Left-handed Media Research Articles

The coexistence of TE–TM surface waves in uniaxially anisotropic left-handed materials

We investigate theoretically the characteristics of surface waves in uniaxially anisotropic left-handed materials. The constraints for the existence of TE and TM polarized surface waves in uniaxially anisotropic left-handed materials are identified. We discuss mainly whether TE and TM polarized surface modes may coexist in the same frequency domain at the interface between one isotropic regular medium and another uniaxially anisotropic left-handed medium. It is shown that the answer to the coexistence of TE and TM surface modes is really positive. The Poynting vector and the density of energy associated with surface modes are calculated. Depending on the system parameters either TE or TM surface modes has the time averaged Poynting vector directed opposite or same to the mode phase velocity. In the presence of anisotropy, negative refraction does not need to be left-handed. We show that the characteristics of surface waves in uniaxially anisotropic left-handed media are significantly different from that in isotropic left-handed media.

Excitation of surface and volume electromagnetic waves in left-handed media by an electron bunch

We study theoretically the Vavilov-Cerenkov radiation from a nonrelativistic electron bunch moving in free space over a left-handed medium. It is shown that in the frequency range in which the refractive index of the medium is negative, Vavilov-Cerenkov radiation leads to simultaneous excitation of volume and surface electromagnetic waves in the same frequency range. The wave vector of the surface wave in the plane of an interface of two media is greater in magnitude than the corresponding quantity for the volume wave. The energy fluxes of volume and surface waves in the left-handed medium are studied. The radiation pattern of the bunch is found.

Energy compensated mode in a waveguide composed of lossy left-handed metamaterial

We reveal that stimulated Raman process can be one of the effective ways to compensate the energy loss intrinsic to the optical modes in waveguides composed of left-handed metamaterial. We evaluate the effect of the energy compensating process by using the guided mode’s wave functions multiplied by the envelope functions, which describe the stimulated Raman energy compensating process. Such an evaluation shows that the energy of the optical signal mode in the waveguide with lossy left-handed media can successfully be compensated.

Accurate modeling of the optical properties of left-handed media using a finite-difference time-domain method

This paper contains an important message regarding the numerical modeling of left-handed media (LHM) using the finite-difference time-domain (FDTD) method which remains at the moment one of the main techniques used in studies of these exotic materials. It is shown that conventional implementation of the dispersive FDTD method leads to an inaccurate description of evanescent waves in the LHM. This defect can be corrected using spatial averaging at the interfaces. However, a number of results obtained using the conventional FDTD method have to be reconsidered. For instance, accurate simulation of subwavelength imaging by the finite-sized slabs of left-handed media does not reveal the cavity effect reported by Chen [Phys. Rev. Lett. 92, 107404 (2004)]. Hence the finite transverse dimension of LHM slabs does not have significant effects on the subwavelength image quality, contrary to previous assertions.

Electrodynamics of Left-Handed Medium

It is shown that negative electric permittivity ε and magnetic permeability μ recently discovered in a photonic crystal in the vicinity of the Γ-point are properties of propagating modes only. The evanescent modes rather decay than increase in the bulk of the crystal though they may be amplified by surface waves. If surface support such waves, the evanescent waves may improve the image of a thin Veselago lens. It is shown that a “perfect lens” contradicts to the wave optics and a criterion of “superlensing” is formulated.

Near field in quantum electrodynamics: Green functions, Lorentz condition, “nonlocality in the small”, frustrated total reflection

The local field contribution to some three- and four-level coherent atomic vapors is considered, and a significant modification to optical properties due to dipole-dipole interaction between neighboring atoms is discussed. It is found that the local field effect can reduce loss of a four-level N-type vapor medium at the resonant frequency in both the steady and transient cases. In order to achieve a left-handed medium with a negative refractive index, a scenario to realize simultaneously negative permittivity and permeability inside a mixed coherent atomic vapor by using quantum coherence effect is suggested. One of the remarkable features of the present scheme is such that it can lead to a controllable manipulation of negative refractive index of an atomic vapor by using external coupling and signal fields. This may be a new scheme to fabricate the negatively refracting materials based on quantum optical approach.

Study of the field emitted by a source placed inside a two-dimensional left-handed metamaterial

We studied the properties of electromagnetic waves that were emitted from a source placed inside a left-handed medium based on a two-dimensional labyrinth. While the arguments of geometrical optics suggest that the field emitted from the source would be focused outside the left-handed medium no matter where the source was placed, our results proved the contrary. We found that the field emitted from the source was focused outside the left-handed medium when the source was placed inside the medium at a certain distance away from the interface. Moreover, our results showed that the field emitted from the source was focused on the subwavelength dimensions outside the left-handed medium.

