Left-handed materials do not make a perfect lens

By means of an analysis on evanescent waves in left-handed materials (LHM), we show that within a slab of such a medium, sandwiched between two positive refraction media, there is amplification of evanescent waves in ideal lossless, dispersiveless media; however, contrary to previous claims, this is limited to a finite width of the slab so that it prevents their restoration and perfect focusing. We illustrate this by considering their coupling to propagating waves through a tunnel barrier containing a slab of LHM. Further, we show that the effect of absorption, necessarily present in such materials, may drastically change any evanescent amplifying wave into a decaying one.     

Evanescent waves of an annular left-handed material lens

The imaging system formed by an annular left-handed material （LHM） lens as well as the evanescent waves in the lens are simulated numerically with a finite-difference time-domain （FDTD） method. For b - a 〉 λ （a and b are respectively the inner and outer radii of the annular lens, and λ is the wavelength）, when a point source is placed at an internal grid point, we demonstrate that the evanescent waves are produced around the internal interface, and cannot propagate outwards. As for b - a 〈λ ）,, the evanescent waves appear around both the internal and the external interfaces, which remarkably implies the coupling between the two interfaces. Hence it can be inferred that the evanescent waves around the external interface participating in the super-resolution imaging result from the coupling of the evanescent waves around the interface. Moreover, the partly uncomprehended properties of the evanescent waves in the LHM slab are also disclosed. It is conducive to understanding the evanescent waves in the LHMs further.     

Numerical analysis of propagation characteristics of electromagnetic wave in lossy left-handed material media

The propagation characteristics of electromagnetic wave in lossy left-handed materials (LHM) are studied using finite-difference time-domain (FDTD) method base on auxiliary differential equation (ADE) technology. The LHM medium is realized with lossy Drude models for both the negative electric permittivity and the negative magnetic permeability. The discretized ADE-FDTD equations are derived in detail. The incident wave used in the simulation is a multiple cycle m-n-m pulses source. The term of Poynting's vector E_xH_y was calculated. These numerical results demonstrate conclusively that the phase velocity direction of electromagnetic wave propagation and the direction of the Poynting vectors are anti-parallel in LHM. The amplitude of electric field is reduced with the enhancive distance of LHM slab. It is also demonstrated that the energy of electromagnetic wave in the LHM slab is obviously attenuated, and the attenuation of energy becomes stronger with the angular plasma frequency ω_p increasing. These results indicate that LHM stealth is effective in theory, and reasonable selection of the large negative index of refraction can greatly enhance its effectiveness.     

Guided modes in slab waveguides with a left handed material cover or substrate

We study guided modes propagating along a dielectric slab waveguide with a left handed material (LHM) cover or substrate. The dispersion relation is derived by using normalized waveguide parameters. An analytical method is then proposed to calculate the universal dispersion curves. Different from a slab waveguide with a LHM core, we find that guidance properties are strongly dependent on dielectric permittivity ε and magnetic permeability μ of the substrate and cover layers. For oscillating guided modes, fundamental zero order mode is not always absence, sometimes it exists in a restricted range of normalized propagation constant. First order mode behaves as other higher order modes and exists up to infinite high frequency. Higher order modes have no double degeneracy in the case of LHM cover layer. For surface guided modes, the existence and the type of the mode solutions with respect to different parameters are classified systematically and discussed in detail. Unlike a slab waveguide with a LHM core where the dispersion curve of TE₁ surface mode continues with that of oscillating TE₁ mode, the dispersion curve of TE₁ surface mode continues with that of oscillating TE₀ mode. It seems that the two different kinds of modes compensate each other to form one whole mode. Both TE and TM guided modes are discussed.     

TM waves in cylindrical superlattices (LANS) bounded by left-handed material (LHM)

The investigation of TM wave propagation inside a cylindrical waveguide composed of antiferromagnetic/nonmagnetic superlattices (LANS), bounded by left-handed material (LHM), is presented. We have derived the eigenmode equation and obtained the solutions for TM propagation modes. We found that the waveguide supports backward TM waves since both electric permittivity and magnetic permeability of the LHM are negative. We also illustrated the dependence of the wave index n _x on the magnetic fraction f ₁ and the reduced radius of the LANS. The largest propagation lengths of TM waves and the best confinement are achieved for the thinnest LANS of less magnetic material. Moreover, we displayed the influence of the magnetic permeability μ _h and the electric permittivity ε _h of the LHM on the power flow of TM waves. Larger wave indices have been switched by increasing μ _h and ε _h .     

