Negative Effective Permittivity Research Articles

On the electrical characteristics of complementary metamaterial resonators

In this letter, a method to obtain the electrical characteristics of complementary split ring resonators (CSRRs) coupled to planar transmission lines is presented. CSRRs have been recently proposed by some of the authors as new constitutive elements for the synthesis of metamaterials with negative effective permittivity, and they have been applied to the fabrication of metamaterial-based circuits in planar technology. The method provides the electrical characteristics of CSRRs (including the intrinsic resonant frequency and the unloaded Q-factor), as well as the coupling capacitance between line and CSRRs, and the parameters of the host line. Parameter extraction from the proposed method is applied to two different structures corresponding to the basic cells of left handed (LH) and negative permittivity lines. The method is of actual interest for the design of microwave circuits and metamaterials based on these complementary resonant particles

Numerical simulations of negative-index refraction in a lamellar composite with alternating single negative layers

Negative-index refraction is achieved in a lamellar composite with epsilon-negative (ENG) and mu-negative (MNG) materials stacked alternatively. Based on the effective medium approximation, simultaneously negative effective permittivity and permeability of such a lamellar composite are obtained theoretically and further proven by full-wave simulations. Consequently, the famous left-handed metamaterial comprising split ring resonators and wires is interpreted as an analogy of such an ENG-MNG lamellar composite. In addition, beyond the effective medium approximation, the propagating field squeezed near the ENG/MNG interface is demonstrated to be left-handed surface waves with backward phase velocity.

Design and double negative property verification of C band left‐handed metamaterial

AbstractIn this article, a left‐handed (LH) metamaterial with miniaturized unit cell and broad bandwidth is designed. Its relative bandwidth is 56.4%, and the unit cell electrical size is 0.067 at the central frequency where the LH metamaterial is available. The effective permittivity and effective permeability are extracted from the transmission and reflection data at normal incidence for the LH metamaterial proposed here. The double negative (DNG) property is shown by the simultaneously negative effective permittivity and effective permeability and is confirmed by the equivalent circuit. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1732–1736, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21763

Measurement of negative permittivity and permeability from experimental transmission and reflection with effects of cell misalignment

The measurement of the negative effective permittivity and permeability of a material is a direct way to verify its left-handed properties. In this paper, a transmission experiment for a left-handed material (LHM) sample is performed in a parallel plate waveguide. The effective frequency dispersive permittivity and permeability are retrieved from the experimental scattering data and found to be simultaneously negative in a specific frequency range. The simulation results also show that the misalignments of the metallic inclusions of the LHM introduce some dips to the retrieved curves, which prevent us from obtaining ideal curves following the Lorentz or Drude model.

Tunable metamaterial transmission lines based on varactor-loaded split-ring resonators

In this paper, it is demonstrated that varactor-loaded split-ring resonators (VLSRRs) coupled to microstrip lines can lead to metamaterial transmission lines with tuning capability. Both negative permeability (mu<0) and double (or left-handed) negative media have been designed and fabricated with tuning ranges as wide as 30%. The negative effective permeability is provided by the VLSRRs in a narrow band above their resonant frequency, which can be bias controlled by virtue of the presence of diode varactors. To achieve a negative effective permittivity in the left-handed structure, metallic vias emulating shunt inductances are periodically placed between the conductor strip and the ground plane. The lumped-element equivalent-circuit models of the designed structures have been derived. It has been found that these models provide a good qualitative description of device performance. Since the VLSRR microstrip line and the line loaded with both VLSRRs and vias exhibit stopband and bandpass behavior, respectively, the ideas presented in this study can be applied to the design of narrowband tunable frequency-selective structures with compact dimensions. This is the first time that a tunable left-handed transmission line, based on SRRs, is proposed

Negative effective permeability and left-handed materials at optical frequencies

We present here the design of nano-inclusions made of properly arranged collections of plasmonic metallic nano-particles that may exhibit a resonant magnetic dipole collective response in the visible domain. When such inclusions are embedded in a host medium, they may provide metamaterials with negative effective permeability at optical frequencies. We also show how the same inclusions may provide resonant electric dipole response and, when combining the two effects at the same frequencies, left-handed materials with both negative effective permittivity and permeability may be synthesized in the optical domain with potential applications for imaging and nano-optics applications.

Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies

A three-dimensional lattice of micron-scale coated spheres is shown to have an isotropic negative index of refraction at infrared frequencies. The materials used are entirely non-magnetic. The Mie scattering theory of the constituent spheres is used in the effective medium theory. The physical mechanisms and procedures are presented in the design of a negative effective permeability with solid polaritonic spheres, as well as a negative effective permittivity with solid Drude spheres. It is then shown that a collection of polaritonic spheres coated with a thin layer of Drude material can exhibit a negative index of refraction at infrared frequencies. Comparison with numerical photonic band structure calculations verifies the theory.

