Effective Permittivity Tensor Research Articles

Resonance Enhancement of the Faraday Effect in a agnetoplasmonic Composite

The paper presents the results of a theoretical and experimental study of the enhancement of the magneto-optical Faraday effect in a magnetoplasmonic nanocomposite, caused by localized plasmon resonance (LPR) in metal nanoparticles. The nanocomposite comprises a three-layer structure of self-assembled gold nanoparticles in a bismuth-substituted iron-garnet matrix. It is shown theoretically and experimentally that the enhancement of the magneto-optical Faraday effect is determined by the action of a magnetic field on the magnetoplasmonic composite as an effective medium as a whole. In this case, in the magnetoplasmonic nanocomposite, the Faraday effect is enhanced at the LPR wavelengths and is slightly weakened in the region of short wavelengths relative to the LPR. It is theoretically shown that the complex gyration index in the off-diagonal terms of the effective permittivity tensor for the magnetoplasmonic composite, in addition to rotation of the polarization plane, leads to the appearance of alternating ellipticity in the vicinity of the plasmon resonance, which is observed in the form of asymmetry of magneto-optical rotation.

A semi-analytic method for the computation of the effective properties of composites of two isotropic constituent materials

We develop a computational framework for the semi-analytic representation of the effective transport properties of two-component composite materials, in the spirit of Bergman’s spectral representation. The components of the effective permittivity (or conductivity) tensor are expanded as power series in a contrast parameter between the two phases. The coefficients (the moments of a spectral measure) of these expansions are determined recursively through the numerical evaluations of integrals defined solely on the boundary between the constituent phases, and discretized by high-order (possibly exponentially converging) quadrature schemes. The high precision reached by these coefficients allows the series representation to be recast into Padé approximants (or continued fractions) to provide analytical expressions valid over large (possibly infinite) regions of the parameter complex plane. Examples, thus far limited to two-dimensional rhombic unit cells, demonstrate that the method is reliable for microgeometries and material parameters for which other methods are far less dependable. The analytical representations are particularly useful to study the optical or electrostatic resonant behaviour of some composite materials.

An asymptotic homogenization formula for complex permittivity and its application

The $\mathbb R$-linear boundary value problem in a multiply connected domain on a flat torus is considered. This problem is closely related to the Riemann-Hilbert problem on analytic functions. The considered problem arises in the homogenization procedure of random media with complex constants which express the permittivity of components. A new asymptotic formula for the effective permittivity tensor is derived. The formula contains location of inclusions in symbolic form. The application of the derived formula to investigation of the morphology of the tumor cells in disordered biological media is discussed.

Plane wave diffraction on a layer of asymmetric hyperbolic metamaterial

We consider the diffraction of a plane wave on a layer of symmetric hyperbolic metamaterial made of metal and SiO2 layers. It is shown that the reflection coefficient depends not only on the angle of incidence, but also on the direction of incidence relative to the anisotropy axis. In an arbitrary fall, a plate of an asymmetric hyperbolic metamaterial creates scattered waves of both polarizations. Keywords: hyperbolic metamaterial, diffraction, effective permittivity tensor, homogenization.

Field enhancement in hydrogen storage by periodic layered structures

This paper investigates, through the field enhancement factor, the increase of hydrogen adsorption around the interface between a layer of hydrogen and a periodic layered structure under different incidence angles of an applied transverse magnetic polarized electromagnetic field. This periodic layered structure is composed of n-binary unit cells based on alternating a thin layer of gold with a thin layer of a metamaterial with equal negative relative permittivity while the relative permeability of the first and the second material's unit cell is considered equal to 1 and -1, respectively. We apply the effective medium theory to replace this layered structure with a single slab of a homogeneous material with an effective permittivity tensor and an effective permeability tensor. We use the Transfer Matrix Method to analyze the reflectivity spectra at the hydrogen/slab interface for adjustable layers’ thicknesses and then we derive the field enhancement factor. We obtain a significant increase of the field enhancement factor of the structure in comparison with the field enhancement factor around the interface between a layer of hydrogen and a structure composed of one gold layer.

