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A finite photonic layered system alternating usual media with a dispersive metamaterial with two central layers in a PT- symmetric arrangement is investigated under the oblique incidence of an electromagnetic wave. We have found a defect mode within the gap, and we have studied its optical properties under the influence of gain and loss distributed in these central layers. As a consequence of PT-symmetry in the system, we find that exceptional points can be attracted to or repelled from each other depending on which side of the frequency band under study. Below the plasmon frequency, repulsion occurs between pairs of exceptional points, while above it they attract each other. • Defect mode within the PP-gap. • Influence of the non-Hermiticity on the gap and defect properties. • Exceptional points can be attracted or repelled in layered systems with metamaterial inclusions. [ABSTRACT FROM AUTHOR]

• Compact Tunable negative Metamaterial for enhancing 5G network performance. • Frequency-Tunable Tri-Hexagon and Tri-Square Split Ring Resonator for Bandwidth Optimization. • Empowering 5G with Double Negative (DNG) Properties. • Fabrication of the proposed metamaterial experimental result to verify the overall performance. This paper introduces a compact tuneable metamaterial (MTM) unit cell featuring a tri-hexagon and tri-square split ring resonator (THTSSSR) structure designed for 5G communication applications. Metamaterials are employed to achieve unique electromagnetic properties not found in natural materials. The design process involves the arrangement of three square rings and three hexagon rings as metallic patches on a Rogers substrate (RT 5880), measuring 7 x 7 mm2 with a thickness of 1.575 mm. The proposed design exhibits double negative (DNG) properties, with resonances in the transmission coefficient (S21) at 3.493 GHz and a bandwidth of −10 dB covering frequencies between 3.057 and 3.711 GHz. Numerical simulations conducted using finite-integration techniques (FIT) in CST Microwave Studio validate the design's effectiveness, with confirmation through the Advanced Design System (ADS). The MTM unit cell demonstrates tuneable attributes, including negative permittivity ranging from 3.39 to 5 GHz and negative permeability from 3.39 to 3.86 GHz. These findings highlight the compactness and tunability of the proposed design, making it promising for 5G communication applications. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We study the mechanism of large positive and negative lateral shift in a prism-waveguide coupling system where the guiding layer is composed of left-handed material with weak absorption. As the giant lateral shift is always dramatically decreased by the loss of guiding layer, we introduce lossy cladding layer and substrate to realize large lateral shift in the above system, theoretical expression of lateral shift is derived and simulation results illustrate the appearance of large lateral shift. [ABSTRACT FROM AUTHOR]

Abstract: We study the large lateral shift in a prism-waveguide system with lossy left-handed material (LHM) guiding layer by use of a loss compensation method of cladding layer and substrate. The necessary conditions for the appearance of large lateral shift are obtained by theoretical analysis and simulation results demonstrate the validity of these conditions. Further calculation shows that in our system large lateral shift exhibits super-high sensitivity to the thickness change of cladding layer and substrate compared with other prism-waveguide systems with a guiding layer composed of thin metal or other ordinary materials. [Copyright &y& Elsevier]

Abstract: As left-handed materials and metamaterials are becoming more prevalent, we examine the effect of negative permeability upon levitation force. We first consider two half spaces of differing permeability and a point magnetic source, so that the method of images may be employed. We determine that the resulting force may be larger than for conventional magnetic materials. We then illustrate the inclusion of a finite sample thickness. [Copyright &y& Elsevier]

Abstract: A kind of planar left-handed metamaterial (LHM) with unique configurations is demonstrated, which offers an approach in building dual-band negative-index materials. Simulated and experimental results predict two left-handed transmission bands near 11.1 and 14.6GHz. Dual bands of negative refractive indexes are verified using the retrieval procedure. Field and current distribution at the dual magnetic resonance are also examined. The effective electromagnetic parameters show that by carefully adjusting dimensions of the unit cell, electric and magnetic resonances can be coexistent at some frequency ranges with both negative permittivity and negative permeability. The idea can help us designing planar negative-index materials with multibands. [ABSTRACT FROM AUTHOR]

