Right-handed Material Research Articles

Goos-Hänchen and Imbert-Fedorov shifts of vortex beams at air–left-handed-material interfaces

In this paper, we present a systematic study of beam shifts and angular momenta of paraxial vortex beams at air--left-handed-material (LHM) interfaces. It is shown that, compared to their counterparts at air--right-handed-material (RHM) interfaces, the spatial Goos-H\"anchen (GH) and Imbert-Fedorov (IF) shifts remain the same, while the angular GH and IF shifts are reversed at air-LHM interfaces. The spatial and angular shifts of paraxial vortex beams have their respective origins in transverse angular momenta and transverse linear momenta. The spatial GH and IF shifts remain unreversed as a result of both reversions of transverse angular momenta and $z$-component linear momentum, while the angular GH and IF shifts are reversed because the $z$-component linear momentum is reversed and the transverse linear momenta are unreversed at air-LHM interfaces. In addition, we perform a quantitative analysis on spin-orbit angular momentum conversion and orbit-orbit angular momentum conversion, which further helps us understand the essence of vortex beam shifts at air-LHM interfaces and their fundamental distinctions from those at air-RHM interfaces.

Tuned switching of surface waves by a liquid crystal cap layer in one-dimensional photonic crystals

In this paper, we theoretically study the electromagnetic surface waves localized at the interface between a homogeneous dielectric medium and a semi-infinite, one-dimensional photonic crystal (1D PC). The semi-infinite 1D PC is made of alternative layers of right-handed (RH) and dispersive left-handed (LH) materials in the presence of a liquid crystal (LC) cap layer. In this structure, we derive the surface waves dispersion relation with tunable switching and localization by using an analytical direct matching procedure within the Kronig-Penny model. It is shown that, for both of layer arrangements, the variation of molecules orientation of the LC cap layer acts as an effective tool to tune the type (tuned switching) and localization of the surface waves and it also can create a surface mode with maximum localization in the first frequency bandgap.

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 nL = −1, the transverse intensity distribution of the Airy beam can return to its original state.

Creating electromagnetic cavities using transformation optics

We investigate the potential of transformation optics for the design of novel electromagnetic cavities. First, we determine the dispersion relation of bound modes in a device performing an arbitrary radial coordinate transformation and we discuss a number of such cavity structures. Subsequently, we generalize our study to media that implement azimuthal transformations, and show that such transformations can manipulate the azimuthal mode number. Finally, we discuss how the combination of radial and azimuthal coordinate transformations allows for perfect confinement of subwavelength modes inside a cavity consisting of right-handed materials only.

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.

Anderson localization in metamaterials with compositional disorder

We consider one-dimensional periodic-on-average bi-layered models with random perturbations in dielectric constants of both basic slabs composing the structure unit-cell. We show that when the thicknesses da and db of basic layers are essentially nonequal, da ≠ db, the localization length Lloc is described by the universal expression for two cases: (a) both layers are made from right-handed materials (the RH–RH model), (b) the a layers are of a right-handed material while the b layers are of a left-handed material (the RH–LH model). For these models the derived expression for Lloc includes all possible correlations between two disorders. However, when da = db the RH–LH model exhibits a highly nontrivial properties originated from inhomogeneous distribution of the phase of propagating wave, even in the case of white-noise disorder. We analytically show that in this case the localization length diverges in the conventional second order in perturbation parameters. Therefore, recently numerically discovered anomalies in Lloc are due to the next order of approximation. On the other hand, for the RH–RH model the general expression for Lloc remains valid for da = db as well.

A compact polarization splitter utilizing directional coupler with left-handed material

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.

Investigation of optical properties of Tamm states in higher bands of multilayer stacks including right and left handed materials

We study the electromagnetic surface wave localizing, the so-called surface Tamm states, at an interface separating a left-handed metamaterial (LHM) and a semi-infinite one-dimensional photonic crystal made of alternative left-handed metamaterial and right-handed materials. We show that the existence of metamaterial causes the Tamm states with backward energy flow and allows flexible control of dispersion properties of the surface modes. We study the effect of the physical parameters of the photonic crystal on the dispersion properties and the group velocity of the Tamm states. We also study dispersion properties of the Tamm states in higher order photonic band gaps of the photonic crystal and compare our results with the case when the LHM medium is replaced by a right-handed material (RHM).

