Left-handed Material Slab Research Articles

Comment on: “Tunable surface waves supported by graphene-covered left-handed material structures” [Opt. Commun. 489 (2021) 126874

In a recent article (Yaqoob et al., 2021), Yaqoob et al. studied the tunable electromagnetic surface wave propagation on the graphene-covered left-handed material (LHM) slab backed by the perfect electric conductor (PEC). They derived the dispersion relations for both transverse electric (TE) and transverse magnetic (TM)-polarized surface waves, and then used the relations for two types of LHMs according to the spectral range, i.e., GHz- and THz-LHM. The present Comment points out although the system under consideration (i.e., graphene-covered LHM) is itself physically challenging, the results for THz-LHM are also rather unreal because the frequency regime to accomplish the calculations falls within the high THz frequency band. In such a frequency band, the conductor substrate no longer behaves like a PEC and thus the results are rather unreal when considering THz-LHM. We note that the metal, for example, gold or silver may be modeled as a PEC, but only for a few THz. Moreover, when considering GHz-LHM, we obtain new forms of dispersion relations for both TE and TM surface waves. We find that our dispersion relations do not agree with the results obtained by Yaqoob et al.

Study on the propagation properties of TM electromagnetic wave in Lossy left‐handed material based on CUDA‐implemented parallel

By using the method of Finite Difference Time Domain (FDTD) and the technology of Compute Unified Device Architecture (CUDA), the propagation characteristics of electromagnetic waves in Left-Handed Materials (LHM) have been studied in this paper. The LHM slab was matched with the free space and the secondary focusing phenomenon of LHM was simulated. Compared with the serial FDTD program, our work showed that this method had a high accuracy. The phase compensation effect and the inverse Snell effect of LHM were also discussed by using the parallel FDTD method based on CUDA, which further proved that our results were consistent with the theoretical study. By comparing the calculation time of traditional FDTD program with that of the CUDA based parallel FDTD program, we conclude that the latter is more efficient than the former. This parallel method can be used as a more efficient way to study LHM.

Plasmon modes supported by left-handed material slab waveguide with conducting interfaces

Theoretical analysis of left-handed material core layer waveguide in the presence of interface free charge layers is presented. The thickness of the interface charge layer can be neglected compared with the incident wavelength. The tangential component of the magnetic field is no longer continuous due to the conducting interfaces. The non-homogeneous boundary conditions are solved and the corresponding dispersion relation is found. The dispersion properties are studied. The proposed structure is found to support even as well as odd plasmon modes. Moreover, the structure shows abnormal dispersion property of decreasing the effective index with the increase of the frequency which means negative group velocity.

Dynamic Propagation of Quadratically Chirped Airy Beams in the Right-Handed and Left-Handed Material Slabs

We analytically and numerically investigate the dynamic propagation of the quadratically chirped Airy beams in right-handed material (RHM) and left-handed material (LHM) slabs. Based on the analytical expressions and numerical calculations, we find that through choosing the appropriate value of the quadratic chirp, one can modify the diffraction, the intensity distribution, the propagation path, and acceleration and deceleration of the quadratically chirped Airy beams to meet the actual usage accordingly. In addition, we also demonstrate the effect of the quadratic chirp on the Poynting vector and the angular momentum of the quadratically chirped Airy beams, respectively. Furthermore, we explore the gradient and scattering forces on a Rayleigh dielectric particles induced by the quadratically chirped Airy beams.

A Minimized 2-D Left-Handed Material Spiral Unit Cell With Rotation Symmetry for Midrange Wireless Power Transfer

This letter presents a technique for designing left-handed material (LHM) unit cell, and a minimized 2-D low-loss LHM square spiral unit cell ( $38~ \text {mm} \times 38 ~\text {mm} \times 1.6 ~\text {mm}$ ) with rotation symmetry is developed in the frequency band 13.56–14 MHz. Two LHM slabs with $5 \times 5$ unit cell array are added to the transmission and receiving antennas, respectively, and the power transfer efficiency has increased greatly.

