We analyze nonlinear properties of microstructured materials with negative refraction, the so-called left-handed metamaterials. We demonstrate that the hysteresis-type dependence of the magnetic permeability on the field intensity allows changing the material properties from left- to right-handed and back. Using the finite-difference time-domain simulations, we study wave transmission through the slab of nonlinear left-handed material, and predict existence of temporal solitons in such materials. We demonstrate also that nonlinear left-handed metamaterials can support both TE- and TM-polarized self-trapped localized beams, spatial electromagnetic solitons. Such solitons appear as single- and multi-hump beams, being either symmetric or antisymmetric, and they can exist due to the hysteresis-type magnetic nonlinearity and the effective domains of negative magnetic permeability.
A theory of self-induced transparency of surface TM-mode propagating along a interface separating conventional and left-handed metamaterials is developed. A transition layer sandwiched between connected media is described using a model of a two-dimensional gas of quantum dots. Explicit analytical expressions for a surface optical soliton in the presence of single and biexciton transitions, depending on the magnetic permeability of the left-handed medium, are obtained with realistic parameters which can be reached in current experiments. It is shown that the sign of the total energy flow the su…
We study the electromagnetic surface waves localized at an interface separating a one-dimensional photonic crystal and left-handed metamaterial, the so-called surface Tamm states. We demonstrate that the metamaterial allows for a flexible control of the dispersion properties of surface states, and can support the Tamm states with a backward energy flow and a vortex-like structure.
Left-handed metamaterials make perfect lenses that image classical electromagnetic fields with significantly higher resolution than the diffraction limit. Here we consider the quantum physics of such devices. We show that the Casimir force of two conducting plates may turn from attraction to repulsion if a perfect lens is sandwiched between them. For optical left-handed metamaterials this repulsive force of the quantum vacuum may levitate ultra-thin mirrors.
We predict that nonlinear left-handed metamaterials can support both TE- and TM-polarized self-trapped localized beams, spatial electromagnetic solitons. Such solitons appear as single- and multi-hump beams, being either symmetric or antisymmetric, and they can exist due to the hysteresis-type magnetic nonlinearity and the effective domains of negative magnetic permeability.
We study the beam reflection from a layered structure with a left-handed metamaterial. We predict a giant lateral (Goos-Hanchen) shift and splitting of the beam due to the resonant excitation of surface polaritons with a vortex-like energy flow between the right- and left-handed materials.
We study the effect of disorder on the effective magnetic response of composite left-handed metamaterials and their specific properties such as negative refraction. We show that relatively weak disorder in the split-ring resonators can reduce and even completely eliminate the frequency domain where the composite material demonstrates the left-handed properties. We introduce the concept of the order parameter to describe novel physics of this effect.
We study the second-harmonic generation in left-handed metamaterials with a quadratic nonlinear response. We demonstrate a novel type of the exact phase matching between the backward propagating wave of the fundamental frequency and the forward propagating wave of the second harmonics. We show that this novel parametric process can convert a surface of the left-handed metamaterial into an effective mirror totally reflecting the second harmonics generated by an incident wave. We derive and analyze theoretically the coupled-mode equations for a semi-infinite nonlinear metamaterial. We also study…
A bulk left-handed metamaterial with fishnet structure is investigated to show the optical loss compensation via surface plasmon amplification, with the assistance of a Gaussian gain in PbS quantum dots. The optical resonance enhancement around 200 THz is confirmed by the retrieval method. By exploring the dependence of propagation loss on the gain coefficient and metamaterial thickness, we verify numerically that the left-handed response can endure a large propagation thickness with ultralow and stable loss under a certain gain coefficient.