Analytical solution for SH wave propagating through a graded plate of metamaterial

A physical model for the shear horizontal (SH) wave propagating from left-handed material (LHM) through a graded or transition layer to right-handed material (RHM) has been proposed in this paper. After the comparison of the basic wave equations of the electromagnetic, longitudinal, and SH waves, it is found that they take similar differential form. The analytical solutions have been found for power law, hyperbolic, and polynomial profiles. Numerical waveforms of the amplitude and phase of the displacement are obtained for the corresponding profiles. It is found that the waveforms are symmetric for the power law and hyperbolic profiles, and that the waveform for the polynomial profile is shifted and non-symmetric. The shift along with the anti-symmetric profile may provide a way to monitor the wave behavior of the metamaterials.

Dark localized structures in a cavity filled with a left-handed material

We consider a nonlinear passive optical cavity filled with left-handed and right-handed materials and driven by a coherent injected beam. We assume that both left-handed and right-handed materials possess a Kerr focusing type of nonlinearity. We show that close to the zero-diffraction regime, high-order diffraction allows us to stabilize dark localized structures in this device. These structures consist of dips in the transverse profile of the intracavity field and do not exist without high-order diffraction. We analyze the snaking bifurcation diagram associated with these structures. Finally, a realistic estimation of the model parameters is provided.

Possible realization of negative refraction in Bose-Einstein condensates

It is well known that negative refraction (NR) can be achieved in left-handed materials. Recently, it is suggested that NR can also be realized in certain active right-handed materials. However, no experimental realization of that has been achieved yet. In this paper, further theoretical constraints on the material parameters are obtained, a possible experimental realization based on the Bose-Einstein condensation (BEC) is proposed, and the detecting method to verify NR is suggested. The feasibility of the proposal is demonstrated. Our conclusion is that this new type of NR can probably be realized in the BEC.

Control of direction of Goos–Hänchen shift on reflection from a weakly absorbing medium

The Goos–Hänchen effect of reflected beams at the interface between isotropic medium and weakly absorbing medium was studied. We find that there is a lateral shift when a light beam travels through the interface for reflected beam for TM wave. The influence of permeability and permittivity on the Goos–Hänchen shift was discussed, respectively. When the weakly absorbing medium is right-handed material the imaginary of magnetic permeability will control the direction and magnitude of the shift. On the contrary, when the weakly absorbing medium is left-handed material, the refractive index of the isotropic medium determines the direction and magnitude of the shift.

Plasmon polariton and〈n〉=0non-Bragg gaps in superlattices with metamaterials

We consider one-dimensional photonic superlattices made up of alternate layers of a right-handed nondispersive material and a metamaterial with Drude-type dielectric permittivity and magnetic permeability. By thoroughly investigating the dispersion relation for the propagation of obliquely incident optical fields obtained from Maxwell's equations and the transfer-matrix technique, we demonstrate that, in the long-wavelength limit, the dispersion is the same that one would obtain by considering a homogeneous effective medium with Drude-type responses at shifted electric and magnetic plasmon frequencies. Moreover, we show that the plasmon polariton and $\ensuremath{\langle}n\ensuremath{\rangle}=0$ non-Bragg gaps correspond to regions of the low-energy spectrum where the effective medium is absorptive, exhibiting an imaginary effective refraction index.

Complex conjugate media: Alternative configurations for miniaturized lasers

We show that complex conjugate materials, in which the ratio of the complex electrical permittivity and the complex conjugate magnetic permeability is real, are characterized by a real refractive index and thus allow non-attenuated propagation of electromagnetic waves. Although complex conjugated media obey the same Snell law as common right-handed non-magnetic materials with the same refractive index, they differ from the latter through the reflection and transmission coefficients of electromagnetic waves. The complex conjugate materials could have important applications in miniaturized optical amplifiers and lasers.

Dispersion properties of nonlinear surface waves in one-dimensional photonic crystals with a nonlinear self-defocusing cap layer of left-handed metamaterial

In this paper we investigate analytically the localized surface waves (SWs) based on the first integral of the nonlinear Helmholtz wave equation in a semi-infinite one-dimensional photonic crystal (1DPC) truncated with a self-defocusing nonlinear cap layer of a left-handed material (LHM). The intensity-dependent properties of nonlinear SWs at the interface between air background and 1DPC are of two types: conventional photonic crystal (PC) and left-handed PC (made of alternate LHM and right-handed material) ones. It is shown that there are unusual SWs with different peculiarities for these two types of PC. To confirm our results, we also compared the results obtained by this method and the alternative method based on δ-function, for the structure with a very thin nonlinear cap layer.