Generalized effective-field approximation for inhomogeneous medium with inclusions in multilayered shells

An approach is proposed for calculating effective physical characteristics of a inhomogeneous medium with several levels of nesting of its microstructure --- the generalized effective-field approximation. With the help of this approach, an expression is obtained for an effective permittivity tensor of an inhomogeneous medium with ellipsoidal inclusions in a multilayered shell, the boundaries of all layers of which are ellipsoids. The proposed approach allows to take into account probabilistic distributions of orientations and forms of inclusions, as well as the presence of several types of inclusions. Two cases of matrix composites are considered: 1) with spherical isotropic inclusions with a multilayered shell; 2) with ellipsoidal anisotropic inclusions with a multilayered shell. For an inhomogeneous medium with homogeneous inclusions, this approximation is shown to produce the same result as the generalized singular approximation. Keywords: inhomogeneous medium, composite, matrix, inclusion, multilayered shell, generalized effective-field approximation, generalized singular approximation, effective permittivity.

Обобщенное приближение эффективного поля для неоднородной среды с включениями в многослойной оболочке

An approach is proposed for calculating effective physical characteristics of a inhomogeneous medium with several levels of nesting of its microstructure - the generalized effective-field approximation. With the help of this approach, an expression is obtained for an effective permittivity tensor of an inhomogeneous medium with ellipsoidal inclusions in a multilayered shell, the boundaries of all layers of which are ellipsoids. The proposed approach allows to take into account probabilistic distributions of orientations and forms of inclusions, as well as the presence of several types of inclusions. Two cases of matrix composites are considered: 1) with spherical isotropic inclusions with a multilayered shell; 2) with ellipsoidal anisotropic inclusions with a multilayered shell. For an inhomogeneous medium with homogeneous inclusions, this approximation is shown to produce the same result as the generalized singular approximation.

Tunable physical effects in Bi-mica hyperbolic structures

Recent years, the need to create tunable THz devices emerged due to rapid development of THz photonics. As a rule, such devices are based on semiconductors and phase change materials, and the use of hyperbolic media based on these materials is a promising approach to realize terahertz wave near-field control. In this work, the dispersion of complex effective permittivity tensor of a layered structure consisting of 40 nm, 70 nm and 120 nm semimetallic Bi films on a top of 21 μm mica dielectric substrate, calculated on the basis of THz time-domain spectroscopy method, is used to theoretically estimate such effects as Purcell enhancement, Van Hove singularity, and Compton effect. The influence of continuous-wave optical pumping onto the optical properties of Bi-based hyperbolic medium and related effects is also studied in this work. The studied effects may be used in THz radiation enhancement, thermoelectric engineering and thermophotovoltaics, optical and electronic detection, molecular sensing, and even in development of spasers. The obtained results prove the possibility of application of Bi-mica composite in a development of fast-acting terahertz hyperbolic materials which are easy to produce due to their simple structure.

Magneto-Optical Activity in Nonmagnetic Hyperbolic Nanoparticles.

Active nanophotonics can be realized by controlling the optical properties of materials with external magnetic fields. Here, we explore the influence of optical anisotropy on the magneto-optical activity in nonmagnetic hyperbolic nanoparticles. We demonstrate that the magneto-optical response is driven by the hyperbolic dispersion via the coupling of metallic-induced electric and dielectric-induced magnetic dipolar optical modes with static magnetic fields. Magnetic circular dichroism experiments confirm the theoretical predictions and reveal tunable magneto-optical activity across the visible and near infrared spectral range.