We describe the properties of birefringent left-handed metamaterials and introduce the concept of a birefringent perfect lens. We demonstrate that, in a sharp contrast to the conventional left-handed perfect lens at $ε=μ=-1$, where $ε$ is the dielectric constant and $μ$ is the magnetic permeability, the birefringent left-handed lens can focus either TE or TM polarized waves or both of them, allowing a spatial separation of the TE and TM images. We discuss several applications of the birefringent left-handed lenses such as the beam splitting and near-field diagnostics at the sub-wavelength scal…
A scheme of left-handed metamaterial (LHM) composed of superconducting quantum interference devices (SQUIDs) and conducting wires is proposed. The permeability of a probe field can be smoothly tuned over a wide range with another electromagnetic (coupling) field due to quantum interference effect. Similar to electromagnetically induced transparency (EIT) of atomic systems, the absorption of the probe field can be strongly suppressed even in the case of negative permeability. There are two passbands of negative refractive index with low loss, which can be tuned with the coupling field.
The Doppler shift is investigated in one-dimensional system with moving source. Theoretical findings are confirmed in numerical simulations of optical and acoustical waves propagation in simple metamaterial model, showing the reversed shift and the existence of multiple frequency modes. The properties of these waves are discussed. The effect of absorption on the phenomenon is outlined.
We derive the formula of the complex Doppler shift in a two-dimensional, dispersive metamaterial and we show that a moving, monochromatic radiation source generates multiple frequency modes. The role of the group velocity is stressed and the Doppler shifted radiation field exhibits features of the Cherenkov effect. The presented theory is also applicable to the case of a moving, nonoscillating charge and explains many peculiar characteristics of the Cherenkov radiation in lefthanded metamaterials such as the backward direction of power emission, the constant radiation angle and the lack of vel…
We demonstrate that left-handed resonance transmission from metallic metamaterial, composed of periodically arranged double rings, can be extended to visible spectrum by introducing an active medium layer as the substrate. The severe ohmic loss inside metals at optical frequencies is compensated by stimulated emission of radiation in this active system. Due to the resonance amplification mechanism of recently proposed lasing spaser, the left-handed transmission band can be restored up to 610 nm wavelength, in dependence on the gain coefficient of the active layer. Additionally, threshold gains…
In this paper we explored the scattering behavior of thin cylinders made of LHM and coated by a monoatomic graphene layer. A spectral tunability of the resonance peaks is evidenced by altering the chemical potential of the graphene coating, a fact that occurs at any state of polarization of the incident plane wave in opposition to the case of scatterers of dielectric core. On the contrary, no invisibility condition can be satisfied for dielectric environments. A singular performance is also found for cylinders with permittivity and permeability near zero. Practical implementations of our resul…
We perform a theoretical investigation on the Goos-Hächen (GH) shift in one-dimensional photonic crystals (1DPCs) containing left-handed metamaterials (LHMs). We find an unusal effect of the GH shift near the photonic band-crossing structure, which is located at the condition, $% -k_{z}^{(A)}d_{A}=k_{z}^{(B)}d_{B}=mπ$ $(m=1,2,3...)$, under the inclined incident angle, here A denotes the LHM layer and B denotes the dielectric layer. Above the frequency of the band-crossing point (BCP), the GH shift changes from negative to positive as the incident angle increases, while the GH shift changes rev…
Following our recent theoretical development of the concept of nano-inductors, nano-capacitors and nano-resistors at optical frequencies and the possibility of synthesizing more complex nano-scale circuits, here we theoretically investigate in detail the problem of optical nano-transmission-lines (NTL) that can be envisioned by properly joining together arrays of these basic nano-scale circuit elements. We show how, in the limit in which these basic circuit elements are closely packed together, the NTLs can be regarded as stacks of plasmonic and non-plasmonic planar slabs, which may be designe…
Electromagnetic metamaterials are man-made structures that have novel properties such as a negative refraction index, not attainable in naturally occurring materials. Although negative index materials (NIMs) in microwave frequencies were demonstrated in 2001, it has remained challenging to design NIMs for optical frequencies especially those with both negative permittivity and negative permeability [known as left-handed metamaterials (LHMs)]. Here, by going beyond the traditional concept of the combination of artificial electronic and magnetic meta-atoms to design NIMs, we propose a novel LHM …
We predict that optical Bloch oscillations can be observed in layered structures with left-handed metamaterials and zero average refractive index where the layer thickness varies linearly across the structure. We demonstrate a new type of the Bloch oscillations associated with coupled surface waves excited at the interfaces between the layers with left-handed material and conventional dielectric.
