Spatial Dispersion Effects Research Articles

Scattering suppression from arbitrary objects in spatially dispersive layered metamaterials

Concealing objects by making them invisible to an external electromagnetic probe is coined by the term ``cloaking.'' Cloaking devices, having numerous potential applications, are still facing challenges in realization, especially in the visible spectral range. In particular, inherent losses and extreme parameters of metamaterials required for the cloak implementation are the limiting factors. Here, we numerically demonstrate nearly perfect suppression of scattering from arbitrary-shaped objects in spatially dispersive metamaterial acting as an alignment-free concealing cover. We consider a realization of a metamaterial as a metal-dielectric multilayer and demonstrate suppression of scattering from an arbitrary object in forward and backward directions with perfectly preserved wave fronts and less than 10% absolute intensity change, despite spatial dispersion effects present in the composite metamaterial. Beyond the usual scattering suppression applications, the proposed configuration may be used for a simple realization of scattering-free detectors and sensors.

Near field radiative heat transfer between two nonlocal dielectrics

We explore in the present work the near-field radiative heat transfer between two semi-infinite parallel nonlocal dielectric planes by means of fluctuational electrodynamics. We use a theory for the nonlocal dielectric permittivity function proposed by Halevi and Fuchs. This theory has the advantage to include different models performed in the literature. According to this theory, the nonlocal dielectric function is described by a Lorenz-Drude like single oscillator model, in which the spatial dispersion effects are represented by an additional term depending on the square of the total wavevector k. The theory takes into account the scattering of the electromagnetic excitation at the surface of the dielectric material, which leads to the need of additional boundary conditions in order to solve Maxwell׳s equations and treat the electromagnetic transmission problem. The additional boundary conditions appear as additional surface scattering parameters in the expressions of the surface impedances. It is shown that the nonlocal modeling deviates from the classical 1/d2 law in the nanometer range at distances still larger than the ones where quantum effects are expected to come into play.

Effect of spatial dispersion on the topological transition in metamaterials

We investigate the topological transition in metamaterials considering a structure composed of the uniaxial electric scatterers. Our study is based on the discrete dipole model, which allows us to take into account the effects of spatial dispersion in the structure. The nonlocal effects lead to the existence of the transition region between elliptic and hyperbolic dispersion regimes. The transition region corresponds to the ``mixed'' regime when quasielliptic and quasihyperbolic isofrequency contours are present simultaneously. In the present work, we show that this regime may occur when the effective permittivity of the structure calculated by the Clausius-Mossotti formula approaches either zero or infinity. We determine the boundaries between the different dispersion regimes for uniaxial metamaterials composed of electric scatterers and perform a detailed study of the metamaterial dispersion properties in the mixed regime. Possible verification of the mixed regime existence is proposed.

Self-induced torque in discrete uniaxial metamaterials

We consider a torque acting on an electric dipole placed in anisotropic uniaxial metamaterial. The metamaterial is modeled as a cubic lattice of uniaxial polarizable particles. The torque arises from the response of the anisotropic structure polarized by the field of the test dipole. We calculate the self-induced torque taking into account the effects of frequency and spatial dispersion and also the effect of losses. We demonstrate that the maximal absolute values of the torque are achieved in the transition region between elliptic and hyperbolic dispersion regimes of the metamaterial.

Generalized effective-medium theory for metamaterials

We present an effective-medium model for calculating the frequency-dependent effective permittivity $\ensuremath{\epsilon}(\ensuremath{\omega})$ and permeability $\ensuremath{\mu}(\ensuremath{\omega})$ of metamaterial composites containing spherical particles with arbitrary permittivity and permeability. The model is derived from the zero-scattering condition within the dipole approximation, but does not invoke any additional long-wavelength approximations. As a result, it captures the effects of spatial dispersion and predicts a finite effective refractive index and antiresonances in $\ensuremath{\epsilon}(\ensuremath{\omega})$ and $\ensuremath{\mu}(\ensuremath{\omega})$, in agreement with numerical finite-element calculations.

