Direct calculation of permeability and permittivity for a left-handed metamaterial
TL;DR: In this article, an electromagnetic metamaterial was fabricated and demonstrated to exhibit a "left-handed" (LH) propagation band at microwave frequencies, a situation never observed in naturally occurring materials or composites.
Abstract: Recently, an electromagnetic metamaterial was fabricated and demonstrated to exhibit a “left-handed” (LH) propagation band at microwave frequencies. A LH metamaterial is one characterized by material constants—the permeability and permittivity—which are simultaneously negative, a situation never observed in naturally occurring materials or composites. While the presence of the propagation band was shown to be an inherent demonstration of left handedness, actual numerical values for the material constants were not obtained. In the present work, using appropriate averages to define the macroscopic fields, we extract quantitative values for the effective permeability and permittivity from finite-difference simulations using three different approaches.
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TL;DR: In this paper, the authors present a homogenization technique in which macroscopic fields are determined via averaging the local fields obtained from a full-wave electromagnetic simulation or analytical calculation.
Abstract: Over the past several years, metamaterials have been introduced and rapidly been adopted as a means of achieving unique electromagnetic material response. In metamaterials, artificially structured—often periodically positioned—inclusions replace the atoms and molecules of conventional materials. The scale of these inclusions is smaller than that of the electromagnetic wavelength of interest, so that a homogenized description applies. We present a homogenization technique in which macroscopic fields are determined via averaging the local fields obtained from a full-wave electromagnetic simulation or analytical calculation. The field-averaging method can be applied to homogenize any periodic structure with unit cells having inclusions of arbitrary geometry and material. By analyzing the dispersion diagrams and retrieved parameters found by field averaging, we review the properties of several basic metamaterial structures. © 2006 Optical Society of America OCIS codes: 160.0160, 160.1190, 260.2110, 350.5500.
581 citations
TL;DR: It is shown that, in this line, left-handedness can be achieved without losses over an unlimited bandwidth, from the cutoff of the resulting high-pass filter to infinity, with excellent agreement with theory.
Abstract: A transmission line (TL) approach of left-handed (LH) materials is proposed. The transmission characteristics of an ideal LH-TL are presented, the constitutive parameters of an equivalent LH material are derived and shown to be negative, and some LH-transmission paradoxes are explained. Next, a method to design an artificial LH-TL in the form of an ideal lumped-elements ladder network is described and illustrated with simulation results. It is shown that, in this line, left-handedness can be achieved without losses over an unlimited bandwidth, from the cutoff of the resulting high-pass filter to infinity, with excellent agreement with theory. Finally, a microstrip implementation of the LH line for microwaves, using interdigital capacitors and stub inductors, is demonstrated, with moderate insertion loss and a broad bandwidth of the order of 100%.
558 citations
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...It should be noted that the expression derived here for strongly differs from the resonant expression characterizing previously reported LH materials [2], [8], [30], [31]....
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TL;DR: In this article, a composite medium consisting of insulating magnetodielectric spherical particles embedded in a background matrix is studied and it is shown that the effective permeability and permittivity of the mixture can be simultaneously negative for wavelengths where the spherical inclusions are resonant and that the medium results in an effective "double negative" media.
Abstract: We study a composite medium consisting of insulating magnetodielectric spherical particles embedded in a background matrix. Using results from the literature going back as far as Lewin (1947), we show that the effective permeability and permittivity of the mixture can be simultaneously negative for wavelengths where the spherical inclusions are resonant and that the medium results in an effective "double negative (DNG) media". Materials of this type are also called negative-index materials, backward media (BW), and left-handed materials. This type of material belongs to a more general class of metamaterials. The theoretical results presented here show that composite media having much simpler structure than those reported in the literature can exhibit negative permeability and permittivity over significant bandwidths.
407 citations
TL;DR: In this article, the authors developed an effective medium description of a two-dimensional photonic band-gap medium composed of dielectric cylinders of large Dielectric constant, and derived an effective permittivity and permeability for the composite.
Abstract: We develop an effective medium description of a two-dimensional photonic band-gap medium composed of dielectric cylinders of large dielectric constant. Using the transfer matrix method we have calculated reflection coefficients for a slab of the composite and plane-wave incidence, as well as the (complex) wavevector for the infinite system. From these quantities we derive an effective permittivity and permeability for the composite. In the case of p-polarized incidence the composite displays a negative magnetic permeability at microwave frequencies due to single-scatterer resonances in the medium.
340 citations
TL;DR: In this article, the dispersion relations of the surface polaritons of a slab made of a material which has dispersive permittivity and permeability, and is left-handed over a frequency band in the microwave range of several GHz, are investigated.
Abstract: The dispersion relations of the surface polaritons of a slab made of a material which has dispersive permittivity and permeability, and is left-handed over a frequency band in the microwave range of several GHz, are investigated. Four branches of p polarized surface polaritons and two branches of s polarized ones are found to exist. The possibility of experimentally observing the surface polaritons by the attenuated total reflection method is demonstrated.
204 citations
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10,495 citations
TL;DR: In this paper, it was shown that microstructures built from nonmagnetic conducting sheets exhibit an effective magnetic permeability /spl mu/sub eff/, which can be tuned to values not accessible in naturally occurring materials.
Abstract: We show that microstructures built from nonmagnetic conducting sheets exhibit an effective magnetic permeability /spl mu//sub eff/, which can be tuned to values not accessible in naturally occurring materials, including large imaginary components of /spl mu//sub eff/. The microstructure is on a scale much less than the wavelength of radiation, is not resolved by incident microwaves, and uses a very low density of metal so that structures can be extremely lightweight. Most of the structures are resonant due to internal capacitance and inductance, and resonant enhancement combined with compression of electrical energy into a very small volume greatly enhances the energy density at critical locations in the structure, easily by factors of a million and possibly by much more. Weakly nonlinear materials placed at these critical locations will show greatly enhanced effects raising the possibility of manufacturing active structures whose properties can be switched at will between many states.
8,135 citations
TL;DR: A composite medium, based on a periodic array of interspaced conducting nonmagnetic split ring resonators and continuous wires, that exhibits a frequency region in the microwave regime with simultaneously negative values of effective permeability and permittivity varepsilon(eff)(omega).
Abstract: We demonstrate a composite medium, based on a periodic array of interspaced conducting nonmagnetic split ring resonators and continuous wires, that exhibits a frequency region in the microwave regime with
8,057 citations
TL;DR: In this article, an effective description for a metalodielectric photonic bandgap (PBG) material was developed for a semi-infinite and slab observables.
Abstract: An effective description is developed for a metalodielectric photonic bandgap (PBG) material far beyond the quasi-static limit of traditional effective-medium theories. An analytic approach, recently presented by the authors, is further advanced to provide the complete effective permittivity and permeability functions. Reflection and transmission coefficients are presented for both TM and TE oblique plane-wave incidence, based on the determination of the equivalent impedance for each lattice plane in the crystal and the transfer-matrix method for reconstructing the effect of successive lattice planes. An analysis of the semi-infinite and slab observables yields the anisotropic effective refractive index, effective permittivity, and effective permeability, thus completing the macroscopic description of the interaction of electromagnetic waves with the medium. Among the novel aspects of the analysis is the equivalence of our PBG system with a physically dispersive system at ultraviolet frequencies and the derivation and explanation of the development of high dispersive magnetization (permeability) for these media, independently of the microscopic magnetic properties of the metallic implants.
44 citations