We present a theoretical study of electromagnetic surface waves localized at an interface separating a conventional uniform medium and a semi-infinite 1-D photonic crystal made of alternate left-handed metamaterial and right-handed material which we refer to as left-handed photonic crystal. We find novel type of surface mode's structure, the so-called surface Tamm states and demonstrate that the presence of metamaterial in the photonic crystal structure allows for a flexible control of the dispersion properties of surface states, and can support the Tamm states with a backward energy flow and …
Using detailed simulations we investigate the magnetic response of metamaterials consisting of pairs of parallel slabs or combinations of slabs with wires (including the fishnet design) as the length-scale of the structures is reduced from mm to nm. We observe the expected saturation of the magnetic resonance frequency when the structure length-scale goes to the sub-micron regime, as well as weakening of the effective permeability resonance and reduction of the spectral width of the negative permeability region. All these results are explained by using an equivalent resistor-inductor-capacitor…
We suggest a principle for isolation of circularly polarized waves in magnetically active extreme-parameter metamaterials. Using theoretical analysis and numerical simulations, we show that metamaterials with extreme parameters, such as epsilon-near-zero materials (ENZ), when merged with magneto-optical materials, become transparent for forward circularly polarized waves of a given handedness and opaque for backward propagating waves of the same handedness. We theoretically study two possible implementations of such hybrid materials: (1) the case of metal-dielectric stacks; and (2) rectangular…
It is shown that artificial magnetism with relatively large frequency bandwidth can be obtained from periodic arrangements of dielectric rings. Combined with dielectric rods, dielectric rings can provide 3D isotropic left-handed metamaterials being an advantageous alternative to metallic split ring resonators and/or metallic wires when un-detectability by low frequency external magnetic fields is desired. Furthermore it is shown that dielectric rings can be also combined with natural plasma-like media to obtain a left-handed metamaterial.
We demonstrate that non-magnetic ($μ\equiv 1$) left-handed materials can be effectively used for waveguide imaging systems. We also propose a specific THz realization of the non-magnetic left-handed material based on homogeneous, naturally-occurring media.
Some novel quasi-planar chiral inclusions, feasible from standard photo-etching techniques, are proposed. It is shown that such inclusions can be designed in order to present balanced electric, magnetic and magneto-electric polarizabilities. Using these inclusions, random and periodic bi-isotropic artificial metamaterials exhibiting a balanced positive/negative refractive index can be build up. These metamaterials would exhibit reasonable bandwidths and excellent matching to free space.
The electronic Lorentz theory is employed to determine the electromagnetic response of planar split-ring metamaterials. Starting from the dynamics of individual free carriers, the effective permittivity tensor of the metamaterial is calculated. Whenever the split ring lacks in-plane mirror symmetry, the corresponding permittivity tensor has a crystallographic structure of an elliptically dichroic medium, and the metamaterial exhibits optical properties of planar chiral structures. Its transmission spectra are different for right-handed vs. left-handed circular polarization of the incident wave…
The Doppler effects for the reflected wave from a moving media are systemically analyzed in this paper. The theoretical formula for the Doppler shift in the left-handed material, which is described by Drude's dispersion model, is presented. This formula is examined by first-principles numerical experiments, which are in agreement with the theoretical results.