Artificial magnetism at terahertz frequencies from three-dimensional lattices of TiO_2 microspheres accounting for spatial dispersion and magnetoelectric coupling

We employ the generalized Lorentz-Lorenz method to investigate how both magnetoelectric coupling and spatial dispersion influence the artificial magnetic capabilities at terahertz frequencies of the representative case of a metamaterial consisting of a three-dimensional (3D) lattice of TiO2 microspheres. The complex wavenumber dispersion relations pertaining to modes supported by the array, traveling along one of the principal axes of the array with electric or magnetic field polarized transversely and longitudinally (with respect to the mode traveling direction), are studied and thoroughly characterized. One mode with transverse polarization is dominant at any given frequency for the analyzed dimensions, proving that the 3D lattice can be treated as a homogeneous medium with defined electromagnetic material parameters. We show, however, that bianisotropy is a direct consequence of magnetoelectric coupling, and the dyadic expressions of both effective and equivalent material parameters are derived. In particular, we analyze the effect of spatial dispersion on the effective parameters relative to a composite material made by a 3D lattice of TiO2 microspheres with filling fraction around 30% and near the first Mie magnetic dipolar resonance. Finally, we homogenize the metamaterial in terms of equivalent index and impedance, and by comparison with full-wave simulations, we explain the presence of the unphysical antiresonance permittivity behavior observed in previous work.

The Effects of Spatial Dispersion on Power Flow Along a Printed-Circuit Tensor Impedance Surface

In this communication, expressions for the group velocity and the direction of power flow along an idealized tensor impedance boundary condition (TIBC) and a printed-circuit tensor impedance surface (PCTIS), are found. A PCTIS consists of a patterned metallic cladding over a grounded dielectric substrate. The patterned metallic cladding is modeled by a tensor impedance sheet. Expressions for the surface impedance of a TIBC and a PCTIS are reviewed. From these expressions, the group velocity and direction of power flow are derived as a function of transverse wave vector. A PCTIS exhibits spatial dispersion due to the electrical thickness of its substrate while a TIBC does not. As a result of this spatial dispersion, a PCTIS can have the same surface impedance as a TIBC for a given transverse wave vector, but a different direction of power flow. The expressions for direction of power flow along a TIBC and a PCTIS are verified with a full-wave electromagnetic solver.

Check on a nonlocal Maxwellian theory of sound propagation in fluid-saturated rigid-framed porous media

A macroscopic nonlocal theory of sound propagation in homogeneous rigid-framed porous media permeated with a viscothermal fluid has been recently proposed in this journal. It accounts for the first time for the full temporal and spatial dispersion effects, independently of the nature of the microgeometry. In this paper this new Maxwellian theory is validated in the case of sound propagation in cylindrical circular tubes, by showing that it matches exactly the long-known direct Kirchhoff–Langevin’s solutions.

Importance of Mueller matrix characterization of bianisotropic metamaterials

We present a study on the optical properties of metamaterial layers containing U-shaped resonators. Using Finite Element Methods, we show that the description of the optical properties on one isolated resonator requires taking into account permittivity, permeability and magneto-electric tensors. The effect of weak spatial dispersion in arrays of resonators can be reproduced by adding two elements in the permittivity and magneto-electric coupling tensors. We show how the symmetries of the Mueller matrix of the sample can be used to discriminate the contributions of the different tensor elements. Generalized ellipsometry measurements made on a sample realized by e-beam lithography confirm the qualitative findings of the theoretical study. A quantitative determination of the different elements of permittivity, permeability and magneto-electric coupling is obtained by using oscillators with Lorentzian lineshape, to fit to the measurements.

Effects of spatial dispersion at intraband transitions in multiple quantum well structures

Effects of spatial dispersion in reflection of light from multiple quantum well structures of different symmetry have been investigated. It has been shown that with inclined incidence of linearly polarized light on the system of symmetry C∞v, the reflected wave starts to manifest the circular polarization. Upon the incidence of s(p)-polarized light on the structure of the D2d symmetry, the reflected wave starts to manifest p(s) component, while in the case of the point symmetry C2v, this phenomenon also occurs for the normal incidence. The magneto-spatial dispersion in the magnetic field lying in the structure plane leads to the same conversion of polarization. Dependences of the polarization-sensitive reflection coefficients on the incidence angle are calculated. The microscopically gyrotropic contributions to the dielectric permittivity of the multiple quantum well structures are calculated for the intraband frequency range. Evaluations show that the effects of spatial dispersion in such systems can be observed experimentally.

