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.

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.

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.

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.

A power divider based on a new kind of composite right/left-handed transmission line (CRLH TL) unit

A new power divider, composed of a novel composite right/left-handed (CRLH) transmission line (TL) unit, is proposed. The properties of the power divider based on four CRLH TL unit cells are investigated theoretically. By adjusting the parameters of the capacitors and the inductors, the power divider shows perfectly symmetric power division at 5.13 GHz, return loss up to ?24 dB, with the transmitted power being close to ?3.1 dB. The phenomena are demonstrated by simulation results. Being compact in size and low-cost, the proposed power divider is very suitable for microwave and millimeter wave integrated circuits.

Novel resonator based on composite right/left-handed transmission lines

A new approach was introduced to analyze composite right/left-handed transmission lines （CRLH TLs）. The Bloch impedance and the dispersion relations are directly obtained from the S parameters of the unit cells. The LH and RH frequency bands are then identified by the real parts of the Bloch impedance and the phase delay of the unit cells. The new approach has some advantages over the LC parameters extraction method introduced by Caloz et a1.（2004）. Based on the new approach, a novel resonator is designed using CRLH TLs. The simulation and experimental results accorded well with the theoretical analysis. The novel resonator may have potential applications in filters with high harmonic suppression and compact structures,

A planar left-handed metamaterial based on electric resonators

A planar left-handed metamaterial（LHM） composed of electric resonator pairs is presented in this paper. Theoretical analysis, an equivalent circuit model and simulated results of a wedge sample show that this material exhibits a negative refraction pass-band around 9.6GHz under normal-incidence and is insensitive to a change in incidence angle. Furthermore, as the angle between the arm of the electric resonators and the strip connecting the arms increases, the frequency range of the pass-band shifts downwards. Consequently, this LHM guarantees a relatively stable torlerence of errors when it is practically fabricated. Moreover, it is a candidate for designing multi-band LHM through combining the resonator pairs with different angles.

Dual-band left-handed metamaterials fabricated by using tree-shaped fractal

A method of fabricating dual-band left-handed metematerials （LHMs） is investigated numerically and experimen- tally by single-sided tree-like fractals. The resulting structure features multiband magnetic resonances and two electric resonances. By appropriately adjusting the dimensions, two left-handed （LH） bands with simultaneous negative per- mittivity and permeability are engineered and are validated by full-wave eigenmode analysis and measurement as well in the microwave frequency range. To study the multi-resonant mechanism in depth, the LHM is analysed from three different perspectives of field distribution analysis, circuit model analysis, and geometrical parameters evaluation. The derived formulae are consistent with all simulated results and resulting electromagnetic phenomena, indicating the ef- fectiveness of the established theory. The method provides an alternative to the design of multi-band LHM and has the advantage of not requiring two individual resonant particles and electrically continuous wires, which in turn facilitates planar design and considerably simplifies the fabrication.

（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.

Left-handed properties of a composite structure with metallic wires in a homogeneous Lorentz medium

The electromagnetic properties of a composite structure with metallic wires in a Lorentz medium were studied. The results show that the electromagnetic properties of the medium host influence the plasma resonance of metallic wires and the left-handed character of the composite. The plasma frequency of metallic wires reduces with the rise of permittivity or permeability of the medium host. Also, the negative permeability of the medium can destroy the wires’ plasma resonance and prevent the realization of left-handed properties. The high loss of medium permittivity or permeability also inhibits the metallic plasma resonance. The negative influence of the media host on the left-handed properties of the composite structure can be effectively reduced by proper structure design, such as introducing a nonmagnetic medium in the host or using an anisotropic medium.

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.

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.

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.

A tunable dual-broad-band branch-line coupler utilizing composite right/left-handed transmission lines

A tunable dual-broad-band branch-line coupler (BLC) utilizing composite right/left-handed (CRLH) transmission lines is presented. Two λ/4 segments consisting of CRLH transmission lines are added to each port to broaden the dual bands of the branch-line coupler. Numerical simulation and optimal design of the novel coupler are presented. The dual bands of the novel coupler are tunable and broad. The 1-dB bandwidth of each pass band is more than 16% of the central frequency.

Enhanced Kerr nonlinearity in a left-handed three-level atomic system driven by a bichromatic field

China） Enhanced Kerr nonlinearity in a left-handed atomic system consisting of three levels driven by a bichromatic field is presented in this paper. Based on bichromatic field coherence, the real parts of the permittivity and permeability can obtain negative values simultaneously in the same detuning frequency region. By adjusting the frequency difference and the Rabi frequencies of the bichromatic field, the multi-band left-handed behavior of the presented atomic metamaterial is exhibited. Meanwhile, the enhanced Kerr nonlinearity can be realized in this multi-band left-handed three-level atomic system. It is shown that the third-order susceptibility possesses focusing or defocusing properties in the same frequency band.

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.

Propagation of Gaussian beams family through a Kerr-type left-handed metamaterial

In this paper the propagation of elegant Hermite-cosh-Gaussian, elegant Laguerre Gaussian, and Bessel Gaussian beams through a Kerr left-handed metamaterial （LHM） slab have been studied. A split-step Fourier method is used to investigate the propagation of laser beams through this media. Numerical simulation shows that Gaussian beams have different focusing behaviors in a Kerr LHM slab with positive or negative nonlinearity. Beam focusing happens in slabs with positive nonlinearity and not in slabs with negative nonlinearity; however, negative nonlinearity is required for a Kerr LHM slab to act like a lens. Additionally, the focusing properties of beams can be controlled by controlling the thickness of the slab or the input power of the incident beam. A multilayer structure is also proposed to have beam focusing by thinner slabs and passing longer distances.

All-dielectric left-handed metamaterial based on dielectric resonator:design,simulation and experiment

Dipoles with Lorentz-type resonant electromagnetic responses can realise negative effective parameters in their negative resonant region. The electric dipole and magnetic dipole can realise, respectively, negative permittivity and negative permeability, so both the field distribution forms of electric and magnetic dipoles are fundamentals in designing left-handed metamaterial. Based on this principle, this paper studies the field distribution in high-permittivity dielectric materials. The field distributions at different resonant modes are analysed based on the dielectric resonator theory. The origination and influence factors of the electric and magnetic dipoles are confirmed. Numerical simulations indicate that by combining dielectric cubes with different sizes, the electric resonance frequency and magnetic resonance frequency can be superposed. Finally, experiments are carried out to verify the feasibility of all-dielectric left-handed metamaterial composed by this means.