We analyze transmission of electromagnetic waves through a periodic band-gap structure consisting of slabs of a left-handed metamaterial and air. Using the effective parameters of the metamaterial derived from its microscopic structure, we study, with the help of the transfer-matrix approach and by means of the finite-difference-time-domain numerical simulations, the transmission properties of such a left-handed photonic crystals in a novel type of band gap associated with the zero averaged refractive index. We demonstrate that the transmission can be made tunable by introducing defects, which…
Some physically interesting properties and effects of wave propagation in biaxially anisotropic left-handed materials are investigated in this paper. We show that in the biaxially gyrotropic left-handed material, the left-right coupling of circularly polarized light arises due to the negative indices in permittivity and permeability tensors of gyrotropic media. It is well known that the geometric phases of photons inside a curved fiber in previous experiments often depend on the cone angles of solid angles subtended by a curve traced by the direction of wave vector of light, at the center of p…
In this Letter, it is claimed that, in addition to the Chiao-Wu geometric phase and optical Aharonov-Carmi geometric phase, there exists a new interesting geometric phase caused by the helicity inversion of photons in the optical fiber composed periodically of left- and right- handed (LRH) media. By making use of the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, we calculate this geometric phase. It is emphasized that this geometric phase should not been neglected when considering the anomalous refraction on the interfaces between left- and rig…
The linear and nonlinear surface waves propagating along the interface separating isotropic conventional and uniaxially anisotropic left-handed materials is investigated. The conditions of the existence of surface TM-modes is determined. It is shown that surface waves can be formed when the components of the permittivity and permeability tensors of the uniaxially anisotropic left-handed materials are simultaneously negative. A transition layer sandwiched between connected media is described using a model of a two-dimensional gas of quantum dots. Explicit analytical expressions for a surface op…
A wedge-shaped structure made of split-ring resonators (SRR) and wires is numerically simulated to evaluate its refraction behavior. Four frequency bands, namely, the stop band, left-handed band, ultralow-index band, and positive-index band, are distinguished according to the refracted field distributions. Negative phase velocity inside the wedge is demonstrated in the left-handed band and the Snell's law is conformed in terms of its refraction behaviors in different frequency bands. Our results confirmed that negative index of refraction indeed exists in such a composite metamaterial and also…
We analyze nonlinear guided waves in a planar waveguide made of a left-handed material surrounded by a Kerr-like nonlinear dielectric. We predict that such a waveguide can support fast and slow symmetric and antisymmetric nonlinear modes. We study the symmetry breaking bifurcation and asymmetric modes in such a symmetric structure. We analyze nonlinear dispersion properties of the guided waves, and show that the modes can be both forward and backward.
Employing a nonlinear left-handed transmission line as a model system, we demonstrate experimentally the multi-stability phenomena predicted theoretically for microstructured left-handed metamaterials with a nonlinear response. We show that the bistability is associated with the period doubling which at higher power may result in chaotic dynamics of the transmission line.
We study a ring cavity filled with a slab of a right-handed material and a slab of a left-handed material. Both layers are assumed to be nonlinear Kerr media. First, we derive a model for the propagation of light in a left-handed material. By constructing a mean-field model, we show that the sign of diffraction can be made either positive or negative in this resonator, depending on the thicknesses of the layers. Subsequently, we demonstrate that the dynamical behavior of the modulation instability is strongly affected by the sign of the diffraction coefficient. Finally, we study the dissipativ…
We study the propagation of quasi-discrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with split ring resonators. By considering the relevant transmission line analogue, we derive a nonlinear lattice model which is studied analytically by means of a quasi-discrete approximation. We derive a nonlinear Schr{ö}dinger equation, and find that the system supports bright envelope soliton solutions in a relatively wide subinterval of the left-handed frequency band. We perform systematic numerical simulations, in the framework of the nonlinear lattice model, to study the p…
A multi-layered structure consisting of alternate right-handed material (RHM) and left-handed material (LHM)is considered and the unusual narrow transmission bands are explained as the competitive results of the Bragg condition and the transparent condition. These unusual narrow transmission bands may exist regardless whether the optical length of the LHM layer cancels the optical length of the RHM layer or not. This unusual transmission property may disappear when the reflection coefficient for each interface is small and the optical length of the LHM layer does not cancel the optical length …
We study parametric amplification in nonlinear left-handed transmission lines, which serve as model systems for nonlinear negative index metamaterials. We experimentally demonstrate amplification of a weak pump signal in three regimes: with the signal in the left-handed band, with the signal in the stop band, and with the signal at a defect frequency. In particular, we demonstrate the amplification of the incident wave by up to 15dB in the left-handed regime.
