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

1/f1/f noise in variable range hopping conduction

A mechanism of $1/f$ noise due to traps formed by impurities which have no neighbors with close energies in their vicinity is studied. Such traps slowly exchange electrons with the rest of conducting media. The concentration of traps and proportional to it $1/f$ noise exponentially grow with decreasing temperature in the variable range hopping regime. This theory provides smooth transition to the nearest neighbor hopping case where it predicts a very weak temperature dependence

Propagation of waves in metallic photonic crystals at low frequencies and some theoretical aspects of left-handed materials

An analytical theory of low frequency electromagnetic waves in metallic photonic crystals with a small volume fraction of a metal is presented. The evidence of the existence of such waves has been found recently via experiments and computations. We have obtained an exact dispersion equation for omega (k) and studied the cutoff frequency omega_0 = omega(0) as a function of parameters of the photonic crystal. An analytical expression for the permittivity epsilon is calculated. It is shown, that if the crystal is embedded into a medium with negative mu, it has no propagating modes at any frequency. Thus, such a compound system is not a left-handed material (LHM). The recent experimental results on the LHM are discussed.Comment: 8 pages, 3 figure

Imaging of Low Compressibility Strips in the Quantum Hall Liquid

Using Subsurface Charge Accumulation scanning microscopy we image strips of low compressibility corresponding to several integer Quantum Hall filling factors. We study in detail the strips at Landau level filling factors $\nu =$ 2 and 4. The observed strips appear significantly wider than predicted by theory. We present a model accounting for the discrepancy by considering a disorder-induced nonzero density of states in the cyclotron gap.Comment: 5 pages, 3 figure

A Renormalization-Group approach to the Coulomb Gap

The free energy of the Coulomb Gap problem is expanded as a set of Feynman diagrams, using the standard diagrammatic methods of perturbation theory. The gap in the one-particle density of states due to long-ranged interactions corresponds to a renormalization of the two-point vertex function. By collecting the leading order logarithmic corrections we have derived the standard result for the density of states in the critical dimension, d=1. This method, which is shown to be identical to the approach of Thouless, Anderson and Palmer to spin glasses, allows us to derive the strong-disorder behaviour of the density of states. The use of the renormalization group allows this derivation to be extended to all disorders, and the use of an epsilon-expansion allows the method to be extended to d=2 and d=3. We speculate that the renormalization group equations can also be derived diagrammatically, allowing a simple derivation of the crossover behaviour observed in the case of weak disorder.Comment: 16 pages, LaTeX. Diagrams available on request from [email protected]. Changes to figure 4 and second half of section

Dielectric photonic crystal as medium with negative electric permittivity and magnetic permeability

We show that a two-dimensional photonic crystal (PC) made from a non-magnetic dielectric is a left-handed material in the sense defined by Veselago. Namely, it has negative values of both the electric permittivity $\epsilon$ and the magnetic permeability $\mu$ in some frequency range. This follows from a recently proven general theorem. The negative values of $\epsilon$ and $\mu$ are found by a numerical simulation. Using these values we demonstrate the Veselago lens, a unique optical device predicted by Veselago. An approximate analytical theory is proposed to calculate the values of $\epsilon$ and $\mu$ from the PC band structure. It gives the results that are close to those obtained by the numerical simulation. The theory explains how a non-zero magnetization arises in a non-magnetic PC.Comment: 11 pages 4 figure

The Effects of Disorder on the ν=1\nu=1 Quantum Hall State

A disorder-averaged Hartree-Fock treatment is used to compute the density of single particle states for quantum Hall systems at filling factor $\nu=1$. It is found that transport and spin polarization experiments can be simultaneously explained by a model of mostly short-range effective disorder. The slope of the transport gap (due to quasiparticles) in parallel field emerges as a result of the interplay between disorder-induced broadening and exchange, and has implications for skyrmion localization.Comment: 4 pages, 3 eps figure

Thomas-Fermi-Poisson theory of screening for latterally confined and unconfined two-dimensional electron systems in strong magnetic fields

We examine within the self-consistent Thomas-Fermi-Poisson approach the low-temperature screening properties of a two-dimensional electron gas (2DEG) subjected to strong perpendicular magnetic fields. Numerical results for the unconfined 2DEG are compared with those for a simplified Hall bar geometry realized by two different confinement models. It is shown that in the strongly non-linear screening limit of zero temperature the total variation of the screened potential is related by simple analytical expressions to the amplitude of an applied harmonic modulation potential and to the strength of the magnetic field.Comment: 12 pages, 12 figure

Anomalous magnetophotoluminescence as a result of level repulsion in arrays of quantum dots

Selectively excited photoluminescence (SPL) of an array of self-organized In$_{0.5}$Ga$_{0.5}$As quantum dots has been measured in a magnetic field up to 11T. Anomalous magnetic field sensitivity of the SPL spectra has been observed under conditions for which the regular photoluminescence spectra is insensitive to the magnetic field due to large inhomogeneous broadening. The anomalous sensitivity is interpreted in terms of the repulsion of excited levels of the dots in a random potential. A theory presented to describe this phenomena is in excellent agreement with the experimental data. The data estimated the correlation in the positions of excited levels of the dots to be 94%. The magnetic field dependence allows the determination of the reduced cyclotron effective mass in a dot. For our sample we have obtained $m_em_h/(m_e+m_h)=0.034m_0$.Comment: 12 revtex preprint pages + 4 ps figures, uuencode

Optical properties of arrays of quantum dots with internal disorder

Optical properties of large arrays of isolated quantum dots are discussed in order to interpret the existent photoluminescence data. The presented theory explains the large observed shift between the lowest emission and absorption energies as the average distance between the ground and first excited states of the dots. The lineshape of the spectra is calculated for the case when the fluctuations of the energy levels in quantum dots are due to the alloy composition fluctuations. The calculated lineshape is in good agreement with the experimental data. The influence of fluctuations of the shape of quantum dots on the photoluminescence spectra is also discussed.Comment: 7 pages (twocolumn) LATEX, 6 Postscript figure