Transmission properties of fractal Cantor distribution with left-handed materials

Transmission properties of fractal Cantor distribution with left-handed materials （LHM） are investigated. The transmittance and reflectance spectra can be calculated by using the optical transmission matrix method. Comparing with the conventional Cantor multilayers, these structures with LHM have double functions of stopbands and defects. Through adjusting the thickness of dielectric layers, the properties of stopbands and defects can be obtained, respectively. For stopbands, a broad stopband filter is studied. For defect modes, multi-frequencies narrow passband filters are proposed.

Subwavelength rectangular cavity partially filled with left-handed materials

In this paper, we present the electromagnetic analysis of a rectangular cavity partially filled with a left-handed material slab. Our theoretical investigation shows that there exist novel resonant modes in the cavity, and such a cavity becomes a subwavelength cavity. The eigenvalue equation of the cavity is derived and the resonant frequencies of the novel modes are calculated by using numerical simulation. We also discuss the stability of the novel resonant modes and show the best condition under which a useful rectangular cavity of subwavelength dimensions with tolerable stability is obtained.

From electromagnetic bandgap to left-handed metamaterials:modelling and applications

In this paper, numerical modelling of left-handed materials （LHMs） is presented using in-house and commercial software packages. Approaches used include the finite-difference time-domain （FDTD） method, finite element method （FEM） and method of moments （MoMs）. Numerical simulation includes verification of negative refraction and ＂perfect lenses＂ construction, investigation of evanescent wave behaviour in layered LHMs, reversed Shell＇s Law in electromagnetic band gap （EBG）-like structures and construction of LHMs using modified split ring resonators （SRRs）. Numerical results were verified to be in good agreement with theory, At the end of this paper, potential applications of LHMs in microwave engineering are discussed.

Characteristics of surface waves in anisotropic left-handed materials

We report the coexistence of TE and TM surface modes in certain same frequency domain at the interface between one isotropic regular medium and another biaxially anistotropic left-handed medium. The conditions for the existence of TE and TM polarized surface waves in biaxially anisotropic left-handed materials are identified, respectively. The Poynting vector and the energy density associated with surface modes are calculated. Depending on the system parameters, either TE or TM surface modes can have the time averaged Poynting vector directed to or opposite to the mode phase velocity. It is seen that the characteristics of surface waves in biaxially anisotropic left-handed media are significantly different from that in isotropic left-handed media.

Super energy flows in a waveguide filled with air and left-handed materials

The phenomena of super energy flows are studied theoretically and numerically in a parallel-plate waveguide which is filled with two layered equally-thick different media, i.e. air and specific left-handed materials （LHM） with εr1 = -1/（1 ＋δ） ＋iγ and μr1 = -（1 ＋ δ） ＋ iγ. In this special waveguide, two-directional super-energy flows are excited by a three-dimensional horizontal electric dipole at the same time, which has transmission patterns different from those of two-dimensional source and three-dimensional vertical electric dipole. We also show that the retardation and loss in LHM are sensitive to the amplitude of super power densities, and the dimensions of waveguide determine the propagating modes, which makes super energy flows more practical.

Design and analysis of doped left-handed materials

We devise three sorts of doped left-handed materials （DLHMs） by introducing inductors and capacitors into the traditional left-handed material （LHM） as heterogeneous elements. Some new properties are presented through finitedifference time-domain （FDTD） simulations. On the one hand, the resonance in the traditional LHM is weakened and the original pass band is narrowed by introducing inductors. On the other hand, the original pass band of the LHM can be shifted and a new pass band can be generated by introducing capacitors. When capacitors and inductors are introduced simultaneously, the resonance of traditional LHM is somewhat weakened and the number of original pass bands as well as its bandwidth can be changed.

