Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial

Abstract

Metamaterials are periodic structures, patterned on a scale much shorter than the operating wavelength. Though they are made of positive index materials at small length scale, these structures exhibit abnormal dispersion characteristics at large scale. The material can indeed exhibit a strong anisotropy, or behave as a medium of negative index of refraction-associated with negative values of the permittivity and permeability. In such periodic media, propagation of light, or generally of electromagnetic waves, can be backward. The wave vector, k, electric field, E, and magnetic field, H, then constitute an indirect trihedron, where k and the Poynting vector, S, are antiparallel. In this case, they are termed left handed materials as proposed by Veselago in 1968 [1].The breakthrough, however, was provided in 1999 by Pendry et al. in [2], when they presented several examples of how one can obtain negative values of and from conductors. The most interesting of them was a split-ring resonator, an array of which provided a negative value of over a portion of its resonance frequency range. The combination of the rods and split-ring resonators yielded an artificial medium possessing both a negative and over a narrow frequency range. Encouraged by the implications of these results, a team at the University of California at San Diego built a composite medium along these lines at microwave frequencies, and made measurements that clearly demonstrated that this medium exhibited a negative index of refraction [3]. These measurements proved that the physical effect is real and leaded to a series of fascinating, novel, and practical microwave components. Among these are forward or backward directional couplers with improved features like arbitrary coupling ratios, shorter coupling lengths, broader bandwidths, etc. Other coupling components with improved features include branch-line couplers and hybrid rings. A different type of novel component that followed directly from the backward-wave property is a leaky wave antenna that can be frequency scanned or electronically scanned from backward endfire through broadside to forward endfire.Beyond this inversion of the phase velocity with respect to the direction of propagation of energy, the main impact of a negative refractive index, n, may be found in the negative refraction [3][4][5]. Both the incident and refracted beam are then on the same side of the normal to the refraction interface, as predicted by Snell's law, with a negative refractive index. Under this condition, any radiating source placed in front of a slab of negative refractive index shows focusing effects within and outside the slab under near field conditions. One can thus build flat lenses (Veselago/Pendry lenses), whose properties are invariant upon translation parallel to their surface. Besides this, as proposed recently by Smith et al. [4], one prospect is also to avoid the diffraction limit with the so-called "superlens effect." In the far field limit using a vanishing index [4] may also contribute to the colli...

The Forward Transmission Matrix (Ftm) Method for S-Parameter Analysis of Microwave Circuits and Their Metamaterial Counterparts

“…The design frequency of 0.9 GHz lies within the lowest fundamental band (i.e., 1.2 GHz). Note that the electromagnetic wave in this band takes place as a backward-wave mode which is identified by the negative slope of the Brillouin diagram and is the hallmark of left-handed metamaterial-TLs [7,8,16]. The design criteria of 0.125π phase shift at 0.9 GHz and the stop band between 1.2 and 2.5 GHz are indeed satisfied.…”

“…Metamaterials have stirred up exciting new dimensions in the fields of Electromagnetics and Physics in the past decade [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Here we focus on metamaterial transmission lines (TL) also known as left-handed transmission lines [9,10,[13][14][15][16][17][18][19][20][21][22][23][24].…”

“…The paper also serves as an introduction to the design and operation of the metamaterialsbased devices [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] which will be analyzed using the proposed method along with their conventional equivalents. We develop a systematic nodal analysis approach based on the Kirchhoff's current rule which is tailored to the high frequency networks by ABCD matrix representation of the circuit branches.…”

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Uniaxial PML Absorbing Boundary Condition for Truncating the Boundary of DNG Metamaterials

“…Recently, several papers have exposed the usefulness of double negative (DNG) medium with negative permittivity and permeability [2][3][4][5]. However, in order to further study unusual electromagnetic phenomena in DNG medium, full-wave numerical simulations have become more and more important.…”