Using an extended plane-wave-based transfer-matrix method, the photonic band structures and the corresponding transmission spectrum of a two-dimensional left-handed photonic crystal are calculated. Comparisons between the periodic structure with a single left-handed cylindric rod are made, and many interesting similarities are found. It is shown that, due to the localized surface polaritons presented by an isolated left-handed rod, there exist many exciting physical phenomena in high-dimensional left-handed photonic crystals. As direct results of coupling of the localized surface polaritons of…
The spectrum of guided modes of linear chain of dielectric and left-handed cylinders is analyzed. The structure of eigenfrequences is much more richer if cylinders are made from the left-handed material with both permittivity and permeability negative. he number of guided modes is much larger, and their interaction with incident electromagnetic wave is much stronger. For some value of the wave vector, no guided modes were found. We discuss how these specific properties of guided modes correspond to folded bands, observed recently in photonic structureswith left-handed components.
We review some recent (mostly ours) results on the Anderson localization of light and electron waves in complex disordered systems, including: (i) left-handed metamaterials, (ii) magneto-active optical structures, (iii) graphene superlattices, and (iv) nonlinear dielectric media. First, we demonstrate that left-handed metamaterials can significantly suppress localization of light and lead to an anomalously enhanced transmission. This suppression is essential at the long-wavelength limit in the case of normal incidence, at specific angles of oblique incidence (Brewster anomaly), and in the vici…
We show that the periodic array of left-handed cylinders possesses a rich spectrum of guided modes when the negative permeability of cylinders equals exactly to minus value of permeability of embedding media. These resonances strongly influences propagation of electromagnetic waves through photonic structures made from left-handed materials. A series of Fano resonances excited by incident wave destroys the band frequency spectrum of square array of left-handed cylinders and increases considerably the absorption of transmitted waves.
We study the propagation of surface polaritons in a left-handed curved slab, i.e. a curved slab made of a negative-refractive-index material. We consider the effects of the slab curvature on their dispersion relations and attenuations. We show more particularly that surface polaritons with a "left-handed behavior" (i.e. with opposite group and phase velocities) propagate without any attenuation.
We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile changing according to a hyperbolic tangent function along the propagation direction. We derive expressions for the field intensity along the graded index structure, and we show excellent agreement between the analytical solution and the corresponding results obtained by accurate numerical simulations. Our model straightforwardly allows for arbitrary spectral di…
We have developed an approach allowing us to resolve the problem of non-conventional Anderson localization emerging in bilayered periodic-on-average structures with alternating layers of right-handed and left-handed materials. Recently, it was numerically discovered that in such structures with weak fluctuations of refraction indices, the localization length $L_{loc}$ can be enormously large for small wave frequencies $ω$. Within the fourth order of perturbation theory in disorder, $σ^2 \ll 1$, we derive the expression for $L_{loc}$ valid for any $ω$. In the limit $ω\rightarrow 0$ one gets a q…
We study the transmission properties of a nonlinear periodic structure containing alternating slabs of a nonlinear right handed material and a linear left handed material. We find that the transmission associated with the zero averaged- refractive- index gap exhibits a bistable characteristic that is relatively insensitive to incident angle. This is in contrast to the nonlinear behavior of the usual Bragg gap
In nature, the beetle Chrysina gloriosa derives its iridescence by selectively reflecting left-handed circularly polarized light only. Here, for the first time, we introduce and demonstrate the optical analogue based on an ultrathin metamaterial, which we term circular dichroic metamirror. A general method to design the circular dichroic metasmirror is presented under the framework of Jones calculus. It is analytically shown that the metamirror can be realized by two layers of anisotropic metamaterial structures, in order to satisfy the required simultaneous breakings of n-fold rotational (n>2…
We theoretically investigate the existence and properties of hybrid surface waves forming at interfaces between left-handed materials and dielectric birefringent media. The existence conditions of such waves are found to be highly relaxed in comparison to the original hybrid surface waves, discovered by Dyakonov, in configurations involving birefringent materials and right-handed media. Hybrid surface waves in left-handed materials feature remarkable properties: (i) a high degree of localization and (ii) coexistence of several guided solutions. The existence of several hybrid surface waves for…
Using complex plane analysis we show that left-handed slab may support either leaky slab waves, which are backward because of negative refraction, or leaky surface waves, which are backward or forward depending on the propagation direction of the surface wave itself. Moreover, there is a general connection between the reflection coefficient of the left-handed slab and the one of the corresponding right-handed slab (with opposite permittivity and permeability) so that leaky slab modes are excited for the same angle of incidence of the impinging beam for both structures. Many negative giant late…
We propose the use of a left-handed material in an optical waveguide structure to reduce its thickness well below the wavelength of light. We demonstrate that a layer of left-handed material, added to the cladding of a planar waveguide rather than to its core, allows for good light confinement in a subwavelength thin waveguide. We attribute the observed behavior to the change in phase evolution of electromagnetic waves in the guide. This technique can be used for the miniaturization of photonic integrated circuits.