Effect of Spatial Dispersion on Surface Waves Propagating Along Graphene Sheets

We investigate the propagation of surface waves along a spatially dispersive graphene sheet, including substrate effects. The proposed analysis derives the admittances of an equivalent circuit of graphene able to handle spatial dispersion, using a nonlocal model of graphene conductivity. Similar to frequency-selective surfaces, the analytical admittances depend on the propagation constant of the waves traveling along the sheet. Dispersion relations for the supported TE and TM modes are then obtained by applying a transverse resonance equation. Application of the method demonstrates that spatial dispersion can dramatically affect the propagation of surface plasmons, notably modifying their mode confinement and increasing losses, even at frequencies where intraband transitions are the dominant contribution to graphene conductivity. These results show the need to correctly assess spatial dispersion effects in the development of plasmonic devices at the low THz band.

Laboratory studies of the dynamic of resonance cones formation in magnetized plasmas

The paper is devoted to experimental studies of formation of resonance cones in magnetized plasmas by pulsed RF source in the lower-hybrid (whistler) and the upper-hybrid frequency ranges. It is shown that in both frequency ranges, resonance cones exhibit similar dynamics after switching-on the RF source: at first, wide maxima of radiation are formed in non-resonance directions, which then become narrower, with their direction approaching the resonance one. While the resonance cones are being formed, one observes a fine structure in the form of secondary radiation maxima. It is shown that the characteristic formation time of stationary resonance cones is determined by the minimal value of the group velocity of the quasi-electrostatic waves excited by the antenna. In the low-temperature plasma, this value is limited in the lower-hybrid frequency range by the spatial spectrum of the emitting antenna and in the upper-hybrid range, by the effects of spatial plasma dispersion.

Negative permeability and negative refraction in composite systems with finite-size inclusions

It is shown that the spatial dispersion in composite systems formed by inclusion of finite size spheres may lead to negative group velocity and, subsequently, to negative refraction. Longitudinal and transverse electromagnetic modes exhibiting negative dispersion are found in the system of finite size charged clouds. It is also shown that similar mechanism due to the electric quadrupole coupling leads to excitation of longitudinal and transverse eigenmodes with negative dispersion in a random set of nonmagnetic metal spheres embedded in a dielectric host. It is shown that the negative refraction related to the spatial dispersion effects may alternatively be viewed as a result of simultaneously negative permittivity and permeability.

Universality classes and critical phenomena in confined liquid systems

It is well known that the similar universal behavior of infinite-size (bulk) systems of different nature requires the same basic conditions: space dimensionality; number components of order parameter; the type (short- or long-range) of the intermolecular interaction; symmetry of the fluctuation part of thermodynamical potential. Basic conditions of similar universal behavior of confined systems needs the same supplementary conditions such as the number of monolayers for a system confinement; low crossover dimensionality, i.e., geometric form of restricted volume; boundary conditions on limiting surfaces; physical properties under consideration. This review paper is aimed at studying all these conditions of similar universal behavior for diffusion processes in confined liquid systems. Special attention was paid to the effects of spatial dispersion and low crossover dimensionality. This allowed us to receive receiving correct nonzero expressions for the diffusion coefficient at the critical point and to take into account the specific geometric form of the confined liquid volume. The problem of 3D \Leftrightarrow 2D dimensional crossover was analyzed. To receive a smooth crossover for critical exponents, the Kawasaki-like approach from the theory of mode coupling in critical dynamics was proposed. This ensured a good agreement between data of computer experiment and theoretical calculations of the size dependence of the critical temperature T_{c}(H) of water in slitlike pores. The width of the quasi-elastic scattering peak of slow neutrons near the structural phase transition in the aquatic suspensions of plasmatic membranes (mesostructures with the typical thickness up to 10 nm) was studied.

