Erratum to: “Comment on: ‘Electromagnetic wave propagation in single-wall carbon nanotubes’ [Phys. Lett. A 333 (2004) 303]” [Phys. Lett. A 364 (2007) 515]

Here we plot the correct form of Fig. 2 in [H. Khosravi, A. Moradi, Phys. Lett. A 364 (2007) 515].     

Comment on: “Electromagnetic wave propagation in single-wall carbon nanotubes” [Phys. Lett. A 333 (2004) 303]

In a recent article [L. Wei, Y.-N. Wang, Phys. Lett. A 333 (2004) 303], Li Wei and You-Nian Wang studied the propagation of electromagnetic wave in single-wall carbon nanotubes and presented different expressions of the dispersions relations of TE and TM modes, respectively. Here we have derived the correct form of the dispersion relation for TM mode on low-frequency electromagnetic wave. It is shown numerically that asymptotic behaviours of the TM and TE modes are quite similar in single-wall carbon nanotubes.     

Controlling of Slope of Carrier-Envelope Phase of Few-Cycle Laser Pulses on Propagation Distance near the Focus

The effect of focusing geometry on slope of carrier-envelope （CE） phase ФCE versus propagation distance from the focus in few-cycle laser pulses is investigated. The slope could be adjusted by changing the distance L between the waist of the incident beam and the lens. At the focus, 偏dФCE/O（Z/ZR） = 0 when L = 0, and 偏dФCE/偏d（z/zR） = -2 when L = ∞. The longer the distance L, the steeper the curve of the CE phase at the focus.     

Frequency Response of Multilayer Media Comprised of Double-Negative and Double-Positive Slabs

We present the interactions of the electromagnetic waves with multilayer media formed by double-negative and double-positive slabs to find the frequency response of the structure. The double-negative slabs are analytically realized by using the frequency dispersive cold plasma medium. Numerical examples are performed using an in-house developed simulation programme code. The variation of the reflectance and the transmittance with the emphasis on the plasma frequencies is observed in these examples.     

Rigorous electromagnetic analysis of dual-closed-surface microlens arrays

In this paper, we investigated the focal performance of the dual-closed-surface microlens arrays (DCSMAs) based on rigorous electromagnetic theory and boundary element method (BEM) in the case of TE polarization. The DCSMAs are designed with different substrate thickness and different distance between microlenses. DCSMAs designed according to different wavelengths are surveyed. The DCSMAs with different incident angles are also studied. Several focusing performance measures, such as the focal spot size, the focal position on the preset focal plane, the diffraction efficiency and the normalized transmitted power, are presented. Numerical results indicate the DCSMAs with different parameters can implement focusing beams and the focal performance of DCSMAs is easily influenced by the substrate thickness and the incident wavelength. Furthermore, the optimal thickness for the maximal diffraction efficiency of the DCSMAs is given. It is expected that the DCSMAs may be used as a parallel processing device in micro-optics systems.     

Total reflection of electromagnetic waves propagating from an isotropic medium to an indefinite metamaterial

The existence conditions for total reflection and the corresponding critical angle at the interface separating an isotropic medium and an indefinite metamaterial for TE- and TM-polarized electromagnetic waves are obtained. For different kinds of indefinite metamaterial, there appear different total reflection phenomena. Particularly, the anomalous total reflection in which the incident angle is smaller than the critical angle and the Brewster’s angle can be smaller than the critical angle can occur for anti-cutoff medium. Furthermore, the omnidirectional total reflection exists for the always cutoff medium and anti-cutoff medium. The total reflection depends on the thickness of indefinite metamaterial when the indefinite metamaterial is finite, and the photon tunneling phenomenon can occur when the thickness of indefinite metamaterial is smaller than wavelength.     

A polarization-dependent wide-angle three-dimensional metamaterial absorber

In this paper, a polarization-dependent wide-angle three-dimensional metamaterial absorber with a near-unity absorbance was presented. The metamaterial absorber structure is composed of coplanar electric and magnetic resonators. By carefully adjusting the structural dimensions, less-than-unity ε and/or μ can be realized. To match the impedance of free space, the structural dimensions were adjusted so that ε=μ, which guarantees minimum reflection. Since the resonance-based structure is made of metallic resonators and lossy substrates, the imaginary part of refractive index is large, which guarantees strong absorption of transmitted waves. Full-wave simulations confirmed the effectiveness of the proposed three-dimensional metamaterial absorber.     

