Metamaterial Model Research Articles

Analytical modelling of double-negative composites

Analytical model of metamaterials comprising lattices of small resonant scatterers and (optionally) infinite wires is developed for the case when the planar grids of magnetic dipoles alternate with those of electric dipoles (or those of wires) along the direction of the wave propagation. An important question on the possibility to extract material parameters from measurements or simulations of the plane-wave scattering matrix for finite-thickness slabs of left-handed metamaterials is revisited. It is shown that the class of Bloch lattices (for which this extraction makes sense) is broader than one could judge upon the previous works. Also, it is shown that the spatial dispersion that destroys the operation of double-negative media can arise for the oblique propagation with respect to crystal planes even if it is not revealed from the analysis of the normal propagation.

Drude 모형 특성을 갖는 메타 물질의 임계각에 관한 연구

In this paper, the refraction angles and the critical angles of metamaterials which is assumed by the Drude model are analytically studied. To analyze the electromagnetic reflection and the transmission properties of metamaterial slab, we used -1 for the permeability and the permittivity at 30 GHz in Drude model for metamaterials in this paper, respectively. Due to the variation of signes of material constants for frequency ranges in Drude model, the derived refraction angle and the critical angles for each frequency ranges are differently observed. The results in this paper show that the properties the refraction angles and the critical angles for the broadband in metamaterials can be used to understand the electromagnetic properties of metamaterials and microwave applications.

Surface modes of negative-parameter interfaces and the importance of rounding sharp corners

Surface (plasmon) resonances or electrostatic surface modes are possible on an interface between two materials with permittivity of opposite signs, and interfaces with permeability of opposite signs can support similar magnetostatic surface modes. This paper contains a review of the possible surface modes in several canonical geometries, and also numerical results demonstrating the importance of these surface modes for metamaterial modeling. Particular emphasis is placed on the unphysically singular surface modes that an ideal sharp wedge appears to support, and on how losses and rounded corners influence these modes.

Numerical determination of frequency behavior in cloaking structures based on L-C distributed networks with TLM method

The increasing interest in metamaterials with negative refractive index has been prompted by a variety of promising optical and microwave applications. Often, the resulting electromagnetic problems to be solve are not analytically derivable; therefore, numerical modeling must be employed and the Transmission Line Modeling (TLM) method constitutes a possible choice. After having greatly simplified the existing TLM techniques for the modeling of metamaterials, we propose in this paper to carry out a frequency study of cloaking structure.

Lamellar model of the left-handed metamaterials composed of metallic split-ring resonators and wires

Left-handed materials composed of split ring resonators (SRRs) and wires are investigated in the viewpoint of lamellar composite with epsilon-negative (ENG) and mu-negative (MNG) materials staked alternatively. Several configurations of the SRR-wire metamaterial are numerically simulated to confirm its left-handed response as an analogy to the ENG–MNG lamellar model.

Physical configuration and performance modeling of all-dielectric metamaterials

In this paper, physical concept and performance analysis of all-dielectric metamaterials are presented. Metamaterials with desired material parameters $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\epsilon},\ifmmode\pm\else\textpm\fi{}\ensuremath{\mu})$ are developed by creating electric and magnetic resonant modes. Dielectric disk and spherical particle resonators are considered as the great candidates for establishing the dipole moments (metamaterial alphabet). A full wave finite difference time domain technique is applied to comprehensively obtain the physical insights of dielectric resonators. Near-field patterns are plotted to illustrate the development of electric and magnetic dipole fields. Geometric-polarization control of the dipole moments allows $\ensuremath{\epsilon}$ and $\ensuremath{\mu}$ to be tailored to the application of interest. All-dielectric double negative metamaterials are designed. Engineering concerns, such as loss reduction and bandwidth enhancement are investigated.

Accurate modelling of left-handed metamaterials using a finite-difference time-domain method with spatial averaging at the boundaries

The accuracy of finite-difference time-domain (FDTD) modelling of left-handed metamaterials (LHMs) is dramatically improved by using an averaging technique along the boundaries of LHM slabs. The material frequency dispersion of LHMs is taken into account using auxiliary differential equation (ADE) based dispersive FDTD methods. The dispersive FDTD method with averaged permittivity along the material boundaries is implemented for a two-dimensional (2-D) transverse electric (TE) case. A mismatch between analytical and numerical material parameters (e.g. permittivity and permeability) introduced by the time discretisation in FDTD is demonstrated. The expression of numerical permittivity is formulated and it is suggested to use corrected permittivity in FDTD simulations in order to model LHM slabs with their desired parameters. The influence of switching time of source on the oscillation of field intensity is analysed. It is shown that there exists an optimum value which leads to fast convergence in simulations.