Oscillating guided modes in a symmetric five-layer slab waveguide with anisotropic-dispersive left-handed material

A symmetric five-layer slab waveguide with anisotropic and dispersive left-handed material (LHM) in the core and righthanded material (RHM) in other layers is investigated. Through Maxwell’s equations and a transfer matrix method, the dispersion equations for the TE oscillating guided modes are obtained. Under consideration of two extremely anisotropic cases, some mode dispersion curves are plotted. The zero-order TE oscillating guided mode exists. Meanwhile, with the increase of mode number, their dispersion curves move to left or right, corresponding to positive or negative dielectric permittivity and magnetic permeability in the longitudinal direction. Besides, as the core thickness increases, mode dispersion properties change and three propagation properties appear: positive group velocity, negative group velocity and zero group velocity. The negative group velocity indicates the characteristics of the left-handed materials, and the zero group velocity implies that electromagnetic waves are trapped in the waveguide completely.

Controlled switching of surface waves in 1D photonic crystals by a thin nonlinear cap layer

In this paper, we investigate the electromagnetic surface waves localized at the interface of the homogeneous dielectric medium and a semi-infinite one-dimensional photonic crystal (1D PC), theoretically. The semi-infinite 1D PC is made of alternative layers of left-handed (LH) and right-handed (RH) materials in the presence of a thin nonlinear cap layer. We consider magnetic permeability and electric permittivity of LH layers being dispersive and non-dispersive. We used an analytical direct matching procedure within the Kronig-Penny model to analyze the dispersion behavior of surface waves with controllable localization. It is shown that the thin nonlinear cap layer acts as a tool to change the backward surface waves to forward ones and vice versa and it plays an important role on the localization of them. Also we show that when the LH layers are chosen dispersive, negative dispersion of surface waves are obtained in a wide range of radiation angle and frequency, and we propose an approach to calculate the applied electric field intensity that leads to switching of surface waves from backward to forward and creating a surface mode with maximum localization.

Anderson localization of classical waves in weakly scattering metamaterials

We study the propagation and localization of classical waves in one-dimensional disordered structures composed of alternating layers of left- and right-handed materials (mixed stacks) and compare them with structures composed of different layers of the same material (homogeneous stacks). For weakly scattering layers, we have developed an effective analytical approach and have calculated the transmission length within a wide range of the input parameters. This enables us to describe, in a unified way, the localized and ballistic regimes as well as the crossover between them. When both refractive index and layer thickness of a mixed stack are random, the transmission length in the long-wave range of the localized regime exhibits a quadratic power wavelength dependence with different coefficients of proportionality for mixed and homogeneous stacks. Moreover, the transmission length of a mixed stack differs from the reciprocal of the Lyapunov exponent of the corresponding infinite stack. In both the ballistic regime of a mixed stack and in the near long-wave region of a homogeneous stack, the transmission length of a realization is a strongly fluctuating quantity. In the far long-wave part of the ballistic region, the homogeneous stack becomes effectively uniform and the transmission length fluctuations are weaker. The crossover region from the localization to the ballistic regime is relatively narrow for both mixed and homogeneous stacks. In mixed stacks with only refractive-index disorder, Anderson localization at long wavelengths is substantially suppressed, with the localization length growing with wavelength much faster than for homogeneous stacks. The crossover region becomes essentially wider and transmission resonances appear only in much longer stacks. The effects of absorption on one-dimensional transport and localization have also been studied, both analytically and numerically. Specifically, it is shown that the crossover region is particularly sensitive to losses, so that even small absorption noticeably suppresses frequency dependent oscillations in the transmission length. All theoretical predictions are in an excellent agreement with the results of numerical simulations.

The experimental investigation of the discrete mode in the zero-average-refractive-index gap

We experimentally investigate the discrete mode in the zero-average-refractive-index gap (the zero-n—gap) of the one-dimensional periodical structures containing left-handed materials (LHMs) and right-handed materials (RHMs). When the discrete mode conditions are satisfied in the zero-n gap, there are no discrete propagating modes, but the zero-n—gap completely vanishes. This behavior is attributed to the dispersive property of LHMs and RHMs. In addition, the theoretical expectation of the discrete modes with no sidelobes in the zero-n—gap never occurs in experiment because the LHMs is intrinsically dispersive.

Beyond the zero-diffraction regime in optical cavities with a left-handed material

The combination of right-handed and left-handed materials offers the possibility to design devices in which the mean diffraction is zero. Such systems are encountered, for example, in nonlinear optical cavities, where a true zero-diffraction regime could lead to the formation of patterns with arbitrarily small sizes. In practice, the minimal size is limited by nonlocal terms in the equation of propagation. We study the nonlocal properties of light propagation in a nonlinear optical cavity containing a right-handed and a left-handed material. We obtain a model for the propagation, including two sources of nonlocality: the spatial dispersion of the materials in the cavity, and the higher-order terms of the mean field approximation. We apply these results to a particular case and derive an expression for the parameter fixing the minimal size of the patterns.