Propagation properties of the chirped Airy vortex beams through left-handed and right-handed material slabs

We present an investigation on the propagation properties of the chirped Airy vortex (CAiV) beams through slabs of left-handed materials (LHMs) and right-handed materials (RHMs). We discuss the influence of chirped parameter C on the propagation of the CAiV beams through LHM and RHM slabs. Our simulation results show that a maximum accelerated velocity appears during the propagation process. The intensity concentration of the CAiV beams increases with the absolute value of the chirped parameter. The peak intensity of the CAiV beams changes abruptly, and the chirped parameter plays an active role on the difference of the maximum and the minimum. In the energy flow, we find that the effects of the chirped parameter on the strength of the vortex are different at different propagation distances.

Dispersion properties of lossy, dispersive, and anisotropic left-handed material slab waveguide

An asymmetric three-layer slab waveguide with air as a substrate, lossless dielectric medium as a guiding layer, and lossy, dispersive, and anisotropic left-handed material (LHM) as a cladding was investigated. The LHM cladding layer was assumed to exhibit positive permittivity and permeability in the transverse directions and negative ones along the longitudinal direction (z-axis). The dispersion equations were derived and corresponding dispersion curves were plotted and studied for TE and TM polarized light. The dispersion properties were studied with different parameters of the proposed structure. A set of interesting features were observed such as the existence of the fundamental mode in a narrow frequency range, positive group velocity which becomes faster as the frequency increases, and crucial dependence of the dispersion curves on the anisotropy of the LHM cladding.

左手平板材料对正弦高斯光束的光斑影响

左手平板材料对正弦高斯光束的光斑影响

Antireflection Coating at Metamaterial Waveguide Structure by Using Superlattices (LANS)

The characteristics of electromagnetic wave reflection and transmission by multilayered structures consisting of a pair of left-handed material (LHM) and superlattices (LANS) slabs inserted between two semi-infinite dielectric media are investigated for photovoltaic and solar energy applications. Maxwell’s equations are used to determine the electric and magnetic fields of the perpendicular polarized wave incident at each layer. Snell’s law is applied and the boundary conditions are imposed at each layer interface to calculate the reflected and transmitted coefficients of the structure. The reflected, transmitted powers are determined using these coefficients by a recursive method. The reflected and transmitted powers are computed in both visible and microwave spectral band with the appropriate LHM for each band and appropriate location of LANS in the structure. They are illustrated as a function of the incident wavelength, angle of incidence, magnetic fraction of LANS and thickness of the slabs with the emphasis on the appropriate refractive indices. I found that, zero reflectance and maximum transmittance of the incident powers are achieved for visible spectral band at a single frequency if LHM and LANS have the same refractive index of opposite signs with the same width and more magnetic material of LANS while the reflected power is zero for less magnetic material of LANS in the microwave spectral band which realizes antireflection coating in this structure.

A symplectic FDTD algorithm for the simulations of lossy dispersive materials

A high-order symplectic finite-difference time-domain (SFDTD) algorithm, based on the matrix splitting, the symplectic integrator propagator and the auxiliary differential equation (ADE) technique, is presented. The algorithm is applied to the lossy Lorentz–Drude dispersive model. With the rigorous and artful formula derivation, the detailed formulations are provided. Moreover, the present algorithm can also be applicable to the lossy Drude and Lorentz dispersive model in a straightforward manner. An excellent agreement is achieved between the SFDTD-calculated and exact theoretical results when calculating the transmission coefficient in simulation of metal films. Focusing action of the matched left-handed materials (LHMs) slab is also achieved as the second example in the two-dimensional space. Numerical results for a more realistic structure, the simulation of periodic arrays of silver split-ring resonators (SRRs) using the Drude dispersion model, are also included, and the results agree well with those obtained by the finite element method (FEM).