Left-handed materials in magnetized metallic magnetic thin films

The authors＇ theoretical investigation on the high-frequency response of magnetized metallic magnetic films showed that magnetic films may become left-handed materials （LHMs） near the ferromagnetic resonance frequency of incident waves with right-handed circular polarization （RCP） and linear polarization （LP）. The frequency range where LHM exists depends on the waves polarization, the magnetic damping coefficient, and the ferromagnetic characteristic frequency corn of the film. There also exists a critical damping coefficient ac, above which the left-handed properties disappear completely.

Higher order implicit CNDG-PML algorithm for left-handed materials

By incorporating the higher order concept,the piecewise linear recursive convolution(PLRC)method and CrankNicolson Douglas-Gunn(CNDG)algorithm,the unconditionally stable complex frequency shifted nearly perfectly matched layer(CFS-NPML)is proposed to terminate the left-handed material(LHM)domain.The proposed scheme takes advantages of CFSNPML formulation,the higher order concept PLRC method and the unconditionally stable CNDG algorithm in terms of absorbing performance,computational efficiency,calculation accuracy and convenient implementation.A numerical example is carried out to demonstrate the effectiveness and efficiency of the proposed scheme.The results indicate that the proposed scheme can not only have considerable absorbing performance but also maintain the unconditional stability of the algorithm with the enlargement of time steps.

Superpositions of Laguerre-Gaussian Beams in Strongly Nonlocal Left-handed Materials

We present beam solutions of the strongly nonlocal nonlinear Schrodinger equation in left-handed mate- rims （LHMs）. Different Laguerre-Ganssian （LG） necklace beams, such as symmetric and asymmetric single layer and multilayer necklace beams are created by the superposition of two single beams with different topological charges. Such superpositions are then propagated through LHMs, displaying linear diffraction. It is found that the superposition of two LGnm beams with opposite topological charges does not show rotational behavior and that there exists rotation for other topological charge combinations. Our theory predicts that the accessible solitons cannot exist in LHMs.

Design of Structural Left-handed Material based on Topology Optimization

An effective method to design structural Left-handed material（LHM） was proposed. A commercial finite element software HFSS and S-parameter retrieval method were used to determine the effective constitutive parameters of the metamaterials, and topology optimization technique was introduced to design the microstructure configurations of the materials with desired electromagnetic characteristics. The material considered was a periodic array of dielectric substrates attached with metal film pieces. By controlling the arrangements of the metal film pieces in the design domain, the potential microstructure with desired electromagnetic characteristics can be obtained finally. Two different LHMs were obtained with maximum bandwidth of negative refraction, and the experimental results show that negative refractive indices appear while the metamaterials have simultaneously negative permittivity and negative permeability. Topology optimization technique is found to be an effective tool for configuration design of LHMs.

TM modes in asymmetric slab waveguides with left-handed material

Three-layer slab waveguide with left-handed materials （LHM） is discussed using the Maxwell＇s equations and their equations of dispersion relation for TM modes are obtained. By seeking the power of the slab waveguide, their equations of effective thickness for TM modes are obtained. Furthermore, the interrelated equations for right-handed materials （RHM） slab waveguide are introduced and their curves plotted. To find new properties for LHM slab waveguide, the equations and their curves for the LHM and RHM slab waveguide are compared respectively.

Propagation of Airy beams from right-handed material to left-handed material

Based on the ABCD matrix formalism,the propagation property of an Airy beam from right-handed material（RHM） to left-handed material（LHM） is investigated.The result shows that when the Airy beam propagates in the LHM,the intensity self-bending due to its propagation in the RHM can be compensated.In particular,if the propagation distance in the RHM is equal to that in the LHM and the refractive index of the LHM is n L =-1,the transverse intensity distribution of the Airy beam can return to its original state.

Microwave left-handed composite material made of slim ferrite rods and metallic wires

This paper reports on experimental study of the microwave properties of a composite material consisting of ferrite and copper wires. It finds that the slim ferrite rods can modify the magnetic field distribution through their anisotropy, so that the ferrite＇s negative influence on the copper wires＇ plasma will be reduced. Left-handed properties are observed even in the specimen with close stuck ferrite rods and copper wires.