Effects of spatial dispersion on the Casimir force between graphene sheets

The Casimir force between graphene sheets is investigated with emphasis on the effect from spatial dispersion using a combination of factors, such as a nonzero chemical potential and an induced energy gap. We distinguish between two regimes for the interaction - T=0 $K$ and $T\neq 0$ $K$. It is found that the quantum mechanical interaction (T=0 $K$) retains its distance dependence regardless of the inclusion of dispersion. The spatial dispersion from the finite temperature Casimir force is found to contribute for the most part from $n=0$ Matsubara term. These effects become important as graphene is tailored to become a poor conductor by inducing a band gap.

Efficient generation of high beam-quality attosecond pulse with polarization-gating Bessel-Gauss beam from highly-ionized media

Single attosecond pulse generation with polarization gating Bessel-Gauss beam in relatively strongly-ionized media is investigated. The results show that Bessel-Gauss beam has the ability to suppress the spatial plasma dispersion effects caused by high density of free electrons, thus the laser field can maintain its spatial profile through highly-ionized medium. This indicates the use of Bessel-Gauss beam has advantages over Gaussian beam in high harmonic generation under high ionization conditions. In our scheme, significant improvement of spatiotemporal properties of harmonics is achieved and an isolated attosecond pulse with high beam quality is filtered out using polarization gating.

Proper and improper modes of the left-handed material waveguides

The guided, complex, and virtual modes of the planar left-handed material waveguides are studied. The modal dispersion and field distributions are analyzed for the systems with step and parabolic profiles of dielectric permittivity and magnetic permeability. It is shown that anomalously high magnitudes of the magnetic fields may be observed in such structures. Effects of material nonlinearity and spatial dispersion are discussed.

Analytically describing the temperature-dependent constitutive parameters of an electromagnetic metamaterial

Analogous to mechanical systems, modeling the electromagnetic (EM) performance of large and complex metamaterial structures requires the use of effective-medium/constitutive properties. Constitutive properties are critical for efficiently bridging the gap between subwavelength geometry and performance at the mesoscale. In this article, the temperature-dependent effective medium properties for a metamaterial electric-inductive-capacitive (ELC) resonator are described analytically. ELC structures are commonly used in metamaterial designs to provide a tailored electric response to EM waves. An equivalent circuit model, coupled with analytic expressions for the capacitances, inductance, and resistance of the ELC resonator, is utilized to describe how thermally induced mechanical strain and changes in material properties manifest as temperature-dependent permittivity and permeability curves for the metamaterial. The resulting analytic expressions account for the effects of spatial dispersion and losses. This article also details how the process may be expanded to similarly describe the temperature-dependent constitutive properties of metamaterial magnetic resonators.

Spatial Nonlocality in the Calculation of Hamaker Coefficients

We study the effects of spatial dispersion or nonlocality in the calculation of the Hamaker coefficient. Using a hydrodynamic model to describe the dielectric function of the materials, we show that at small separations, less that 10 nm, the Hamaker coefficient decreases significantly when a nonlocal dielectric is used. As a case study we compute the van der Waals interaction between two Au nanospheres and between two Au parallel nanorods. In both cases, the interaction energy shows variations of up to 2 orders of magnitude between the local and nonlocal cases. We show that at the nanoscale the usual approach to the calculation of the Hamaker coefficients has to be modified to properly take into account the dielectric properties of the nanoparticles.

Low-Frequency Dominant-Mode Propagation in Spatially Dispersive Graphene Nanowaveguides

Dispersion properties of the dominant modes supported by different 2-D graphene-based nanowaveguides are studied by means of an exact approach based on the transverse-resonance technique and using an equivalent-circuit representation of graphene sheets which also takes into account the spatially dispersive nature of the graphene conductivity: it is quantitatively shown that neglecting spatial-dispersion effects can cause errors in the determination of the modal properties of extremely slow surface waves, also well below the terahertz regime. The modal features of graphene nanowaveguides are thus investigated in detail showing their potential in future nanoelectromagnetic and nanophotonic applications.