Nanofabrication of planar split ring resonators for negative refractive index metamaterials in the infrared range

Experimental nanofabrication of planar structures for one-dimensional metamaterials designed to achieve a negative effective refractive index in the mid-infrared range (5-10 micrometers) was performed. Double split ring and complementary double split ring resonators (SRR and CSRR) with square and circular geometries, were chosen to be fabricated since these are the basic building blocks to achieve a negative effective dielectric permittivity and magnetic permeability. Scanning probe nanolithography with z-scanner movement was used to fabricate straight-line and curvilinear segments with a line width of 80-120 nm. The geometries were delineated in 20 nm thin silver layers sputter-deposited on a positive photoresist substrate spin-coated on polished single crystal silicon wafers, as well as on polycarbonate slabs. The morphology of the structures was characterized by atomic force microscopy. The feature repeatibility was 60-150 nm, depending on the process conditions and the feature complexity. The nanolithographic groove depth in different samples ranged from 4 nm to 80 nm.

Homogenization of a Wire Photonic Crystal: The Case of Small Volume Fraction

We consider the diffraction of a monochromatic incident electromagnetic field by a bounded obstacle made of parallel high conducting metallic fibers of finite length which are periodically disposed. Our goal is to study the asymptotics of this three‐dimensional Maxwell problem as the period, the thickness of the rods, and the resistivity are simultaneously small. We solve this problem in the case where the filling ratio of fibers vanishes but their capacity remains positive. We find a limit volumic density of current which results in a nonlocal constitutive relation between the electric and displacement fields. This extends previous results obtained in the polarized case where a two‐dimensional effective local equation was found with a possibly negative effective permittivity.

Analysis, modeling, and applications of coaxial waveguide-based left-handed transmission lines

In this paper, a new realization of left-handed transmission lines (LHTLs) is presented. The proposed structure employs a coaxial waveguide structure to host periodic arrays of split-ring resonators (SRRs) and capacitively loaded strips (CLSs). The SRRs and CLSs are radially mounted on the inner conductor of the coaxial waveguide structure, which provides the necessary polarization for the periodic arrays of SRRs and CLSs to exhibit a negative index of refraction over a specific frequency band. The structure of the proposed coaxial waveguide-based LHTL (CW-LHTL) is optimized by studying the effect of inductive and capacitive couplings on the performance of the structure. The properties of CW-LHTL are studied by analyzing the dispersion diagram and extracting its effective permittivity and permeability. The analysis shows that the proposed CW-LHTL exhibits negative effective permittivity and permeability around the resonant frequency of the SRRs. The inductive and capacitive couplings of the SRRs and CLSs of a CW-LHTL unit cell are related to the periodicity of left-handed material (LHM) in free space. Therefore, the proposed CW-LHTL provides a reliable measurement setup to study the behavior of LHM in free space without the need to use a large number of unit cells. The coaxial waveguide measurement setup is also used to analyze different modified SRRs, which have a smaller size while operating at the same resonant frequency. A coaxial waveguide structure housing a unit cell of the proposed SRR is fabricated and tested. The measurement results show that the proposed modified SRR is up to 46% smaller in size in comparison with the traditional SRR. The applications of CW-LHTL in guided microwave systems are also discussed.

Superconducting metamaterials

Evanescent wave amplification has been predicted under the ideal condition that the index of refraction, n=−1+i0 precisely, but is difficult to observe in practice because current metamaterials suffer from high losses. We present experimental results on a metamaterial that employs superconducting Nb metals and low-loss dielectric materials. Results include transmission data on a wire, split-ring resonator, and a combination medium at temperatures between 4.2 and 297K. Evidence of negative effective permittivity, permeability, and a negative effective index passband are seen in the superconducting state between 50MHz and 18GHz. We find a dielectric loss of εeff,2=2.6×10−3 in a superconducting wire array at 10.75GHz.

Low-loss left-handed materials using metallic magnetic cylinders

We discuss materials based on arrays of metallic magnetic cylindrical structures near ferromagnetic resonance with applied magnetic fields at microwave frequencies. We have found that the materials have a negative refraction index by combining the effective negative permittivity and permeability. Numerical finite-difference time-domain simulations were performed, after a very large number of geometries were swept. The simulations reveal that ferromagnetic cylinders, with diameters of 0.1 cm and 0.5 cm apart, and with periodic or random configurations, are left-handed materials with very small losses; i.e., with transmittivity practically unity or no loss. The way to obtain convenient structures and geometries is also discussed.

