Second-harmonic generation in nonlinear left-handed metamaterials

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 numerically the second-harmonic generation by a metamaterial slab of a finite thickness, and reveal the existence of multistable nonlinear effects.Comment: 6 pages, 6 figure

Giant Goos-Hanchen effect at the reflection from left-handed metamaterials

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

Giant Goos-Hanchen effect at the reflection from left-handed metamaterials

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.Comment: 3 pages, 3 figure

Transmission properties of left-handed band-gap structures

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 allow to access selectively two different types of band gaps.Comment: 5 pages, 8 figure

Subwavelength imaging with opaque left-handed nonlinear lens

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.Comment: 3 pages, 3 figure

Chaos and rectification of electromagnetic wave in a lateral semiconductor superlattice

We find the conditions for a rectification of electromagnetic wave in a lateral semiconductor superlattice with a high mobility of electrons. The rectification is assisted by a transition to a dissipative chaos at a very high mobility. We show that mechanism responsible for the rectification is a creation of warm electrons in the superlattice miniband caused by an interplay of the effects of nonlinearity and finite band width.Comment: 4 pages, 4 figures (2 color figs). Sufficient revision in comparison with version1: More explanations on physics of the effect are added. Removed from version1 material will be published elsewher

Nonlinear left-handed metamaterials

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.Comment: 7 pages, 8 figure

Birefringent left-handed metamaterials and perfect lenses

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 $\epsilon=\mu=-1$, where $\epsilon$ is the dielectric constant and $\mu$ 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 scale.Comment: 4 pages 6 figure

Nonlinear magnetoinductive waves and domain walls in composite metamaterials

We describe novel physics of nonlinear magnetoinductive waves in left-handed composite metamaterials. We derive the coupled equations for describing the propagation of magnetoinductive waves, and show that in the nonlinear regime the magnetic response of a metamaterial may become bistable. We analyze modulational instability of different nonlinear states, and also demonstrate that nonlinear metamaterials may support the propagation of domain walls (kinks) connecting the regions with the positive and negative magnetization.Comment: 5 pages, 5 figure

Suppression of left-handed properties in disordered metamaterials

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.Comment: 4 pages, 2 figure