Finite-size effects of a left-handed material slab on the image quality

The characteristics of an imaging system formed by a left-handed material (LHM) slab of finite length are studied, and the influence of the finite length of the slab on the image quality is analyzed. Unusual phenomena such as surface bright spots and negative energy stream at the image side are observed and explained as the cavity effects of surface plasmons excited by the evanescent components of the incident field. For a thin LHM slab, the cavity effects are found rather sensitive to the length of the slab; the bright spots on the bottom surface of the slab may stretch to the image plane and degrade the image quality.     

Propagation of p-polarized waves in a linearly graded index film surrounded by negative index materials

The theory of step-index waveguides is well-established. Most practical slab waveguide structures have a graded-index profile. The basic properties of graded-index planar waveguide structures are similar to those of step-index waveguides with subtle differences. The most common types of graded-index slab waveguides are linearly and exponentially graded-index profiles. We here treat linearly graded-index slab waveguide. In this work, a three-layer waveguide structure with linearly graded-index film is considered. We assume three structures: the first structure comprises a left-handed material (LHM) cladding, the second structure contains a LHM substrate layer and the third has a LHM cladding and substrate. Closed-form expressions for electric and magnetic fields and the characteristic equation are derived. The three normalized parameters: the asymmetry coefficient (a), the normalized film thickness (V) and the normalized guide index (b) are used to study the dispersion properties of the proposed slab waveguide structure.     

包含左手材料的四层平板波导中的光导模

研究一个芯子层是左手材料,其他三层由传统材料构成的四层平板光波导系统,利用图解法对各种TE偏振的导波模式的解进行详细分析.研究表明,四层左手材料光波导既能支持振荡导模,也能支持表面导模,与三层左手材料光波导相比较,此四层波导的导波模式呈现一些新的特性.对于中间传统材料层存在振荡场的情形:芯子层支持振荡导模的光波导中存在基模,并且高阶振荡导模出现模式缺失的性质;芯子层支持表面导模的光波导可以支持基模和多个高阶模式,并且存在模式兼并的性质.对于中间传统材料层存在衰减场的情形,此四层波导结构可等效为三层左手材料光波导.这些新的光波导传输性质对各种光波导器件的制作有潜在的应用价值.     

Structure for localizing electromagnetic waves with a left-handed-medium slab and a conducting plane

A new structure is proposed for localizing electromagnetic waves and energies with a left-handed-medium (LHM) slab and a perfectly electrically conducting (PEC) plane. When a current source is placed in front of a perfectly matched LHM slab with negative permittivity -epsilon0 and negative permeability -mu0 and a PEC plane is placed at the image point, we show rigorously that all the electromagnetic waves are confined in a region between the source and the PEC plane, and the fields outside the region are completely zero. Such an energy-localization system would be useful in medical treatments that use concentrated optical and microwave energies. However, a perfectly matched LHM is unphysical and does not exist in nature. Hence we further study the loss and retardation effects of LHM on the energy localization. Numerical results are presented for the lossy LHM structure to demonstrate the energy localization.     

Electron-beam instability in left-handed media

We predict that two electron beams can develop an instability when passing through a slab of left-handed media (LHM). This instability, which is inherent only for LHM, originates from the backward Cherenkov radiation and results in a self-modulation of the beams and radiation of electromagnetic waves. These waves leave the sample via the rear surface of the slab (the beam injection plane) and form two shifted bright circles centered at the beams. A simulated spectrum of radiation has well-separated lines on top of a broad continuous spectrum, which indicates dynamical chaos in the system. The radiation intensity and its spectrum can be controlled either by the beams' current or by the distance between the two beams.     