Experimental investigation of optically controlled topological transition in bismuth-mica structure

The hyperbolic materials are strongly anisotropic media with a permittivity/permeability tensor having diagonal components of different sign. They combine the properties of dielectric and metal-like media and are described with hyperbolic isofrequency surfaces in wave-vector space. Such media may support unusual effects like negative refraction, near-field radiation enhancement and nanoscale light confinement. They were demonstrated mainly for microwave and infrared frequency ranges on the basis of metamaterials and natural anisotropic materials correspondingly. For the terahertz region, the tunable hyperbolic media were demonstrated only theoretically. This paper is dedicated to the first experimental demonstration of an optically tunable terahertz hyperbolic medium in 0.2–1.0 THz frequency range. The negative phase shift of a THz wave transmitted through the structure consisting of 40 nm (in relation to THz wave transmitted through substrate) to 120 nm bismuth film (in relation to both THz waves transmitted through substrate and air) on 21 µm mica substrate is shown. The optical switching of topological transition between elliptic and hyperbolic isofrequency contours is demonstrated for the effective structure consisting of 40 nm Bi on mica. For the case of 120 nm Bi on mica, the effective permittivity is only hyperbolic in the studied range. It is shown that the in-plane component of the effective permittivity tensor may be positive or negative depending on the frequency of THz radiation and continuous-wave optical pumping power (with a wavelength of 980 nm), while the orthogonal one is always positive. The proposed optically tunable structure may be useful for application in various fields of the modern terahertz photonics.

Highly Sensitive Permittivity Sensor Using an Inhomogeneous Metamaterial Cylindrical Waveguide

Cylindrical waveguides filled with anisotropic metamaterials enable novel wave propagation phenomena. A nanoporous alumina microtube is a manifestation of such an anisotropic waveguide with an effective permittivity tensor (ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ≠ ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">φ</sub> = ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</sub> ). The metamaterial would be considered to be filled homogeneously or inhomogeneously depending on the variation of the size of the nanopores and density of the nanopores. The electromagnetic fields in such metamaterial waveguide are highly sensitive to the refractive index of the material embedded in the nanopores and the variation of the density of the inclusion in the radial direction due to the modal field distributions. We show that there is a large variation in the reflection coefficient (S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> ) of the inhomogeneously filled nanoporous waveguide with an embedded liquid with small variations in the material properties of the liquid. This variation in the S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> parameter can use to determine the purity of liquid. Our results show that the permittivity variations of the inclusion material can be monitored up to the sixth decimal places theoretically. The analysis also indicates that the inhomogeneous metamaterial waveguide is more sensitive compared to both the homogeneously filled metamaterial waveguide and an isotropic waveguide covered with metamaterial clad. This waveguide has potential applications in biomedical and chemical sensing applications.

Induced anisotropy in composite materials with reconfigurable microstructure: Effective medium model with movable percolation threshold

In composite materials, with field-dependent restructuring of the filler material (changes in the mutual arrangement of inclusions), the presence of an external magnetic field induces anisotropy of the dielectric properties, even if the composite is isotropic in the absence of an external field. A modified effective medium approximation is proposed for the calculation of the components of effective permittivity within a class of composites with reconfigurable microstructure, where both phases (the filler and the matrix) are isotropic and the inclusions have spherical shape. The effective physical properties are calculated in the parallel and perpendicular directions to an applied field. The appearance of the anisotropy of the permittivity is simulated by the introduction of two not-equal, possibly variable (field-dependent) percolation thresholds. The implications, of the proposed theoretical approach, are demonstrated for the case of the dielectric properties of magnetoactive elastomers (MAEs). In MAEs with soft polymer matrices, the mutual arrangement of micrometer-sized magnetic inclusions can significantly change in an applied magnetic field. A reasonable agreement between theory and experiment at a measurement frequency of 1 kHz is found, and is improved in comparison to the previous models. The components of the effective permittivity tensor, characterizing the dielectric properties along the direction of the applied magnetic field and in the orthogonal direction, grow with an increasing field. This growth is more pronounced for the permittivity component in the field direction. The possible extensions of the theoretical model and future directions of research are discussed. The presented theoretical approach can be useful for the application-driven development of a number of smart materials, in particular electro- and magnetorheological gels, elastomers and fluids.