Triangular-Mesh-Based FDTD Analysis of Two-Dimensional Plasmonic Structures Supporting Backward Waves at Optical Frequencies

In this paper, the periodic analysis of candidate plasmonic topologies for the implementation of left-handed media at optical frequencies is pursued through a triangular-mesh-based finite-difference time-domain (FDTD), equipped with Floquet boundary conditions. The technique is shown to possess excellent convergence and accuracy properties, as opposed to the conventional rectangular-cell-based FDTD. The latter fails to accurately capture the plasmonic resonant modes excited in the lattices under consideration. The studies presented in this paper are particularly aimed at rigorously investigating the possibility of backward-wave propagation in periodic arrays of plasmonic nanoparticles, along with their potential analogy to microwave negative-refractive index transmission-line metamaterials

Left-Handed Interfaces for Electromagnetic Surface Waves

We show that surface electromagnetic waves (SEMWs) propagating along two-dimensional (2D) interfaces separating different metamaterials can behave analogously to 3D electromagnetic waves in either usual or left-handed media, depending on the permeabilities and/or permittivities of the two materials forming the interface. We derive the conditions when SEMWs carry energy opposite to the phase velocity. In analogy to three-dimensional (3D) left-handed media, we derive both an anomalous Cherenkov emission and a reversed Doppler effect. We also predict a negative refraction at the boundary between two different interfaces, which can be useful for perfect 2D lensing.

Optimal parameter relations to realize high-power transmission in planar waveguide filled with lossy left-handed material

In a planar waveguide filled with two-layered equal-thickness media, in which one is air and the other is a lossy left-handed medium (LHM) with the relative permittivity ε r 1 = - ( 1 + δ ) + i γ ε and permeability μ r 1 = - 1 / ( 1 + δ ) + i γ μ , we show rigorously that extremely high power densities can be generated and transmitted along the waveguide. In such a lossy super waveguide, the poles in the relevant integrals are complex, whose real parts represent the wavenumbers of guided modes propagating along the waveguide and imaginary parts denote the attenuations of guided modes. We find that optimal values of the retardation parameter δ exist once the loss in LHM is given to make the transmitted power be maximum. Compared with the conventional air-filled waveguide, at an observation point 10 wavelengths away from the source, the transmitted power density in the lossy super waveguide can be 10 000 times larger even when the loss is as high as 10 - 4 and the retardation is as large as - 0.0085 .

Electromagnetic Field Behavior in Dispersive Isotropic Negative Phase Velocity/Negative Refractive Index Guided Wave Structures Compatible with Millimeter-Wave Monolithic Integrated Circuits

A microstrip configuration has been loaded with a dispersive isotropic left-handed medium (LHM) substrate and studied regarding its high frequency millimeter-wave behavior near 100 GHz. This has been accomplished using a full-wave integral-equation anisotropic Green's function code configured to run for isotropy. Never before seen electromagnetic field distributions are produced, unlike anything found in normal media devices, using this ab initio solver. These distributions are made in the cross-sectional dimension, with the field propagating in the perpendicular direction. It is discovered that the LHM distributions are so radically different from ordinary media used as a substrate that completely new electronic devices based upon the new physics become a real possibility. The distinctive dispersion diagram for the dispersive medium, consisting of unit cells with split ring resonator-rod combinations, is provided over the upper millimeter-wave frequency regime.

Localization of light in a lamellar structure with left-handed medium : the Light Wheel

A rigorous analysis of the contra-directional coupling between a left-handed waveguide and a right-handed waveguide shows that such a structure supports twin modes with complex (conjugate) propagation constants. Using evanescent coupling or a source inside one of the waveguides, the twin modes can be excited. In this case, light rotates inside the lamellar structure forming an exotic mode : the light wheel. The structure can finally be seen as a new type of cavity and can be used for beam reshaping.

Seidel aberration of left-handed media lens systems

A general study of the Seidel aberration of the lens systems made of left-handed media is presented according to the primary aberration theory. The Seidel aberration of the planar interface between air and left-handed medium was analyzed showing that its surface shape are more abundant when it is free from spherical aberration and it could be applied to real imaging systems. Based on the Seidel sum formulae of thin lens, three types of left-handed media thin lenses free from partial Seidel aberrations are designed with specific parameters. Finally, the Seidel aberration-free lens systems based on the use of left-handed media are presented. It is pointed out that left-handed media can be used to simplify the structure of lens system for the same or superior imaging performance.

A NEW STRUCTURE FOR LOCALIZING ELECTROMAGNETIC ENERGY USING TWO SEMI-INFINITE LEFT-HANDED-MEDIUM SLABS

It is well known that a left-handed-medium (LHM) slab with negative permittivity −e0 and negative permeability −μ0 can be made as a perfect lens for its negative refraction. In this paper, we show that such two semi-infinite lossless LHM slabs can realize electromagnetic energy localization completely through an accurate analysis. If two current sources with the same amplitude and opposite direction are placed at the right edge of the left LHM slab and the perfect-imaging point of the right LHM slab separately, we have demonstrated that all electromagnetic waves are completely confined in a region between the two sources and there is no power radiating outwards the region.