Left-handed metamaterial based superlens for subwavelength imaging of electromagnetic waves

Lenses made of negative index materials have the ability to focus the propagating and evanescent components of electromagnetic waves. Such a possibility enables super resolution, in turn resulting in sharper, subwavelength size images. In this present work, we present subwavelength imaging that was obtained from a one-dimensional left-handed metamaterial (LHM) composed of alternating layers of split-ring resonators and thin wires. We investigated the effect of the thickness of LHM lenses on image size. The left-handed pass band within the negative permittivity and permeability region is shown experimentally and theoretically for different thicknesses of LHM slabs. We also studied the transmission-phase of LHMs with a different number of unit cells along the propagation direction. The phase decreases with the increasing thicknesses of LHM slabs, proving that the phase velocity is negative in the left-handed transmission band. PACS 42.25.-p; 41.20.Jb; 81.05.-t     

Metamaterials: from microwaves to the visible region

In a recent paper, J.B. Pendry [J.B. Pendry, Negative refraction makes a perfect lens, Phys. Rev. Lett. 86 (2000) 3966–3969] has mentioned the possibility of making perfect lenses using a slab of left-handed material with relative permeability and permittivity equal to −1. He gave a demonstration of the vital influence of the evanescent waves in this process, arguing that these waves are amplified inside the slab. In the present paper, we first try to give a rigorous electromagnetic demonstration of Pendry's statement, and we show that in fact the integral expression of the field in a region of space diverges. Since this divergence does not prove that the perfect lens does not exist, we then give a very simple theoretical demonstration that a homogeneous material with both relative permittivity and permeability equal to −1 cannot exist, even for a unique frequency. However, thanks to the heterogeneous nature of a metamaterial, it is shown that a material able to focus light more efficiently than current devices (but not perfectly) could exist. Finally, it is shown that a plane slab of dielectric photonic crystal can also focus light, a property which could be crucial for construction of superlenses in the visible and infrared regions. To cite this article: D. Maystre et al., C. R. Physique 6 (2005).     

Spatial separation of the traveling and evanescent parts of dipole radiation

Electric dipole radiation consists of traveling and evanescent plane waves. When radiation is detected in the far field, only the traveling waves will contribute to the intensity distribution, as the evanescent waves decay exponentially. We propose a method to spatially separate the traveling and evanescent waves before detection. It is shown that when the radiation passes through an interface, evanescent waves can be converted into traveling waves and can subsequently be observed in the far field. Let the radiation be observed under angle theta(t) with the normal. Then there exists an angle theta(ac) such that for 0 < or = theta(t) < theta(ac) all intensity originates in traveling waves, whereas for theta(ac) < theta(t) < pi/2 only evanescent waves contribute. It is shown that with this technique and under the appropriate conditions almost all far-field power can be provided by evanescent waves.     

Effect of surface contamination on the heat of adsorption of gases on metals

In the infrared surface electromagnetic waves (SEW) can propagate several centimeters over a metal and some ferroelectrics. Therefore SEW can be used to integrate overlayer surface absorption over very much larger path lengths than in the usual transmission and reflection surface studies. Using a continuum model, we have calculated the surface electromagnetic wave modes for a dielectric slab on a metal against a third (weakly absorbing) medium. Unlike previous treatments, absorption has been included and the absorption expected using the two prism SEW technique has been calculated. For a thick slab (1 mm or more), we show that the absorption coefficient of the slab material can be obtained very simply. For very thin slabs both surface-plasmon-like modes and surface-phonon-like modes (including Fuchs-Kliewer modes) are found. A new parameter Δ₁ + iΔ₂ is introduced to describe the thin film absorption. It has the physical significance of an effective susceptibility for the metal-coating-overlayer system. Further, its experimental significance is that for the normalized transmission of SEW between two prisms, Δ₂ is a dominating parameter which can be measured. For the two prism experiments, numerical examples show 50 percent absorption at peak for a monolayer of CO on Pt and a 4 percent absorption for CuO on copper. Applications to the study of thin films, catalysis, corrosion and other surface problems are anticipated.     

