the case of anisotropic trapped charge distributions in linear homogeneous isotropic insulators, obtained after an electron irradiation in a scanning electron microscope. This injection leads to the formation of a mirror image. We first establish the characteristics of the mirror image obtained from such anisotropic distribution by linking the mirror diameter to the curvature tensor of the equipotentials thanks to the geometric optics ansatz (GOA). Second, the equipotentials induced by the presence of an anisotropic charge distribution in such isotropic dielectrics have been determined in the case of homeoidal (ellipsoidal) distributions that generalize the classical spherical distributions. Then, for these homeoidal distributions in isotropic dielectrics, the features of the mirror image have been deduced from the previous GOA estimation. Elliptic mirrors can be obtained and calculated in the limit cases of such homeoidal distributions.On the other hand, we consider the non-trivial case of a point charge lying at the interface between the vacuum and a linear homogeneous orthotropic anisotropic dielectric and the determination of its corresponding potential seen from the vacuum. This problem has already been solved in the case of transversal isotropic dielectrics (εx = εy = εr, εr ≠ εz), but we extend in this paper the classical dielectric image problem to the more general case where εx ≠ εy ≠ εz. The equivalent charge and the induced electrostatic potential are evaluated. For these anisotropic insulators, the equipotentials created by a point charge at the interface are found to be ellipsoids and this leads to an elliptic mirror image. The ratio between the two main axis values of the elliptic mirror is proportional to the square root of the ratio of the permittivities values in the plane of the interface. Finally these calculations are used to explain the experimental results obtained by the mirror method on a TiO2 sample that is known to be an anisotropic dielectric.

Electromechanical nonionic gels

The electrically induced bending of nonionic polyvinyl alcohol gels, bending over 90° within 100 ms, is the fastest motion in the field of electroactuation of polymers. This rapid bending produces initial mechanical vibrations followed by a durable displacement that contrasts highly with the relaxation observed with elastomer- and polyelectrolyte-based actuators. Here, we characterize the bending process using video imaging and laser detecting technology and establish a physical model for the electromechanical conversion, based on our observation of an induced solvent migration. Our results show excellent agreement between the measurements and calculations. This study provides general rules for understanding the electrically induced bending of isotropic dielectrics and may also shed light on nonmuscular biological engines.

Plasmonic propagation modes of a structured two-dimensional conducting interface

In this paper, we present a detailed analysis of a two-dimensional lossless and non-dispersive structured conducting interface, which is approximated by a two-dimensional ideal one-component plasma-like conducting sheet enclosed by two isotropic dielectrics. We present a Green's function formalism to analyze the propagation of surface plasmons and find new expressions. We also present analytical extensions of the approach to include loss, and discuss the results and applications of the theory. We study the symmetry properties of eigenmodes and show that the symmetries of the eigenmodes at high-symmetry points of the Brillouin zone are similar to those of the E-polarization eigenmodes of a two-dimensional square-lattice photonic crystal.

Dispersion relation for azimuthal electromagnetic surface waves on a magnetized annular plasma in a metal waveguide with coaxial anisotropic dielectric inner coating

AbstractThe dispersion relation of azimuthal electromagnetic surface waves on a magnetized annular plasma surrounded by a metallic cylindrical coaxial anisotropic dielectric lined waveguide is obtained. The thickness of the dielectric and its location in the waveguide are studied with respect to their effects on the number of spectra observed. The graphs of frequency spectra against the ratio of radii of the annular plasma and η = ωpe/Ωe are plotted. Finally, surface E-modes for coaxial anisotropic and isotropic dielectrics have been investigated.

Resonance methods for microwave studies of dielectrics (Review)

The general properties of microwave resonators with dielectric inclusions, which are important in dielectric measurements, are described. The methods for measuring the permittivity and dielectric losses in isotropic and uniaxial dielectrics with the use of cavity, open, and dielectric resonators are considered. Approximations that are often used in the theory and practice of measurements and limit accuracy are analyzed. The formulas used in calculations and results of measurements of the dielectric parameters of various samples, including films, coatings, and substrates, in the range 1.5–75.0 GHz are presented. The possibilities of local measurements and measurements of parameters of media are discussed.

