Solitary waves in three-dimensional crystal-like structures

The motion of three-dimensional (3D) solitary waves and solitons in nonlinear crystal-like structures, such as photonic materials, is studied. It is demonstrated that collective excitations in these systems can be tailored to move in particular directions of the 3D system. The effect of modulation instability is studied showing that in some cases it can be delayed by using a lensing factor. Analytical results supported by numerical simulations are presented.Comment: 4 page

Diffraction theory and focusing of light by left-handed materials

A diffraction theory in a system consisting of left-handed and right-handed materials is proposed. The theory is based upon the Huygens's principle and the Kirchhoff's integral and it is valid if the wavelength is smaller than any relevant length of the system. The theory is applied to the calculation of the smearing of the foci of the Veselago lens due to the finite wavelength. We show that the Veselago lens is a unique optical instrument for the 3D imaging, but it is not a ``superlens'' as it has been claimed recently.Comment: 7 pages, 2 figure

On the inapplicability of a negative-phase-velocity condition as a negative-refraction condition for active materials

A negative-phase-velocity condition derived by Depine and Lakhtakia [Microwave Opt Technol Lett 41 (2004) 315] for isotropic, homogeneous, passive, dielectric-magnetic materials is inapplicable as a negative-refraction condition for active materials.Comment: replacement for preliminary version submitted earlier by erro

Universal Features of the Time Evolution of Evanescent Modes in a Left-Handed Perfect Lens

The time evolution of evanescent modes in Pendry's perfect lens proposal for ideally lossless and homogeneous, left-handed materials is analyzed. We show that time development of sub-wavelength resolution exhibits universal features, independent of model details. This is due to the unavoidable near-degeneracy of surface electromagnetic modes in the deep sub-wavelength region. By means of a mechanical analog, it is shown that an intrinsic time scale (missed in stationary studies) has to be associated with any desired lateral resolution. A time-dependent cut-off length emerges, removing the problem of divergences claimed to invalidate Pendry's proposal.Comment: 4 pages, 3 figures, title slightly changed, reference added, minor correction

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

Catastrophe optics of caustics in single and bilayer graphene: fine structure of caustics

We theoretically study the scattering of a plane wave of a ballistic electron on a circular n-p junction in single and bilayer graphene. We compare the exact wave function inside the junction to that obtained from a semiclassical formula developed in catastrophe optics. In the semiclassical picture short-wavelength electrons are treated as rays of particles that can get reflected and refracted at the n-p junction according to Snell's law with negative refraction index. We show that for short wavelength and close to caustics this semiclassical approximation gives good agreement with the exact results in the case of single-layer graphene. We also verify the universal scaling laws that govern the shrinking rate and intensity divergence of caustics in the semiclassical limit. It is straightforward to generalize our semiclassical method to more complex geometries, offering a way to efficiently design and model graphene-based electron-optical systems.Comment: 4 pages, 5 figures This manuscript should be published in the proceedings volume of the conference IWEPNM 2010, in the Physica Status Solidi

Veselago lens by photonic hyper-crystals

An imaging system functioning as a Veselago lens has been proposed based on the novel concept of photonic "hyper-crystal" -- an artificial optical medium synthesizing the properties of hyperbolic materials and photonic crystals. This Veselago lens shows a nearly constant negative refractive index and substantially reduced image aberrations. It can find potential applications in photolithography and hot-spots detection of silicon-based integrated circuits.Comment: 4 pages, 3 figures, APL in pres

Left-Handed Surface Waves in a Photonic Structure

It is demonstrated that an isotropic left-handed medium can be constructed as a photonic structure consisting of two dielectric materials, one with positive and another with negative dielectric permittivities epsilon. Electromagnetic waves supported by this structure are the surface waves localized at the dielectric interfaces. These surface waves can be either surface phonons or surface plasmons. Two examples of negative epsilon materials are used: silicon carbide and free-electron gas.Comment: 7 pages, two figure