Transmission properties of asymmetric slab waveguides with left-handed materials

A new dielectric slab waveguide with a left-handed material (LHM) cover and substrate is proposed. The dispersion relations and normalized effective thickness of the asymmetric LHM slab waveguide are investigated, in view of the normalized parameters. A number of unusual properties are found, for example, the fundamental and first-order modes do not exist and higher-order modes have double degeneracy. The propagation modes are absent at the low normalized frequency, and the cutoff frequencies of some LHM slab waveguide modes decrease with increase in the asymmetry measure. Unlike traditional slab waveguides, the V –H curves of the LHM slab waveguides are in one-to-one correspondence. Both TE and TM modes are discussed; in addition, the dispersion relations and normalized effective thicknesses of the TM modes are discussed in detail, when the difference in refractive indices of the film and the substrate is small. The results show that the region of mode coexistence taking place near the cutoff frequency becomes narrower with increase in the difference in refractive indices of the film and the substrate. The influence of this difference on the normalized effective thickness curves is different, and becomes smaller and smaller with increase in the value of the asymmetry measure, if different values of the refractive indices are employed.     

源嵌入正折射率传输线介质板内的倏逝波和成像特性

 提出了点源嵌入正折射率介质板进行亚波长成像的新方法,分析了位于负折射率媒质里的正折射率介质板内外的电压倏逝波和电压传播波分布。正和负折射率媒质分别由2维未加载传输线和2维加载电感、电容传输线网络组成。微波电路和数值仿真结果都显示由于板内增大的倏逝场,在正折射率介质板的两个界面附近出现了很大的电压幅度,该结果证实了该正折射率介质板透镜能够恢复电压倏逝波,从而提高像的分辨率。     

Analysis of the dispersion relations of nonlinear slab-guided waves

The dispersion relations of TE-polarized nonlinear guided waves (NGW) were investigated in detail. These waves travel along a dielectric slab embedded between two different nonlinear media. A simple relation between the effective nonlinear dielectric constants was established. All dispersion curves exhibit a particular transition point, where one evanescent field maximum changes from a virtual into a real one, and vice versa. Depending on the type of the remaining invariant evanescent field maximum, all NGW's split into two families. The lowest-order membres of every family play a particular role. The power flux supported by a NGW is derived, too.Preliminary results were presented at the XVI^th European Congress of Molecular Spectroscopy, Sofia, Bulgaria (1983)     

Extension of the classical Fabry–Perot formula to 1D multilayered structures

In any field theory the interaction of a wave packet with a multilayered potential is of high theoretical and practical relevance. In the present work we show an extension to any number of layers of the classical Fabry–Perot formula that works for any level of absorption, any thickness of the composing layers, any number of layers, any angle of incidence and for evanescent waves as well. More specifically, the ability of dealing with input evanescent waves and complex metal-based structures is of special interest for superlenses analysis and design. Some explicit examples in electromagnetism are also discussed.     

Parametric studies on left-handed metamaterial consist of modified split-ring resonator and capacitance loaded strip

This paper describes a new structure of left-handed metamaterial (LHM) based on parametric studies using Computer Simulation Technology (CST) software. The LHM structure is a combination of the modified square rectangular split ring (MSRR) and the capacitance loaded strip (CLS). In this paper, the parametric studies are used to see the effect of frequency and the negative value range of permeability (μ _r ) and permittivity (ε _r ) toward changes of LHM parameters. The changes in the dimension of MSSR and CLS affect the S ₁₁ and S ₂₁ of the LHM structure which will affect the values of permeability and permittivity. The values of permeability and permittivity were extracted from the reflection and transmission coefficient data. The studies proved that the LHM structure can be designed within the frequency range of interest.     

Focusing and phase compensation of paraxial beams by a left-handed material slab

On the basis of angular spectrum representation, a formalism describing paraxial beams propagating through an isotropic left-handed material (LHM) slab is presented. The treatment allows us to introduce the ideas of beam focusing and phase compensation by LHM slab. Because of the negative refractive index of LHM slab, the inverse Gouy phase shift and the negative Rayleigh length of paraxial Gaussian beam are proposed. It is shown that the phase difference caused by the Gouy phase shift in right-handed material (RHM) can be compensated by that caused by the inverse Gouy phase shift in LHM. If certain matching conditions are satisfied, the intensity and phase distributions at object plane can be completely reconstructed at the image plane.