Finite-element model for three-dimensional optical scattering problems

We present a three-dimensional model based on the finite-element method for solving the time-harmonic Maxwell equation in optics. It applies to isotropic or anisotropic dielectrics and metals and to many configurations such as an isolated scatterer in a multilayer, bi-gratings, and crystals. We discuss the application of the model to near-field optical recording.

Exact electroelastic solutions for penny-shaped cracks under prescribed temperature or thermal flow

This letter provides an exact solution for a thermal penny-shaped crack in piezoelectric media. An arbitrarily distributed temperature field applied on the crack faces is considered first. Closed-form expressions for the stress and electric displacement intensity factors at the crack border are given. Electrically impermeable cracks, electrically permeable cracks, and the permittivity of the medium inside the cracks are considered. Then, crack tip field intensity factors for a prescribed thermal flow on the crack faces are obtained. The solutions are mainly provided for transversely isotropic materials, but results for isotropic materials and dielectrics are also given.

Transmission line formulation for the full-wave analysis of two-dimensional dielectric photonic crystals

Using a matrix formulation it is shown how the full-wave analysis of multilayer photonic crystals can be reduced to the analysis of an equivalent multiconductor transmission line (TL). In the special case of single-layer two-dimensional photonic crystals the inductance and capacitance matrices of this equivalent TL provide the propagation characteristics of the crystal under investigation. Specifically, the determinants of these matrices contain the required information for determining propagation constants and consequently the field distribution of TM and TE propagation modes inside the crystal. Comparison of the numerical results presented in this work with those available in the literature verifies the soundness of the TL formulation introduced. Although the numerical results are presented for lossless isotropic dielectrics, the method is applicable to photonic crystals made of lossy and/or anisotropic dielectrics.

Electrostatic Forces and Stored Energy for Deformable Dielectric Materials

Abstract An isothermal energy balance is formulated for a system consisting of deformable dielectric bodies, electrodes, and the surrounding space. The formulation in this paper is obtained in the electrostatic limit but with the possibility of arbitrarily large deformations of polarizable material. The energy balance recognizes that charges may be driven onto or off of the electrodes, a process accompanied by external electrical work; mechanical loads may be applied to the bodies, thereby doing work through displacements; energy is stored in the material by such features as elasticity of the lattice, piezoelectricity, and dielectric and electrostatic interactions; and nonlinear reversible material behavior such as electrostriction may occur. Thus the external work is balanced by (1) internal energy consisting of stress doing work on strain increments, (2) the energy associated with permeating free space with an electric field, and (3) by the electric field doing work on increments of electric displacement or, equivalently, polarization. For a conservative system, the internal work is stored reversibly in the body and in the underlying and surrounding space. The resulting work statement for a conservative system is considered in the special cases of isotropic deformable dielectrics and piezoelectric materials. We identify the electrostatic stress, which provides measurable information quantifying the electrostatic effects within the system, and find that it is intimately tied to the constitutive formulation for the material and the associated stored energy and cannot be independent of them. The Maxwell stress, which is related to the force exerted by the electric field on charges in the system, cannot be automatically identified with the electrostatic stress and is difficult to measure. Two well-known and one novel formula for the electrostatic stress are identified and related to specific but differing constitutive assumptions for isotropic materials. The electrostatic stress is then obtained for a specific set of assumptions in regard to a piezoelectric material. An exploration of the behavior of an actuator composed of a deformable, electroactive polymer is presented based on the formulation of the paper.

A stable spatio-temporal G-closure and Gm-closure of a set of isotropic dielectrics with respect to one-dimensional wave propagation

The final conclusions of this paper are based on some recent results about the effective dielectric and magnetic constants of composites assembled in space-time from conventional isotropic dielectrics. These results are specifically related to wave propagation in one spatial dimension. For this case, we define and give a full characterization of the so called stable G( G m )-closure of an arbitrary set U of original isotropic dielectrics. We show that a stable G m -closure of any such set coincides with its stable G-closure. This conclusion, valid for spatio-temporal composites, stays in a sharp contrast with a similar result related to spatial composites, where a G m -closure is known to be only a part of G-closure.