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We develop a theoretical description of radiative thermal conductivity in hyperbolic metamaterials. We demonstrate a dramatic enhancement of the radiative thermal transport due to the super-singularity of the photonic density of states in hyperbolic media, leading to the radiative heat conductivity which can be comparable to the non-radiative contribution.

Hyperbolic Metamaterials (HMMs) have recently garnered much attention because they possess the ability for broadband manipulation of the photon density of states and sub-wavelength light confinement. These exceptional properties arise due to the excitation of electromagnetic states with high momentum (high-k modes). However, a major hindrance to practical applications of HMMs is the difficulty in coupling light out of these modes because they become evanescent at the surface of the metamaterial. Here we report the first demonstration of out-coupling of high-k modes in an active HMM using a high-index contrast bulls-eye grating. Quantum dots embedded inside the metamaterial are used for local excitation of high-k modes. This demonstration of light out-coupling from quantum dots embedded in a HMM could pave the way for developing practical photonic devices using these systems.

We show that corrugated surfaces of hyperbolic metamaterials scatter light preferentially inside the media, resulting in a very low reflectance and ultimate dark appearance in the spectral range of hyperbolic dispersion. This phenomenon of fundamental importance, demonstrated experimentally in arrays of silver nanowires grown in alumina membranes, originates from a broad-band singularity in the density of photonic states. It paves the road to a variety of applications ranging from the stealth technology to high-efficiency solar cells and photodetectors.

In the metamaterial with hyperbolic dispersion (an array of silver nanowires in alumina membrane) we have observed six-fold reduction of the emission life-time of dye deposited onto the metamaterials surface. This serves as the evidence of the earlier predicted high density of photonic states in hyperbolic metamaterials., Comment: 3 pages, 1 figures

In this work, we demonstrate a self-standing bulk three-dimensional metamaterial based on the network of silver nanowires in an alumina membrane. This constitutes an anisotropic effective medium with hyperbolic dispersion, which can be used in sub-diffraction imaging or optical cloaks. Highly anisotropic dielectric constants of the material range from positive to negative, and the transmitted laser beam shifts both toward the normal to the surface, as in regular dielectrics, and off the normal, as in anisotropic dielectrics with the refraction index smaller than one. The designed photonic metamaterial is the thickest reported in the literature, both in terms of its physical size 1cm x 1cm x 51 mm, and the number of vacuum wavelengths, N=61 at l=0.84 mm., Comment: 6 pages, 4 figurs

The quasi-bound modes localized on stable periodic ray orbits of dielectric micro-cavities are constructed in the short-wavelength limit using the parabolic equation method. These modes are shown to coexist with irregularly spaced "chaotic" modes for the generic case. The wavevector quantization rule for the quasi-bound modes is derived and given a simple physical interpretation in terms of Fresnel reflection; quasi-bound modes are explictly constructed and compared to numerical results. The effect of discrete symmetries of the resonator is analyzed and shown to give rise to quasi-degenerate multiplets; the average splitting of these multiplets is calculated by methods from quantum chaos theory., Comment: 20 pages, 8 figures, 2 tables, revtex4, submitted to Optics Express

We develop a variational mean-field theory of the ferromagnetic transition in compounds like Lanthanum-Manganite within the framework of the Double-Exchange Model supplemented by modest disorder. We obtain analytical expressions for the transition temperature, its variation with the valence electron-density and its decrease with disorder. We derive an expression for the conductivity for both the paramagnetic and the ferromangetic metallic phases, and study its dependence on the temperature and magnetic field. A simple relation between the resistivity in the ferromagnetic phase and the spontaneous magnetization is found. Our results are in a good agreement with the experimental data on transition temperatures and resistivity in the manganite compounds with relatively small disorder. We comment on the effects of increased disorder.