A Zone Plate as a Tunable Terahertz Filter

A broadband tunable terahertz filter based on a zone plate is demonstrated in our terahertz time domain spec- trometer. The central bandpass frequency covers the whole spectral range of the terahertz wave emitted from a ZnTe emitter, from 0.5 THz to 2.5 THz, and can be tuned continuously by simply moving the zone plate along the terahertz beam path. The peak transmission is about 40% and the bandwidth varies from 0.16 THz to 0.25 THz at different bandpass frequencies when the aperture size is kept constant.     

Focal Shift of Paraxial Gaussian Beams in a Left-Handed Material Slab Lens

Focal shift is inevitable in conventional lens systems due to the Fresnel number and angular aperture. In this Letter, we demonstrate that there is no focal shift when a paraxial Gaussian beam passes through a left-handed material slab lens without absorption or gain. However, the effect is exhibited in the presence of absorption or gain, and becomes larger as the absorption or gain increases. When the absorption is equal to the gain, the phenomenon of the focal shift caused by the gain is more obvious. In addition, the field distribution is not affected by the absorption or gain and always remains Gaussian both in internal and external focus planes.     

Electric and magnetic losses and gains in determining the sign of refractive index

Within the framework of classic electromagnetic theories, we have studied the sign of refractive index of optical medias with the emphases on the roles of the electric and magnetic losses and gains. Starting from the Maxwell equations for an isotropic and homogeneous media, we have derived the general form of the complex refractive index and its relation with the complex electric permittivity and magnetic permeability, i.e. , in which the intrinsic electric and magnetic losses and gains are included as the imaginary parts of the complex permittivity and permeability, respectively, as  = _r + i_i and μ = μ_r + iμ_i. The electric and magnetic losses are present in all passive materials, which correspond, respectively, to the positive imaginary permittivity and permeability _i > 0 and μ_i > 0. The electric and magnetic gains are present in materials where external pumping sources enable the light to be amplified instead of attenuated, which correspond, respectively, to the negative imaginary permittivity and permeability _i < 0 and μ_i < 0. We have analyzed and determined uniquely the sign of the refractive index, for all possible combinations of the four parameters _r, μ_r, _i, and μ_i, in light of the relativistic causality. A causal solution requires that the wave impedance be positive Re{Z} > 0. We illustrate the results for all cases in tables of the sign of refractive index. One of the most important messages from the sign tables is that, apart from the well-known case where simultaneously  < 0 and μ < 0, there are other possibilities for the refractive index to be negative n < 0, for example, for _r < 0, μ_r > 0, _i > 0, and μ_i > 0, the refractive index is negative n < 0 provided μ_i/_i > μ_r/_r.     

Electromagnetic Wave Transmission from Slightly Gaussian Rough Surface of Layered Medium

The electromagnetic wave transmission from the slightly rough surface of three-layered medium is studied, and formulae of the transmission coefficients for different polarizations are derived using the small perturbation method. A Gaussian rough surface is presented for describing rough surface of the layered medium, the influence of permittivity of the layered medium, the mean layer thickness of the intermediate medium, the roughness surface parameters and the incident frequency on the transmission coefficient of HH polarization are obtained and discussed with numerical implementation.     

Unique properties of microwave in interlayer exchange-coupled trilayer ferromagnetic films associated with negative imaginary part of permeability

Based upon Landau-Lifshitz equation and Maxwell's equations, we theoretically investigated properties of normally incident microwave propagation in interlayer exchange-coupled trilayer ferromagnetic film. It is found that, near resonance frequency of optic mode, imaginary part of permeability of one ferromagnetic layer is smaller than zero unusually, i.e., the ferromagnetic layer may be taken as an active medium. Thus a number of unique electromagnetic properties are presented, such as, the ferromagnetic layer becomes a left-handed material near low side of the resonance frequency of optic mode, and both phase velocity and time-averaged Poynting flow of the usually defined forward wave are negative simultaneously near high side of the resonance frequency. This work provides a feasible active medium to demonstrate the unique microwave properties.     