Dynamic phase-change metafilm absorber for strong designer modulation of visible light

AbstractEffective dynamic modulation of visible light properties has been significantly desired for advanced imaging and sensing technologies. In particular, phase-change materials have attracted much attention as active material platforms owing to their broadband tunability of optical dielectric functions induced by the temperature-dependent phase-changes. However, their uses for visible light modulators are still limited to meet multi-objective high performance owing to the low material quality factor and active tunability in the visible regime. Here, a design strategy of phase-change metafilm absorber is demonstrated by making the use of the material drawbacks and extending design degree of freedom. By engineering tunability of effective anisotropic permittivity tensor of VO2-Ag metafilm around near-unity absorption conditions, strong dynamic modulation of reflection wave is achieved with near-unity modulation depth at desired wavelength regions without sacrificing bandwidth and efficiency. By leveraging effective medium theory of metamaterial and coupled mode theory, the intuitive design rules and theoretical backgrounds are suggested. It is also noteworthy that the dynamic optical applications of intensity modulation, coloring, and polarization rotation are enabled in a single device. By virtue of ultrathin flat configuration of a metafilm absorber, design extensibility of reflection spectrum is also verified. It is envisioned that our simple and powerful strategy would play a robust role in development of miniaturized light modulating pixels and a variety of photonic and optoelectronic applications.

Accounting for the influence of granule size distribution in nanocomposites

This paper discusses the effect of the distribution of the granules size in nanocomposites on physical properties within the framework of the quasi-classical size effect. Methods of effective medium for describing nanocomposites are discussed. This paper also notes and discusses the contribution of various mechanisms that affect the optical and magneto-optical properties of such structures, especially in the IR region of the spectrum, where the quasi-classical dimensional effect is most pronounced. The Droude-Lorentz mode describes the contribution of the dimensional effect to the diagonal and non-diagonal components of the effective medium's permittivity tensor. The lognormal distribution of the granule size characteristic of many nanostructures is considered. Based on this approach, the dependences of the standard deviation on the value of the integral as a function of the average size of the granules were obtained. Based on the normalization condition, the numerical value of the standard deviation of the r values and the average particle size were analytically determined. This paper also discusses the fundamental significance of the results obtained – the possibility of applying this approach to all possible distributions. The found value of the average size of nanocomposite granules makes it possible to model various properties of nanocomposite structures, first of all, optical and magneto-optical properties, with the help of known methods within the framework of the effective medium approximation. This is especially important for describing the percolation transition in nanocomposites. The problem being solved is important and relevant, since many interesting and important effects are realized in such magnetic nanocomposites, such as the magneto-optical Kerr effect, the anomalous Hall effect, the giant magnetoresistance, and many others. The results obtained allow us to better describe materials that are widely used in modern electronics and nanoelectronics.

Terahertz routing with graphene magnetic metamaterials

Terahertz wireless communication has emerged as a fast-growing research area. Routing, which is designed to control the propagation of terahertz wave, is of great importance for building the terahertz all-optical communication network. Metamaterials provide a good method for manipulating the terahertz wave, which can be used to realize the wave router. To steer the input wave in different directions, for example negative refraction angle, some structures have been proposed, such as stacked structures and nanowire arrays. However, in these metamaterials, the incident wave is generally limited to transverse magnetic polarization. Here, a new terahertz routing method for transverse electric wave is put forward with using graphene magnetic metamaterials. Theoretical analysis is performed to show that this metamaterial has negative components not only in effective permittivity tensor but also in effective permeability tensor. Routing is realized by topological transitions between different dispersion regimes in this metamaterial. Our finding provides a new candidate for signal routing of terahertz wave.

Nonlocal electrodynamics of homogenized metal-dielectric photonic crystals

The nonlocal effective permittivity tensor for photonic crystals (PCs), having dielectric and metallic inclusions in the unit cell, is calculated and analyzed within the homogenization theory based on the Fourier formalism and the form-factor division approach. A method allowing us to extract the effective bianisotropic metamaterial parameters (permeability and chirality) from the wave vector dependence of the nonlocal effective dielectric response is proposed. Both the original nonlocal dielectric response parameters and the new bianisotropic metamaterial ones reproduce the photonic band structure of the artificial crystal far beyond the long wavelength limit and for a wide class of metal-dielectric structures. To calculate the optical spectra (reflection and transmission) of finite-size PC, the nonlocal homogenization approach is extended with the method of expansion into photonic bulk-modes (Bloch waves). The application of the developed theory is illustrated with well-known forms of metallic inclusions (slabs, thin wires, split-ring resonators) and experimentally confirmed with novel designs based on metallic crosses.