（3＋1）-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material

In this paper a comprehensive framework for treating the nonlinear propagation of ultrashort pulse in metamaterial with dispersive dielectric susceptibility and magnetic permeability is presented. Under the slowly-evolving-wave approximation, a generalized （3＋1）-dimensional wave equation first order in the propagation coordinate and suitable for both right-handed material （I^HM） and left-handed material （LHM） is derived. By the commonly used Drude dispersive model for LHM, a （3＋1）-dimensional nonlinear Schrodinger equation describing ultrashort pulsed beam propagation in LHM is obtained, and its difference from that for conventional RHM is discussed. Particularly, the self-steeping effect of ultrashort pulse is found to be anomalous in LHM.

Wave propagation in parallel-plate waveguides filled with nonlinear left-handed material

A theoretical investigation of field components for transverse electric mode in the parallel-plate waveguides has been studied. In this analysis two different types of waveguide structures have been discussed, i.e., （a） normal good/perfect conducting parallel-plate waveguide filled with nonlinear left-handed material and （b） high-temperature-superconducting parallel-plate waveguide filled with nonlinear left-handed material. The dispersion relations of transverse electric mode have also been discussed for these two types of waveguide structures.

The anomalous radiation force of light on a left-handed material

This paper derives the force of the electromagnetic radiation on left-handed materials （LHMs） by a direct application of the Lorentz law of classical electrodynamics. The expressions of radiation force are given for TE-polarised and TM-polarised fields. The numerical results demonstrate that electromagnetic waves exert an inverse lateral radiation force on each edge of the beams, that is, the lateral pressure is expansive for TE-polarised beams and compressive for TM-polarised beams. The investigation of the radiation force will provide insights into the fundamental properties of LHMs and will provide to better understanding of the interaction of light with LHMs.

Propagation of rotating elliptical Gaussian beams from right-handed material to left-handed material

By applying the ABCD matrix method, we report the propagating properties of the rotating elliptical Gaussian beams（REGBs） from the right-handed material（RHM） to the left-handed material（LHM）. Based on the propagation equation, we obtain the intensity distributions of the REGBs during the propagation. It is found that the rotating direction of the REGBs is opposite in the RHM and the LHM, and the rotation angles tend to be π /2 as the propagation distance is long enough.Then we analyze the relationship between the refractive index and the rotating velocity. Furthermore, the energy flow and the angular momentum（AM） of the REGBs which can rotate are also obtained.

Photon tunneling and transmittance resonance through a multi-layer structure with a left-handed material

This paper investigates the photon tunneling and transmittance resonance through a multi-layer structure including a left-handed material（LHM）. An analytical expression for the transmittance in a five-layer structure is given by the analytical transfer matrix method. The transmittance is studied as a function of the refractive index and the width of the LHM layer. The perfect photon tunneling results from the multi-layer structure, especially from the relation between the magnitude of the refractive index and the width of the LHM layer and those of the adjoining layers. Photons may tunnel through a much greater distance in this structure. Transmittance resonance happens, the peaks and valleys appear periodically at the resonance thickness. For an LHM with inherent losses, the perfect transmittance is suppressed.

TE Modal Dispersion in Dielectric Slab Waveguide with Lossy Left-Handed Metamaterial

In this work, we derived the modal dispersion relation for TEm modes for a symmetric slab waveguide constructed from SiO2 dielectric guiding core material with lossy left-handed material (LHM) as cladding and substrate, and the power confinement factor. The dispersion relations and the power confinement factor were numerically solved for a given set of parameters: allowed frequency range;core’s thicknesses;and TEm mode order. We found that the real part of the effective refractive index decreased with thickness and frequency increase. Moreover, the imaginary part (extinction coefficient) of the effective refractive index has very small values for all thickness in the frequency ranges, which means the waveguide structure is transparent for the used frequencies. The waveguide structure offers good guiding power for all thickness in the frequency range with low power attenuation. The real part of the effective refractive index increases with the increase of mode order, and the power confinement factor decreases with the increase of mode order.

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.