Effective negative refraction index in periodic metal–ferrite–metal film composite

We analyze the refraction index of periodic metal–ferrite–metal film composite in microwave frequencies by the transfer matrix method. We show that the composite can be equal to a homogeneous material with a negative effective refraction index in certain frequencies. Two negative index states have been found in the composite. One has the negative effective permittivity and negative effective permeability simultaneously, and the other only has negative effective permeability. The transition between them can be controlled by the values of electron damping coefficient in the metal films.

Isotropic three-dimensional left-handed metamaterials

We investigate three-dimensional left-handed and related meta-materials based on a fully symmetric multi-gap single-ring SRR design and crossing continuous wires. We demonstrate isotropic transmission properties of a SRR-only meta-material and the corresponding left-handed material which possesses a negative effective index of refraction due to simultaneously negative effective permeability and permittivity. Minor deviations from complete isotropy are due to the finite thickness of the meta-material.

Left handed composite materials in the optical range

The purpose of this paper is to show that semiconductor nano-structures built from non-magnetic InAs/GaAs nano-rings can exhibit simultaneously negative effective permittivity and permeability over a certain optical frequency range. The structures are resonant and have this property near the edge of absorption of the nano-rings. This can be particularly interesting in the investigation of the challenging problem of development of left-handed composite materials in the optical range.

Control of planar nonlinear guided waves and spatial solitons with a left-handed medium

The evidence that double negative media, with an effective negative permittivity, and an effective negative permeability, can be manufactured to operate at frequencies ranging from microwave to optical is ushering in a new era of metamaterials. They are referred to here as 'left-handed', even though a variety of names is evident from the literature. In anticipation of a demand for highly structured integrated practical waveguides, this paper addresses the impact of this type of medium upon waveguides that can be also nonlinear. After an interesting historical overview and an exposure of some straightforward concepts, a planar guide is investigated, in which the waveguide is a slab consisting of a left-handed medium sandwiched between a substrate and cladding that are simple dielectrics. The substrate and cladding display a Kerr-type nonlinear response. Because of the nonlinear properties of the Kerr media, the power flow direction can be controlled by the intensity of the electric field. A comprehensive finite-difference-time-domain (FDTD) analysis is presented that concentrates upon spatial soliton behaviour. An interesting soliton-lens arrangement is investigated that lends itself to a novel cancellation effect.

Stop‐band and band‐pass characteristics in coplanar waveguides coupled to spiral resonators

AbstractCoplanar waveguide (CPW) transmission lines periodically coupled to spiral resonators (SRs) are proposed to obtain very compact band‐pass or rejection‐band structures. The devices consist of a CPW with SRs etched on the back substrate side, underneath the slots. Due to inductive coupling between the line and the spirals, signal propagation is inhibited in the vicinity of the resonant frequency, resulting in a stop‐band structure. However, by periodically loading the line with narrow wires, this behavior is switched to a band‐pass characteristic. This has been interpreted as being due to the coexistence of a negative effective permittivity and permeability in a narrow band above resonance for the composite structure. Since the dimensions of the spirals are very small in comparison to the signal wavelength at resonance, these devices are very compact and can be of interest in applications where miniaturization is mandatory. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 42: 386–388, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20312

Effective negative-/spl epsiv/ stopband microstrip lines based on complementary split ring resonators

In this letter a super-compact stopband microstrip structure is proposed. The frequency gap is produced by an array of complementary split ring resonators (CSRRs)-a concept proposed here for the first time-etched on the ground plane. This behavior is interpreted as due to the presence of a negative effective dielectric permittivity in the vicinity of resonance. The resulting device produces a deep rejection frequency band with sharp cutoff, and a pass band that exhibits very low losses and good matching. Due to the sub-lambda operation of CSRRs, the electrical size of the device is very small.

Study of frequency band gaps in metal–dielectric composite materials

We theoretically investigate the dielectric properties of a granular metal–dielectric composite with negative effective permittivity capable of creating band gaps in a wide range of frequencies. When the effective permittivity of the composite is negative, the electromagnetic (EM) waves will be reflected. The results show that for a given volume fraction lower than the percolation threshold, the effective permittivity of the whole composite can be negative for a certain range of frequencies during which the EM waves are forbidden to propagate in the composite. Considering the different geometrical structure, we discuss the possibility of artificially preparing materials with negative permittivity that would create frequency band gaps. Furthermore, we also investigate a metal–dielectric system with non-spherical inclusion, which leads to multiple frequency gaps for the EM waves.

Experimental study of composite medium with simultaneously negative permeability and permittivity

This paper focuses on a composite medium structure that exhibits simultaneously negative values of effective permeability and permittivity, and our experimental study in an anechoic chamber. The experiment results show that the artificial medium, based on a periodic array of interspaced conducting nonmagnetic split ring resonators and continuous metallic wires, can have a simultaneously negative effective permeability and permittivity within a frequency region in the microwave regime under certain linearly polarized waves.