We introduce the concept of subwavelength imaging with an opaque nonlinear left-handed lens by generating the second-harmonic field. We consider a slab of composite left-handed metamaterial with quadratic nonlinear response and show that such a flat lens can form, under certain conditions, an image of the second-harmonic field of the source being opaque at the fundamental frequency.
We provide rigorous numerical calculations (using the rigorous coupled-wave analysis) of transmission spectra of various metallic and metamaterial one-dimensional gratings and identify plasmonic resonances responsible for enhanced transmission. We argue that the most important mechanism which influences the resonant transmission is the coupling of incident electromagnetic wave with two plasmonic waves: lengthwise plasmons, which propagates along the grating, and crosswise plasmons excited in air gaps.
We study the defect-induced nonlinear transmission of a periodic structure created by alternating slabs of two materials with positive and negative refractive index. We demonstrate bistable switching and tunable nonlinear transmission in a novel type of bandgap that corresponds to the vanishing average refractive index, and compare the observed effects for two types of the bandgaps.
We study nonlinear transmission of an asymmetric multilayer structure created by alternating slabs of two materials with positive and negative refractive index. We demonstrate that such a structure exhibits passive spatially nonreciprocal transmission of electromagnetic waves, the analogue of the electronic diode. We study the properties of this left-handed diode and confirm its highly nonreciprocal and bistable transmittance by employing direct simulations.
A new approach to producing a composite material with negative refraction index is demonstrated. It is shown that a photonic structure consisting of two dielectric materials, with positive and negative dielectric permittivities, can support electromagnetic surface waves which exhibit the unusual electromagnetic property of left-handedness (or negative refraction index). Depending on the dielectric materials, these surface waves localized at the dielectric interfaces can be either surface plasmons, or phonons. The detailed geometry of the structure determines whether this composite left-handed …
The contra-directional coupling between a left-handed monomode waveguide and a right-handed monomode waveguide is rigorously studied using a complex plane analysis. Light is shown to rotate in this lamellar structure forming a very exotic mode which we have called a light wheel. The light wheel can be excited using evanescent coupling or by placing sources in one of the waveguides. This structure can thus be seen as a new type of cavity. It is a way to suppress the guided mode of a dielectric slab.
In this paper, the microwave pulse propagation transferred through a left-handed transmission line using Complementary Omega-Like Structures (COLS) loaded was studied. There was a stop band in transmission from 5.6GHz to 6.1GHz, and the anomalous dispersion was causes in this band. Negative group velocity corresponds to the case in which the peak of the pulse exited before the peak of the incident pulse had entered the sample. The negative group velocity reached (-0.27c~-1.85c).
In this letter we show that equivalent circuits offer a qualitative and even quantitative simple explanation for the behavior of various types of left-handed (or negative index) meta-materials. This allows us to optimize design features and parameters, while avoiding trial and error simulations or fabrications. In particular we apply this unifying circuit approach in accounting for the features and in optimizing the structure employing parallel metallic bars on the two sides of a dielectric film.
Isotropic negative index metamaterials (NIMs) are highly desired, particularly for the realization of ultra-high resolution lenses. However, existing isotropic NIMs function only two-dimensionally and cannot be miniaturized beyond microwaves. Direct laser writing processes can be a paradigm shift toward the fabrication of three-dimensionally (3D) isotropic bulk optical metamaterials, but only at the expense of an additional design constraint, namely connectivity. Here, we demonstrate with a proof of-principle design that the requirement connectivity does not preclude fully isotropic left-hande…