Effect of Dissipation Factor on Reflected and Transmitted Powers of a Structure Containing Left-Handed Material Waveguide

In this paper a waveguide structure consisting of a pair of left-handed material (LHM) and dielectric slabs inserted in vacuum is investigated theoretically. Two cases of the LHM are considered, loss-less case and loss case as well as the frequency dependence of permittivity and permeability of it is taken into account. Maxwell's equations are used to determine the electric and magnetic fields of the incident waves at each layer. Snell's law is applied and the boundary conditions are imposed at each layer interface to calculate the reflected, transmitted and loss powers of the structure. Numerical results are illustrated to show the effect of frequency, angle of incidence and LHM thickness on the mentioned powers when the dissipation factor changes. The obtained results are in agreement with the law of conservation of energy.

All-angle negative refraction and active flat lensing of ultraviolet light

Decades ago, Veselago predicted that a material with simultaneously negative electric and magnetic polarization responses would yield a 'left-handed' medium in which light propagates with opposite phase and energy velocities--a condition described by a negative refractive index. He proposed that a flat slab of left-handed material possessing an isotropic refractive index of -1 could act like an imaging lens in free space. Left-handed materials do not occur naturally, and it has only recently become possible to achieve a left-handed response using metamaterials, that is, electromagnetic structures engineered on subwavelength scales to elicit tailored polarization responses. So far, left-handed responses have typically been implemented using resonant metamaterials composed of periodic arrays of unit cells containing inductive-capacitive resonators and conductive wires. Negative refractive indices that are isotropic in two or three dimensions at microwave frequencies have been achieved in resonant metamaterials with centimetre-scale features. Scaling the left-handed response to higher frequencies, such as infrared or visible, has been done by shrinking critical dimensions to submicrometre scales by means of top-down nanofabrication. This miniaturization has, however, so far been achieved at the cost of reduced unit-cell symmetry, yielding a refractive index that is negative along only one axis. Moreover, lithographic scaling limits have so far precluded the fabrication of resonant metamaterials with left-handed responses at frequencies beyond the visible. Here we report the experimental implementation of a bulk metamaterial with a left-handed response to ultraviolet light. The structure, based on stacked plasmonic waveguides, yields an omnidirectional left-handed response for transverse magnetic polarization characterized by a negative refractive index. By engineering the structure to have a refractive index close to -1 over a broad angular range, we achieve Veselago flat lensing, in free space, of arbitrarily shaped, two-dimensional objects beyond the near field. We further demonstrate active, all-optical modulation of the image transferred by the flat lens.

Effect of Dissipation Factor on Reflected and Transmitted Powers of a Structure Containing Left-Handed Material Waveguide

In this paper a waveguide structure consisting of a pair of left-handed material (LHM) and dielectric slabs inserted in vacuum is investigated theoretically. Two cases of the LHM are considered, loss-less case and loss case as well as the frequency dependence of permittivity and permeability of it is taken into account. Maxwell's equations are used to determine the electric and magnetic fields of the incident waves at each layer. Snell's law is applied and the boundary conditions are imposed at each layer interface to calculate the reflected, transmitted and loss powers of the structure. Numerical results are illustrated to show the effect of frequency, angle of incidence and LHM thickness on the mentioned powers when the dissipation factor changes. The obtained results are in agreement with the law of conservation of energy.

Virtual Singular Scattering of Electromagnetic Waves in Transformation Media Concept

If a scatterer and an observation point (receive) both approach the so-called near field zone of a source of electromagnetic waves, the scattering process becomes singular one which is mathematically attributed to the spatial singularity of the free space Green function at the origin. Starting from less well known property of left-handed material slab to transfer the singularity of the free space Green function by implementing coordinate transformation, we present a phenomenon of virtual singular scattering of electromagnetic wave on an inhomogeneity located in the volume of left – handed material slab. Virtual singular scattering means that a scatterer is situated only virtually in the near field zone of a source, being, in fact, positioned in the far field zone. Such a situation is realized if a scatterer is embedded into a flat Veselago’s lens and approaches the lens’s inner focus because a slab of Veselago medium produces virtual sources inside and behind the slab and virtual scatterer (as a source of secondary waves) from both slab sides. Considering a line-like dielectric scatterer we demonstrate that the scattering efficiency is proportional to product of singular quasistatic parts of two empty space Green functions that means a multiplicative quasistatic singularity of the Green function for a slab of inhomogeneous Veselago medium. We calculate a resonance value of the scattering amplitude in the regime similar to the known Mie resonance scattering.

