Nonlinear properties of left-handed metamaterials

We analyze nonlinear properties of microstructured materials with negative refraction, the so-called left-handed metamaterials. We consider a two-dimensional periodic structure created by arrays of wires and split-ring resonators embedded into a nonlinear dielectric, and calculate the effective nonlinear electric permittivity and magnetic permeability. We demonstrate that the hysteresis-type dependence of the magnetic permeability on the field intensity allows changing the material from left- to right-handed and back. These effects can be treated as the second-order phase transitions in the transmission properties induced by the variation of an external field.Comment: 4 pages, 3 figure

Enhanced parametric processes in binary metamaterials

We suggest double-resonant (binary) metamaterials composed of two types of magnetic resonant elements, and demonstrate that in the nonlinear regime such metamaterials provide unique possibilities for phase-matched parametric interaction and enhanced second-harmonic generation

Refraction at Media with Negative Refractive Index

We show that an electromagnetic (EM) wave undergoes negative refraction at the interface between a positive and negative refractive index material. Finite difference time domain (FDTD) simulations are used to study the time evolution of an EM wave as it hits the interface. The wave is trapped temporarily at the interface and after a long time, the wave front moves eventually in the negative direction. This explains why causality and speed of light are not violated in spite of the negative refraction always present in a negative index material.Comment: 5 pages, 4 figures, submitted to Phys. Rev. Let

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

Near Field Lenses in Two Dimensions

It has been shown that a slab of materials with refractive index = -1 behaves like a perfect lens focussing all light to an exact electromagnetic copy of an object. The original lens is limited to producing images the same size as the object, but here we generalise the concept so that images can be magnified. For two dimensional systems, over distances much shorter than the free space wavelength, we apply conformal transformations to the original parallel sided slab generating a variety of new lenses. Although the new lenses are not `perfect' they are able to magnify two dimensional objects. The results apply equally to imaging of electric or magnetic sub wavelength objects in two dimensions. The concepts have potential applications ranging from microwave frequencies to the visible.Comment: PDF fil

Reverse Doppler effect in backward spin waves scattered on acoustic waves

We report on the observation of reverse Doppler effect in backward spin waves reflected off of surface acoustic waves. The spin waves are excited in a yttrium iron garnet (YIG) film. Simultaneously, acoustic waves are also generated. The strain induced by the acoustic waves in the magnetostrictive YIG film results in the periodic modulation of the magnetic anisotropy in the film. Thus, in effect, a travelling Bragg grating for the spin waves is produced. The backward spin waves reflecting off of this grating exhibit a reverse Doppler shift: shifting down rather than up in frequency when reflecting off of an approaching acoustic wave. Similarly, the spin waves are shifted up in frequency when reflecting from receding acoustic waves.Comment: 4 pages, 3 figure

The negative index of refraction demystified

We study electromagnetic wave propagation in mediums in which the effective relative permittivity and the effective relative permeability are allowed to take any value in the upper half of the complex plane. A general condition is derived for the phase velocity to be oppositely directed to the power flow. That extends the recently studied case of propagation in mediums for which the relative permittivity and relative permeability are both simultaneously negative, to include dissipation as well. An illustrative case study demonstrates that in general the spectrum divides into five distinct regions.Comment: 5 pages, 4 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

Negative Refraction and Left-handed electromagnetism in Microwave Photonic Crystals

We demonstrate negative refraction of microwaves in metallic photonic crystals. The spectral response of the photonic crystal, which manifests both positive and negative refraction, is in complete agreement with band-structure calculations and numerical simulations. The negative refraction observed corresponds to left-handed electromagnetism and arises due to the dispersion characteristics of waves in a periodic medium. This mechanism for negative refraction is different from that in metamaterials.Comment: 13 pages, 4 figure

Novel approach to a perfect lens

Within the framework of an exact analytical solution of Maxwell equations in a space domain, it is shown that optical scheme based on a slab with negative refractive index ($n=-1$) (Veselago lens or Pendry lens) does not possess focusing properties in the usual sense . In fact, the energy in such systems does not go from object to its "image", but from object and its "image" to an intersection point inside a metamaterial layer, or vice versa. A possibility of applying this phenomenon to a creation of entangled states of two atoms is discussed.Comment: 4 pages, 6 figure