Effective Radiative Properties of Tilted Metallic Nanorod Arrays Considering Polarization Coupling

With the advent of new nanomanufacturing techniques has come the rise of the field of nanophotonics and an increased need to determine optical properties of novel structures. Commercial software packages are able to estimate the behavior, but require large resources and heavy computational time. By combining coordinate transforms and Effective Medium Theory (EMT), an effective relative permittivity tensor is defined and further exploited to calculate the polarization-coupled Fresnel coefficients through Maxwell’s equations. A uniaxial simplification is made to show the case of tilted nanorod arrays. To demonstrate the flexibility of this system, the interfacial reflectance has been calculated for both s- and p-polarizations as well as the coupled case with the volume filling fractions of f = 0.10 and 0.30 for silver (Ag) and titanium (Ti) nanorods, and a scenario of a Ag nanorod array with polymethyl methacrylate (PMMA) as the surrounding medium. The exact results computed by the finite-difference time-domain method justify the validity of EMT with polarization coupling taken into account. The effects of incidence angle and azimuthal angle on reflectance are also discussed. The relatively simple nature of this approach allows for fast estimations of the optical properties of various nanostructures.

Robust Extraction of Hyperbolic Metamaterial Permittivity using Total Internal Reflection Ellipsometry.

Hyperbolic metamaterials are optical materials characterized by highly anisotropic effective permittivity tensor components having opposite signs along orthogonal directions. The techniques currently employed for characterizing the optical properties of hyperbolic metamaterials are limited in their capability for robust extraction of the complex permittivity tensor. Here we demonstrate how an ellipsometry technique based on total internal reflection can be leveraged to extract the permittivity of hyperbolic metamaterials with improved robustness and accuracy. By enhancing the interaction of light with the metamaterial stacks, improved ellipsometric sensitivity for subsequent permittivity extraction is obtained. The technique does not require any modification of the hyperbolic metamaterial sample or sophisticated ellipsometry set-up, and could therefore serve as a reliable and easy-to-adopt technique for characterization of a broad class of anisotropic metamaterials.

An Effective Permittivity Tensor of Cylindrically Perforated Dielectrics

In the letter, we propose a simple analytical effective permittivity model of perforated dielectrics composed of through-hole cylindrical perforations. As the perforated dielectrics are uniaxial media, the model respects the anisotropic properties of the material and the results are simple engineering formulas for effective permittivities of ordinary and extraordinary wave for polarization corresponding to parallel and perpendicular orientation with respect to the axis of perforations. The model is based on the 2-D Maxwell Garnett approximation of inhomogeneous media valid for circularly shaped perforations. The analytical results obtained for propagation of transverse electromagnetic wave are verified by unit-cell full-wave simulations of triangular perforations lattice, and a very good agreement is obtained.

Nonlocal response of tunable photonic metamaterials with semiconductor inclusions

Effective parameters of homogenized photonic crystals with a semiconductor bar in the unit cell are calculated and analyzed. The applied homogenization theory is based on the Fourier formalism within the form-factor division approach. The calculated effective parameters, namely, the components of the effective permittivity tensor, are nonlocal since they depend on not only frequency but also the wave vector. Using the nonlocal effective parameters, the complex dispersion relation for photonics modes propagating in a periodic semiconductor–dielectric array can be described even beyond the long-wavelength limit. We have analyzed the temperature dependence of the nonlocal effective parameters for photonic metamaterials composed of InSb square bars in a silica–glass host matrix. In the case of continuous (infinitely long) bars, the metamaterial shows plasma-like behavior with a temperature-dependent effective plasma frequency in the THz range. For the case of cut semiconductor bars, the metamaterial behaves as a dielectric in the lowest frequency band, whose width can also be tuned by varying the temperature. Using the nonlocal effective permittivity, the optical spectra (reflectivity and transmittance) for a slab of InSb square bars in a glass matrix were calculated and analyzed.