Size Reduction of SRRs for Metamaterial and Left Handed Media Design

New sub wavelength resonant particles are proposed. The resonant frequency of the particles is reduced by increasing the length of the resonators and increasing the coupling between resonators. Since this frequency reduction is equivalent to an area reduction, the structure can be used to achieve high compactness levels in Left Handed (LH) based circuits. As illustrative example an LH cell is implemented by using this new resonator. DOI: 10.2529/PIERS060727140931

Imaging and Localization Properties of LHM Superlens Excited by 3D Horizontal Electric Dipoles

The interactions of a slightly lossy left-handed medium (LHM) slab with three-dimensional (3D) horizontal electric dipoles (HEDs)are studied. Different from other types of sources, HED will excite both transverse electric (TE) and transverse magnetic (TM) modes inside the LHM slab. We have investigated the imaging and localization properties of the LHM slab excited by a single HED or two opposite HEDs. We demonstrate that nearly all propagating components and parts of evanescent components emitted by a single HED can be recovered at the image points to achieve the super-resolution. We also show that nearly all electromagnetic energies produced by two opposite HEDs located at image points of the LHM slab are localized in a region between the two sources. Numerical results validate our conclusions.

Antiferromagnetic material with the magnetoelectric effect as an example of a left-handed medium

The propagation of electromagnetic waves in an antiferromagnetic material with the magnetoelectric effect is theoretically studied. The frequency dependences of the wavenumbers, dynamical permeability and permittivity, and reflection coefficient of electromagnetic waves for various energy parameters of the antiferromagnetic material have been obtained. It has been shown that there is a frequency range where the dynamical permeability and permittivity, as well as one of the wavenumbers, are simultaneously negative in the antiferromagnetic material with the magnetoelectric effect. In this case, the antiferromagnetic material is an example of a so-called left-handed medium. The reflection coefficient of electromagnetic waves from the surface of the antiferromagnetic material decreases anomalously in this frequency range.

Backward wave propagation in left-handed media with isotropic and anisotropic permittivity tensors

The backward-wave phenomenon in an isotropic medium is investigated from a purely wave propagation point of view. The functional form for the index of refraction necessary to produce such behavior is derived using the condition that the phase and group-velocity vectors are antiparallel. It is shown that, in the case considered, the backward-wave propagation can be attained only in a medium where the index is negative. A more general case is then considered where the angle between the phase velocity and group velocity is allowed to vary between 90° and 270°. It is shown that such behavior requires propagation through an anisotropic medium where at least one of the axes has a negative index and the general form of the index along each of the three principal axes is derived. The condition that the group velocity must be positive in the transmission passband is then used to obtain the required minimum dispersion for a medium with negative index for both the isotropic and the anisotropic cases.

Perturbation on the perfect lens: the near-perfect lens

We present the full wave solution for a dipole source above a slab of left-handed medium of refractive index n = −1, but with ϵ and μ differing from those ideal values that create the perfect lens through taking ϵ = −(1+δ)−1 and μ = −(1+δ), where δ, and hence ϵ and μ, are real. Any modifications in resolution are therefore not due to loss effects within the lens. Finite solutions for the form of the fields throughout all space are obtained using the method of Hertz potentials, thereby regularizing the singular perfect lens solution. This regularization will facilitate subsequent perturbation analyses. Using an appropriately defined criterion, we examine the sensitivity of the lens resolution to the material imperfection δ. It is found that the resolution converges logarithmically with δ upon that of the perfect lens. Comparison of theoretical results with experimental data suggests that even this slow convergence is the best that can be achieved.

Wave refraction and backward magnon–plasmon polaritons in left-handed antiferromagnet/semiconductor superlattices

Characteristics of the bulk electromagnetic waves in teraHertz frequency region are examined in a left-handed superlattice (SL) which consists of alternating layers of nonmagnetic semiconductor and nonconducting antiferromagnetic materials. General problem on the sign of the refractive index for anisotropic media is considered. It is shown that the phase refraction index is always positive while the group refractive index can be negative when some general conditions are fulfilled. Effective permittivity and permeability tensors of the SL are derived for perpendicular and parallel orientation of the magnetic anisotropy axis with respect to the plane of the layers. Problem of anomalous refraction for transverse electric and transverse magnetic-type polarized waves is examined in such media. Analytical expressions for both the phase and group refractive indices are obtained for various propagated modes. It is shown that, in general, three different types of the refracted waves with different relative orientation of the phase and group velocity vectors are possible in left-handed media. Unusual peculiarities of the backward modes corresponding to the coupled magnon–plasmon polaritons are considered. It is shown, in particular, that the number of the backward modes depends on the free charge carrier's density in semiconductor layers, variation of which allows to create different frequency regions for the wave propagation.