The electrostatic energy of an additional electron on a conducting grain blocks the flow of current through the grain, an effect known as the Coulomb blockade. Current can flow only if two charge states of the grain have the same energy; in this case the conductance has a peak. In a small grain with quantized electron states, referred to as a quantum dot, the magnitude of the conductance peak is directly related to the magnitude of the wavefunction near the contacts to the dot. Since dots are generally irregular in shape, the dynamics of the electrons is chaotic, and the characteristics of Coulomb blockade peaks reflects those of wavefunctions in chaotic systems. Previously, a statistical theory for the peaks was derived by assuming these wavefunctions to be completely random. Here we show that the specific internal dynamics of the dot, even though it is chaotic, modulates the peaks: because all systems have short-time features, chaos is not equivalent to randomness. Semiclassical results are derived for both chaotic and integrable dots, which are surprisingly similar, and compared to numerical calculations. We argue that this modulation, though unappreciated, has already been seen in experiments., Comment: 4 pages, 3 postscript figs included (2 color), uses epsf.sty

We develop a quantitative semiclassical theory for the resosnant tunneling through a quantum well in a tilted magnetic field. It is shown, that in the leading semiclassical approximation the tunneling current depends only on periodic orbits within the quantum well. Further corrections (due to e.g. "ghost" effect) can be expressed in terms of closed, but non-periodic orbits, started at the "injection point". The results of the semiclassical theory are shown to be in good agreement with both the experimental data and numerical calculations., Comment: 25 pages, 15 figures, accepted for publication in Physica D

High-power and highly directional semiconductor cylinder-lasers based on an optical resonator with deformed cross section are reported. In the favorable directions of the far-field, a power increase of up to three orders of magnitude over the conventional circularly symmetric lasers was obtained. A "bow-tie"-shaped resonance is responsible for the improved performance of the lasers in the higher range of deformations, in contrast to "whispering-gallery"-type modes of circular and weakly deformed lasers. This resonator design, although demonstrated here in midinfrared quantum-cascade lasers, should be applicable to any laser based on semiconductors or other high-refractive index materials., Comment: Removed minor discrepancies with published version in the text and in Fig. 4

We develop a quantitative semiclassical formula for the resonant tunneling current through a quantum well in a tilted magnetic field. It is shown that the current depends only on periodic orbits within the quantum well. The theory explains the puzzling evolution of the tunneling spectra near a tilt angle of $30^{\circ}$ as arising from an exchange bifurcation of the relevant periodic orbits., Comment: 4 pages, RevTeX, epsf, 2 PostScript Figures (1 with color)

The anomalously strong scarring of wavefunctions found in numerical studies of quantum wells in a tilted magnetic field is shown to be due to special properties of the classical dynamics of this system. A certain subset of periodic orbits are identified which are nearly stable over a very large interval of variation of the classical dynamics; only this subset are found to exhibit strong scarring. Semiclassical arguments shed further light on why these orbits dominate the experimentally observed tunneling spectra., Comment: RevTeX, 5 pages

A semiclassical theory is developed and compared to experiments on the tunneling resonance spectrum for a quantum well in magnetic field tilted with respect to the tunneling direction. As the tilt angle is increased from zero the classical mechanics of an electron trapped within the well undergoes a smooth transition from integrable to chaotic dynamics. Perturbation theory is invalid for most of the regime of experimental interest, motivating a semiclassical treatment based on short periodic orbits within the well. In this paper we present a unified theory of all the periodic orbits within the well which are of relevance to experiments and show that they are all related to bifurcations of the period-one traversing orbits. An analytic theory is derived for the period and stability of these traversing orbits. An unusual feature of the classical mechanics of this system is the existence of certain important periodic orbits only in finite energy bands. We calculate the widths of these bands and relate them to experimental data. In the forthcoming paper the results for these short periodic orbits are used in conjunction with a novel semiclassical tunneling formula to calculate the magnetotunneling current, which is then compared with experiments., Comment: Uses REVTeX and epsf

An analytic theory is developed for the density of states oscillations in quantum wells in a magnetic field which is tilted with respect to the barrier planes. The main oscillations are found to come from the simplest one or two-bounce periodic orbits. We calculate their period and stability analytically and find an infinite sequence of destabilizations followed by restabilizations as the chaos parameter increases. This phenomenon explains the re-entrant frequency-doubling of the density of states peaks observed in recent magnetotunneling experiments., Comment: 5 pages, 3 postscript figures, submitted to PRL