Abstract: We apply a simple ABCD matrix formalism to investigate beam propagation in left-handed material (LHM) slab systems. Firstly, we derive the expressions for the matrix elements for a single LHM slab. Based on the ABCD matrix, we obtain the field distributions both inside and outside the LHM slab, and the conditions for focusing and phase compensation of the Gaussian beam. Secondly, the derived ABCD law is applied to analyze the propagation properties of Gaussian beams through various cascaded LHM slab systems. The corresponding focusing and phase compensation conditions of the Gaussian beam are also obtained. Our theoretic formalism may be applied as a compact and effective tool for the research of light beam propagation in complex LHM slab systems, since it avoids the complicated integral operation. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Quasi-one-dimensional comb-like photonic crystals with backbone waveguide made of left-handed material are physically fabricated by using transmission lines. The transmission properties are experimentally investigated and it is found that the structures possess a special band gap. The gap does not originate from the conventional Bragg scattering mechanism in that it is invariant with the change of scale length. Moreover, the experimental results indicate that the gap-edges are determined by zero-average permittivity of the branch and backbone and zero permeability of backbone, respectively. Because of the characteristics, it will be convenient to realize a special gap using in microwave and optical engineering. [Copyright &y& Elsevier]

Abstract: The Goos–Hänchen shift at the surface of a uniaxially anisotropic left-handed material film is investigated, for the situation of that there is an arbitrary angle between the optical axis and the interface of the material. The analytical expressions of the Goos–Hänchen shifts are derived, for both cases of that the total reflection occurs and does not occur at the first interface. The sign of the Goos–Hänchen shifts in the two situations is analysed. The results show that the Goos–Hänchen shift of the reflected wave is the same as that of the transmitted one for the case that the total reflection does not occur at the first interface; the Goos–Hänchen shift of the transmitted wave oscillates as the thickness of the film is increased, and its overall tendency is increased; the Goos–Hänchen shift of the transmitted wave realizes its absolute maximum when the transmitted wave resonances, the absolute maximum is almost several 10 times of the wavelength of the incident wave; the Goos–Hänchen shift of the transmitted wave is significantly influenced by the incident angle and the angle between the optical axis and the interface. [Copyright &y& Elsevier]

Abstract: Abnormal transmission is found in meta-material with negative permeability, this transmission is attributed to grating effect. A grating model with an effective negative permeability material is proposed, it is found that indeed the grating model can give a good prediction on the unusual transmission. [Copyright &y& Elsevier]

Abstract: We report our experimental results on two-dimensional left-handed metamaterials (LHM) exhibiting negative refraction and subwavelength imaging. Transmission and reflection spectra of LHM are studied and a left-handed transmission band is observed at the frequencies where both dielectric permittivity and magnetic permeability are negative. Impedance matching is verified both with the experiments and simulations. The two-dimensional LHM structure is verified to have a negative refractive index. We employed three different methods to observe negative refraction; refraction through prism-shaped LHM, beam shifting method, and phase shift experiments. We further demonstrated subwavelength imaging and resolution using LHM superlenses. The effect of thickness on the resolving power is investigated experimentally. [Copyright &y& Elsevier]

Abstract: We studied gap soliton of surface plasmon polaritons (SPPs) at an interface between vacuum and a Kerr nonlinear left-handed material (LHM). Applying multiple scale method, we derived the nonlinear coupled-mode equations for the gap soliton of SPPs. The linear gap is obtained and the bistable behavior of the transmissivity for the finite extend of the surface is presented. [Copyright &y& Elsevier]

Abstract: As a possible candidate for the left-handed metamaterial with negative permeability, a series of Ti, Co-substituted M-type barium hexaferrite BaFe12− x (Ti0.5Co0.5) x O19 (x=0, 1, 2, 3, 4 and 5) was prepared by citrate precursor method. The formation processes of the substituted barium hexaferrite compounds from the precursors were followed by the measurements of powder X-ray diffraction (XRD), Infrared absorption spectra (FT-IR), and thermogravimetry and differential thermal analysis (TG/DTA) coupled with mass spectroscopy (MS). In the case of the non-substituted sample, the formation of the barium hexaferrite is regulated by the thermal decomposition of BaCO3 and the solid-state reactions of BaO and Fe2O3 in the temperature range from 800 to 1100K. The formation temperature of the substituted BaFe12− x (Ti0.5Co0.5) x O19 is higher than that for the non-substituted sample and increases with the value of x, due to the effects of carbonate ions incorporated by the partial substitution of Fe3+ by (Ti0.5Co0.5)3+. On heating up to ca. 1200K, all the substituted samples transform into the magenetoplumbite phase as is the non-substituted sample. The compositional dependence of the magnetic properties of the substituted barium hexaferrite was investigated by the magnetization measurement. The decrease in the magnetic anisotropy was confirmed by the change in the magnetization curve and coercivity H C with the composition x. A negative permeability spectrum was observed in the BaFe9(Ti0.5Co0.5)3O19 in the frequency range from 2 to 4GHz. [Copyright &y& Elsevier]

Abstract: 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 and permeability , 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 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 10000 times larger even when the loss is as high as and the retardation is as large as . [Copyright &y& Elsevier]