Numerical study of a structure containing left-handed material waveguide

In this paper a waveguide structure consisting of a pair of left-handed material (LHM) and dielectric slabs inserted in vacuum is investigated theoretically. Maxwell’s equations are used to determine the electric and magnetic fields of the incident waves at each layer. Snell’s law is applied and the boundary conditions are imposed at each layer interface to calculate the reflected and transmitted powers of the structure. Numerical results are illustrated to show the effects of frequency, angle of incidence and LHM thickness on the transmitted power when the refractive index of the dielectric layer changes. The same procedure is repeated to show the variation of the transmitted power with the change in the mentioned parameters under different values of dissipation factor of the lossy LHM. Consequently, two cases of the LHM are considered, loss-less case and loss case. The results obtained, are in agreement with the law of conservation of energy.

TE surface waves in dielectric slab sandwiched between LHM slabs

In this work, the dispersion relation for TE surface waves has been derived for a slab waveguide constructed from a dielectric material slab sandwiched between two thick layers of left-handed material (LHM). The dispersion relation and the power flow were numerically solved for a given set of parameters: the structural factor, dielectric slab thickness, and the operating frequency on the effective refractive index and power flow. We found that the wave effective refractive index decreases with thickness increase as well as increase in frequency. We found that the effective refractive index increases slightly with increase of structural factor. Also, the power flow increases with thickness and increases with operating frequency.

Transmission Properties of Electromagnetic Waves Through Left-handed Material: A Revisit

The transmission properties of electromagnetic wave through left-handed material (LHM) have been thoroughly investigated. The characterization of signal propagation and evanescent wave amplification through LHM slab has been done on the basis of analytical model equations. The transmission properties have also been addressed from the study of group and phase indices, and anomalous dispersions regions in LHM and right-handed material. Furthermore, the orthogonality of electric and magnetic fields of classical electromagnetism has been seen to be applicable for electric and magnetic plasma buffered by a left-handed (LH) medium.

Influence of left-handed materials on the spontaneous emission spectrum of V-type three-level atom

In this paper, the dynamic properties and the spontaneous emission spectrum of V-type three-level atom near left-handed material slab are investigated. The two orthogonal dipoles of the decay from the two upper levels to the lower level are considered. Due to the focusing and the phase compensation effects of the left-handed materials, the indirect quantum interference between two orthogonal spontaneous emission transitions leads to the fact that the populations in the two upper levels influence each other, the decay rate is enhanced or decreased and the spontaneous emission spectrum is narrowed or widened, depending on the initial atomic state.

Effect of negative permittivity and permeability on the transmission of electromagnetic waves through a structure containing left-handed material

We investigate the characteristics of electromagnetic wave reflection and transmission by multilayered structures consisting of a pair of left-handed material (LHM) and dielectric slabs inserted between two semi-infinite dielectric media. The theoretical aspect is based on Maxwell's equations and matching the boundary conditions for the electric and magnetic fields of the incident waves at each layer interface. We calculate the reflected and transmitted powers of the multilayered structure taking into account the widths of the slabs and the frequency dependence of permittivity and permeability of the LHM. The obtained results satisfy the law of conservation of energy. We show that if the semi-infinite dielectric media have the same refractive index and the slabs have the same width, then the reflected (and transmitted) powers can be minimized (and maximized) and the powers-frequency curves show no ripple. On the other hand if the semi-infinite dielectric media have different values of refractive indices and the slabs have different widths, then under certain conditions the situation of minimum and maximum values of the mentioned powers will be reversed.

Enhanced twinkling in left-handed media

A slab of left-handed material (LHM) with refractive index -1 forms a perfect lens that retains subwavelength information about a source or object. Such lenses are highly susceptible to perturbations affecting their performance. It is shown that illuminating a roughened interface between air and an LHM produces a regime for enhanced focusing of light close to the boundary. This generates caustics that are brighter, fluctuate more, and cause Gaussian speckle at distances closer to the interface than in right-handed matter. These effects present fresh challenges for perfecting the perfect lens.