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

Plasmons and near-field amplification in double-layer graphene

We study the optical properties of double-layer graphene for linearly polarized evanescent modes and discuss the in-phase and out-of-phase plasmon modes for both, longitudinal and transverse polarization. We find a energy for which reflection is zero, leading to exponentially amplified transmitted modes similar to what happens in left-handed materials. For layers with equal densities $n=10^{12}$cm$^{-2}$, we find a typical layer separation of $d\approx500\mu$m to detect this amplification for transverse polarization which may serve as an indirect observation of transverse plasmons. When the two graphene layers lie on different chemical potentials, the exponential amplification either follows the in-phase or out-of-phase plasmon mode depending on the order of the low- and high-density layer. This opens up the possibility of a tunable near-field amplifier or switch.Comment: 9 pages, 8 figure

Are Stars with Planets Polluted?

We compare the metallicities of stars with radial velocity planets to the metallicity of a sample of field dwarfs. We confirm recent work indicating that the stars-with-planet sample as a whole is iron rich. However, the lowest mass stars tend to be iron poor, with several having [Fe/H]<-0.2, demonstrating that high metallicity is not required for the formation of short period Jupiter-mass planets. We show that the average [Fe/H] increases with increasing stellar mass (for masses below 1.25 solar masses) in both samples, but that the increase is much more rapid in the stars-with-planet sample. The variation of metallicity with stellar age also differs between the two samples. We examine possible selection effects related to variations in the sensitivity of radial velocity surveys with stellar mass and metallicity, and identify a color cutoff (B-V>0.48) that contributes to but does not explain the mass-metallicity trend in the stars-with-planets sample. We use Monte Carlo models to show that adding an average of 6.5 Earth masses of iron to each star can explain both the mass-metallicity and the age-metallicity relations of the stars-with-planets sample. However, for at least one star, HD 38529, there is good evidence that the bulk metallicity is high. We conclude that the observed metallicities and metallicity trends are the result of the interaction of three effects; accretion of about 6 Earth masses of iron rich material, selection effects, and in some cases, high intrinsic metallicity.Comment: 19 pages 11 figure