Abstract: We present the first study of the hybridizing effect of different left-handed metamaterials (LHM) based on S-shaped and Ω-shaped resonators. Three different cases of hybridizing are investigated, ten configurations of various hybrid ratio are simulated, fabricated and measured, and a series of different left-handed passbands is obtained, showing that the left-handed passband of the proposed hybrid structure can be controlled by tuning the hybrid ratio. The hybrid left-handed metamaterial proposed in this Letter has potential applications in LHM-based filters, couplers, antennas, etc. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: On the basis of Landau–Lifshitz–Gilbert (LLG) equation, an anomalous ferromagnetic resonance behavior is demonstrated in detail. Coupling between the magnetic moments produces a 3π/2 phase delay for one of the moments ferromagnetic resonance unusually, thus leads the sign of magnetic susceptibility to be opposite to that induced by the usual ferromagnetic resonance. Consequently, a left-handed material (LHM) may be formed near the low-frequency side of the resonance. Particularly, a LHM with negative value of real part of permeability only is predicted. [Copyright &y& Elsevier]

Abstract: Negative magnetic permeability of split ring resonator (SRR) is theoretically investigated in the visible light region. In our calculations, we considered the delay of the current inside the metal SRR in order to estimate the permeability of the SRR precisely. From the results, the silver SRR array with small capacitance exhibits negative permeability in all the visible range. The dependence of the permeability on the filling factor of the SRR elements is also discussed. [Copyright &y& Elsevier]

Abstract: We report the true left-handed transmission of a composite metamaterial (CMM) consisting of periodically stacked split-ring resonator (SRR) and wire elements. The negative permeability (μ <0) gap is demonstrated explicitly by comparing SRR and closed-ring resonator structures. We confirm experimentally that the plasma cut-off frequency of the CMM is determined by the combined dielectric response of SRR and wire elements, and it is much lower than that of the wire-only medium. This is crucial to identify the left-handed transmission bands of the CMM. We further investigate the effect of intralayer and interlayer disorder on the transmission spectrum of CMM arising from misaligned fabrication and stacking of the SRR layers. We found that the intralayer disorder affects the μ <0 gap of SRRs and the left-handed transmission band of CMM significantly, whereas the SRR transmission is rather immune to interlayer disorder. [Copyright &y& Elsevier]

Abstract: In this Letter, we study the properties of one-dimensional quasi-periodic photonic crystal containing left-handed material. In the light of the dispersion relation, we show that one-dimensional quasi-periodic photonic crystal can exhibit complete reflection at a given microwave frequency for all incident angles and both polarizations (s- and p-polarizations). The influence of left-handed material''s permittivity and permeability on the omnidirectional reflection is also discussed. We find that when is larger than , it is difficult to realize the omnidirectional reflection for p-polarization, on the contrary, it is difficult to realize the omnidirectional reflection for s-polarization when is larger than , which is expected to realize omnidirectional reflection in a certain frequency region. The effect of the left-handed material''s absorption on omnidirectional reflection is also investigated. [Copyright &y& Elsevier]

Abstract: We investigate the possibility of preparing left-handed material in a layered alternated nonmagnetic/magnetic composite under different direction of incident electromagnetic wave at the microwave region. We calculate the effective refractive index of the layered composites and find that the effective refractive index varies as a function of the volume fraction of one component of the composite. Especially, within the certain volume fraction of component 1 (or 2) the effective refractive index can be negative at a finite frequency region. Moreover, we find that the direction of the incident electromagnetic wave affects the effective refractive index greatly. When the incident electric field is parallel to the laminations and the magnetic field is perpendicular to the laminations, the volume fraction of component 1 (or 2) range, which causes the effective refractive index to be negative, is relatively wider than that of the opposite case, but the absolute values of the negative refractive index are smaller than that of the opposite case. [Copyright &y& Elsevier]

Surface p- and s-polarized stationary waves propagating along the interface between left-handed electromagnetic meta-material with three types of conventional materials: dielectrics, metals, and magnetic media with negative magnetic permeability μ(ω) are studied. The constraints for the existence of surface modes are identified. It is shown that the frequency domains of existence for p- and s-modes do not overlap and they are quite different for different types of interfaces. The Poynting vector and the density of energy associated with surface mode are calculated. Depending on the system parameters either p- or s-surface mode has the time-averaged Poynting vector directed opposite to the mode phase velocity. [Copyright &y& Elsevier]

