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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.

We study one- and two-dimensional transmission of electromagnetic waves through a finite slab of a dielectric material with negative refraction. In the case when the dielectric slab possesses an intensitydependent nonlinear response, we observe the nonlinearity-induced wave transmission through an opaque slab accompanied by the generation of spatiotemporal solitons. We solve this problem numerically, by employing the finite-difference time-domain simulations, for the parameters of microstructured materials with the negative refractive index in the microwave region, but our results can be useful for a design of nonlinear metamaterials with the left-handed properties in other frequency range.

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.

[1] We analyze nonlinear properties of microstructured materials with the negative refractive index, 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 the wave reflection from a slab of a nonlinear left-handed material and observe generation and propagation of temporal solitons in such materials. We demonstrate also that the nonlinear left-handed metamaterials can support both transverse electric-and transverse magnetic-polarized self-trapped localized beams, spatial electromagnetic solitons. Such solitons appear as single-hump and multihump beams, being either symmetric or antisymmetric, and they can exist because of the hysteresis-type magnetic nonlinearity and the effective domains of negative magnetic permeability.

We analyze transmission of electromagnetic waves through a one-dimensional periodic layered structure consisting of slabs of a left-handed metamaterial and air. We derive the effective parameters of the metamaterial from a microscopic structure of wires and split-ring resonators possessing the left-handed characteristics in the microwave frequency range, and then study, by means of the transfer-matrix approach and the finite-difference time-domain numerical simulations, the transmission properties of this layered structure in a band gap associated with the zero averaged refractive index. By introducing defects, the transmission of such a structure can be made tunable, and we study the similarities and differences of the defects modes excited in two types of the band gaps.

We introduce a novel concept of an inside-out (or inverse) cloak for electromagnetic waves based on the coordinate transformation of Maxwell's equations. This concept can be employed for creating absorbing non-reflecting media as matching layers in numerical simulations. In contrast to the commonly used perfectly matched layers, such absorbing boundaries are characterized by physically meaningful parameters, and the concept can be used in various numerical simulation schemes.