Cavities Involving Metamaterials With an Uncountable Set of Resonant Frequencies

In this letter, it is shown that cavity resonators involving lossless and nondispersive (in a frequency band) double negative metamaterials can behave in a completely different way with respect to the cavities involving only traditional nondispersive double positive media. More precisely, it is proven that resonators with only nondispersive media may have an uncountable set of resonant frequencies. As practical consequences, it is outlined that this fact can represent an unsurmountable difficulty for present-day numerical simulators of electromagnetic eigenproblems and a cause of troubles for numerical solvers of electromagnetic driven problems. The presented result should warn users of numerical simulators against the employment of simplified models of metamaterials.

Lorentz model for metamaterials: Optical frequency resonance circuits

We illustrate the strong connection between optics and high-frequency electronics by presenting circuit calculations for resonant metamaterials in the optical frequency range. An $RLC$ circuit model is considered. Equations for impedances are derived and used to calculate the resonance positions and quality factors of a variety of samples. These calculations are not quasistatic and include interactions between sites. The calculated resonance values show good agreement with simulations and experiments. Single-site quasistatic formulas are derived from the more general equations.

Equivalent circuit model for left-handed metamaterials

A general equivalent circuit model to calculate the effective permeability of various configurations of split-ring resonators (SRRs) is presented. In the proposed model, each column of the SRR units along the axis of the rings is modeled as a quasisolenoid under magnetic induction. The inductance per ring of the infinite column of these rings is calculated, assuming all the rings in this column support the same current. The electromagnetic coupling between these individual columns of the rings is integrated into this circuit model, which is then applied to a two dimensional cross embedded split-ring resonator. The agreement between the predicted results and numerical simulations shows the efficiency of the model in predicting the frequency band of negative permeability.

Wave properties of computational TLM models of metamaterials with negative refractive index

AbstractWe derive and compare the wave properties of transmission‐line‐based negative refractive index metamaterials and their transmission line matrix (TLM) models. The TLM networks are computational replica of reactively loaded periodic structures that support backward waves and constitute artificial media with negative refractive index. After a brief review of the TLM algorithms for three types of nodes, namely the 2D Shunt Node, the 3D Expanded (or Distributed) Node, and the 3D Symmetrical Condensed Node, we formulate and solve the general dispersion equations in 2D and 3D metamaterials based on these nodes. We compare the results with the dispersion properties of both idealized homogeneous metamaterials and of L‐C loaded periodic transmission line structures that have the same cell size as their computational TLM counterparts. Copyright © 2006 John Wiley & Sons, Ltd.

Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks

We present two novel techniques for modeling two- and three-dimensional metamaterials with negative refractive index by transmission-line matrix (TLM) networks. The TLM networks are numerical models of reactively loaded periodic networks that support backward waves and constitute artificial media with negative refractive index. The TLM models, their implementations, and results computed with the models will be presented.

Efficient modeling of novel uniplanar left-handed metamaterials

This paper presents an efficient modeling technique for the derivation of the dispersion characteristics of novel uniplanar metallodielectric periodic structures. The analysis is based on the method of moments and an interpolation scheme, which significantly accelerates the computations. Triangular basis functions are used that allow for modeling of arbitrary shaped metallic elements. Based on this method, novel uniplanar left-handed (LH) metamaterials are proposed. Variations of the split rectangular-loop element printed on grounded dielectric substrate are demonstrated to possess LH propagation properties. Full-wave dispersion curves are presented. Based on the dual transmission-line concept, we study the distribution of the modal fields and the variation of series capacitance and shunt inductance for all the proposed elements. A verification of the left-handedness is presented by means of full-wave simulation of finite uniplanar arrays using commercial software (HFSS). The cell dimensions are a small fraction of the wavelength (approximately /spl lambda//24) so that the structures can be considered as a homogeneous effective medium. The structures are simple, readily scalable to higher frequencies, and compatible with low-cost fabrication techniques.

Reply to “Comment on ‘Existence and design of trans-vacuum-speed metamaterials’ ”

It is clarified further mathematically that the two-time derivative Lorentz metamaterial (2TDLM) model, which was used to achieve the trans-vacuum-speed effects in [Phys. Rev. E 68, 026612 (2003)], has a delayed causal response in agreement with the analytical and numerical results given there. The key point that the analytical (explicit low-pass filtered), and the numerical finite difference time domain and circuit simulator (implicit low-pass filtered) results for information propagation in a nonperfect 2TDLM medium still exhibit the trans-vacuum-speed (TVS) effect, despite the (physically required) imposed absence of the 2TDLM's unusual high-frequency behavior, is also discussed in more detail.

An analytical model of metamaterials based on loaded wire dipoles

We present a model of straight wire dipole scatterers loaded by arbitrary lumped loads in the dipole center. These particles can be used as inclusions of custom-design composite materials or electrically controllable metamaterials. The model, together with the Clausius-Mossotti formula and an analytical model for reflection and transmission in dipole arrays, allows to find loads required to realize the desired electromagnetic properties of the composite and estimate its realizability with the use of various bulk loads.