Abstract: Based on classical electromagnetic theory, characteristics of guided modes in a rectangular waveguide filled with a pair of single-negative layers are studied. The results show that only surface waves of TE mode can propagate in this peculiar waveguide, no TM mode in any forms can propagate in it. In addition, TE waveguide modes will be affected by permeability ratio ? 1/? 2 and dielectric layer thickness ratio P. Finally, from the electric field distribution of TE mode, we find the amplitude and location of the electric field can be adjusted by changing the thickness ratio P. [Copyright &y& Elsevier]

Abstract: We propose a polarization splitter (PS) based on the slow light effect in a three-layer waveguide that consists of left-handed material (LHM) and dielectric layers with no birefringence. Transverse electric (TE) and transverse magnetic (TM) waves can be split by the intrinsic configuration of permittivity and permeability of LHM and dielectric layers. Simulation results are given to discuss the influence of electromagnetic parameters on the properties of our PS, and the capture and release of TE or TM waves are also realized in our PS which provides a flexible method to modulate the switching of different polarization waves. [Copyright &y& Elsevier]

Abstract: We propose a coarse multiplexer–demultiplexer (MUX–DEMUX) for two ITU-T recommended channels based on a directional coupler (DC) with left-handed material (LHM), whose size can be controlled to a thickness less than 1mm. Our MUX–DEMUX can mix and separate two wavelength channels by use of LHM sandwiched between two RHM straight waveguides of a DC. Its operation is by setting the coupling length of one wavelength to be half of that of the other wavelength, which can be easily realized with quite short devices’ length due to the enhancement of the coupling efficiency caused by LHM. At last, the loss effect of LHM is considered. [Copyright &y& Elsevier]

Abstract: We realize tunable giant Goos–Hänchen (GH) shift by adjusting the applied electric field on electro-optic (EO) crystal in a prism–waveguide system in which surface plasmon resonance (SPR) is excited by left-handed material (LHM), and in such a way the giant GH shift can be modulated with high flexibility. Necessary theoretical analysis is given by stationary-phase theory and simulation results illustrate the high sensitivity of tunable giant GH shift which has potential applications in integrated optics, optical sensors and optical modulators. [Copyright &y& Elsevier]

Abstract: We construct a refractive index detection structure based on a prism–waveguide coupling system with double negative (DNG) material guiding layer, where surface plasmon resonance (SPR) is generated and the refractive index of lossless as well as lossy sample can be detected by the location of the incident light at which lateral shift peak appears. Simulation results show that when sample is lossy, more than one lateral shift peaks appear at different incident angle when other parameters are fixed once the intrinsic and radiative dampings satisfy the sufficient condition of equation for a large lateral shift. [Copyright &y& Elsevier]

Abstract: We propose a very compact electro-optical switch based on a directional coupler (DC) with left-handed material (LHM). The embedded LHM will significantly reduce the size of directional coupler, and by apply a proper voltage at the straight waveguide a switch of two channels is realized. Simulation results show that a electro-optical switch with a size of 134μm×5.74μm can be realized. [Copyright &y& Elsevier]

Abstract: A compact polarization splitter (PS) with left-handed material (LHM) sandwiched between two right-handed material (RHM) waveguides of a directional coupler (DC) is proposed. Its operation is by setting the coupling length of TM polarization be half that of TE polarization. Theoretic analysis exhibits that the PS with a very small size of 138.4μm×18.6μm can be realized due to the inclusion of LHM even when the RHM with small birefringence is used. [Copyright &y& Elsevier]

Abstract: A wave-absorber model with air/left-handed medium/right-handed medium/metal structure is proposed. The wave-absorption properties of the structure are theoretically analyzed and numerically simulated. The structure’s parameters are optimized employing a genetic algorithm. The results show that under the conditions of that the wave is normally incident and the structure parameters are well matched, the peak values of the reflectivity can be reduced, the absorbing bandwidth can be broaden and an average reflectance of −12dB can be realized in the frequency range from 0.4GHz to 10GHz. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to show that semiconductor nano-structures built from non-magnetic InAs/GaAs nano-rings can exhibit simultaneously negative effective permittivity and permeability over a certain optical frequency range. The structures are resonant and have this property near the edge of absorption of the nano-rings. This can be particularly interesting in the investigation of the challenging problem of development of left-handed composite materials in the optical range. [Copyright &y& Elsevier]

Summary: On total reflection from a half-space filled with an isotropic, homogeneous, weakly dissipative, dielectric-magnetic medium with negative phase-velocity (NPV) characteristics, it is shown here that a linearly polarized beam can experience either a negative or a positive Goos-Hauml;nchen shift. The sign of the shift depends on the polarization state of the beam as well as on the signs of the real parts of the permittivity and the permeability of the NPV medium. [Copyright &y& Elsevier]