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

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

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

High-frequency hopping conductivity in the quantum Hall effect regime: Acoustical studies

The high-frequency conductivity of Si delta-doped GaAs/AlGaAs heterostructures is studied in the integer quantum Hall effect (QHE) regime, using acoustic methods. Both the real and the imaginary parts of the complex conductivity are determined from the experimentally observed magnetic field and temperature dependences of the velocity and the attenuation of a surface acoustic wave. It is demonstrated that in the structures studied the mechanism of low-temperature conductance near the QHE plateau centers is hopping. It is also shown that at magnetic fields corresponding to filling factors 2 and 4, the doped Si delta- layer efficiently shunts the conductance in the two-dimensional electron gas (2DEG) channel. A method to separate the two contributions to the real part of the conductivity is developed, and the localization length in the 2DEG channel is estimated.Comment: 8pages, 9 figure