Concatenation of plasma filaments created in air by femtosecond infrared laser pulses

We report the first observation of the attachment of two single plasma filaments created collinearly in the atmosphere by IR femtosecond laser pulses. The linked filamentary structure is electrically conductive and emits sub-THz radiation over its entire length. Concatenation is achieved only for a specific time ordering between the two initial laser pulses. The pulse producing the filament closer to the laser source must be retarded with respect to the other pulse. This special time ordering is attributed to the acceleration of light in a self-guided pulse. Received: 4 March 2003 / Published online: 14 May 2003 RID="*" ID="*"Corresponding author. Fax: +33-1/6931-9996, E-mail: stzortz@ensta.fr     

Transmission Properties of One-Dimensional Photonic Crystals Containing Anisotropic Metamaterials

The transmission properties of one-dimensional photonie crystals （1DPCs） containing anisotropic metamaterials are theoretically studied. It is shown that the 1DPCs can possess a similar zero average index （zero-n） gaps, the edges of zero-~ gap are weakly dependent on the incident angles, scale length and the polarization of the electromagnetic wave. When an impurity is introduced, a defect mode appears inside the zeron gap with a very weak dependence on incident angles and sealing. It is found that in such photonic crystals, a transmitted Gaussian pulse with its carrier frequency lying in the lower gap edge, in the defect mode and in the bandgap, can experience a positive or negative group delay and hence a subluminal, ultra.slow or superluminal propagation with small distortions. These properties of the photonic crystals have potential applications in the transfer of information.     

Abrupt change of reflectivity from the strongly anisotropic metamaterial

The wave reflection from a non-magnetic anisotropic metamaterial, whose principal elements of the permittivity tensor have different signs, is investigated in this paper. It is found that, if the orientation of the optical axis is properly chosen, an extremely small change of the transverse wave number will lead to a dramatically change of the reflectivity at the glancing incidence. The physical insight for this abrupt change of reflectivity is also given by the analysis of the imaginary part of the k-surface. Since the metamaterial discussed here have been experimental realized from GHz to optical frequencies, the proposed abrupt change property of reflectivity may find some potential applications in various calibration devices, because of its extremely sensitivity to the transverse wave number.     

Tunable negative index metamaterial using yttrium iron garnet

A magnetic field tunable, broadband, low-loss, negative refractive index metamaterial is fabricated using yttrium iron garnet (YIG) and a periodic array of copper wires. The tunability is demonstrated from 18 to 23 GHz under an applied magnetic field with a figure of merit of 4.2 GHz/kOe. The tuning bandwidth is measured to be 5 GHz compared to 0.9 GHz for fixed field. We measure a minimum insertion loss of 4 dB (or 5.7 dB/cm) at 22.3 GHz. The measured negative refractive index bandwidth is 0.9 GHz compared to 0.5 GHz calculated by the transfer function matrix theory and 1 GHz calculated by finite element simulation.     

Changes in the coherence of quasi-monochromatic electromagnetic Gaussian Schell-model beams propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the mutual coherence function of quasi-monochromatic electromagnetic Gaussian Schell-model (EGSM) beams propagating through turbulent atmosphere is derived analytically. By employing the lateral and the longitudinal coherence length of EGSM beams to characterize the spatial and the temporal coherence of the beams, the behavior of changes in the spatial and the temporal coherence of those beams is studied. The results show that with a fixed set of beam parameters and under particular atmospheric turbulence model, the lateral coherence of an EGSM beam reaches its maximum value as the beam propagates a certain distance in the turbulent atmosphere, then it begins degrading and keeps decreasing along with the further distance. However, the longitudinal coherence length of an EGSM beam keeps unchanging in this propagation. Lastly, a qualitative explanation is given to these results.     

Chiral planar waveguide for guiding single-mode backward wave

Single-mode backward wave is shown to be guided in a planar dielectric waveguide with a strong chiral core. The significant difference of such a waveguide from the traditional one is the guidance of single-mode backward wave, without using negative permittivity and/or negative permeability. In the design, we generalize the idea of total internal reflection to the chiral medium and make a numerical analysis on the reflection with oblique incidence. We deduce rigorously a general solution of incident wave on the boundary of two arbitrary chiral magneto-electric media. We observe that the impedance matching can eliminate the coupling between two eigenwaves in chiral media. With strong chiral core and the matched impedance with cladding, one eigenwave becomes a backward wave and can be guided without transferring to the other eigenwave. If a single-mode propagation condition is satisfied, we will get single-mode backward guided wave. A special interface has been designed to prevent the forward wave entering the waveguide from the source.     

Propagation of Four-Petal Gaussian Beams in Turbulent Atmosphere

An analytical expression for the average intensity of four-petal Gaussian beams in turbulent atmosphere is derived. Studies show that in turbulent atmosphere, the contour lines of four-petal Gaussian beams with lower order N evolve into a number of petals with the increase in propagation distance, the contour lines with higher order N can reserve four-petal distribution at longer propagation distance than that with lower order N. These properties are similar to those in free space. However, with further increases of the propagation distance, the contours lines in turbulent atmosphere are different from those in free space.