Comment on "Perfect imaging with positive refraction in three dimensions"

Leonhard and Philbin [Phys. Rev. A 81, 011804(R) (2010)] have recently constructed a mathematical proof that the Maxwell's fish-eye lens provides perfect imaging of electromagnetic waves without negative refraction. In this comment, we argue that the unlimited resolution is an artifact of having introduced an unphysical drain at the position of the geometrical image. The correct solution gives focusing consistent with the standard diffraction limit

Exciton Beats in GaAs Quantum Wells: Bosonic Representation and Collective Effects

We discuss light-heavy hole beats observed in transient optical experiments in GaAs quantum wells in terms of a free-boson coherent state model. This approach is compared with descriptions based on few-level representations. Results lead to an interpretation of the beats as due to classical electromagnetic interference. The boson picture correctly describes photon excitation of extended states and accounts for experiments involving coherent control of the exciton density and Rayleigh scattering beating.Comment: 4 pages, no figures. Accepted for publication in Solid State Communication

Maxwell's fish-eye lens and the mirage of perfect imaging

Recent claims that Maxwell's fish-eye is a perfect lens, capable of providing images with deep subwavelength resolution, are examined. We show that the imaging properties of a dispersionless fish-eye are very similar to those of an ideal spherical cavity. Using this correspondence, we prove that the correct solution to Maxwell equations in the fish-eye gives image sizes that are consistent with the standard diffraction limit. Perfect focusing is an optical illusion that results from placing a time-reversed source at the position of the geometrical image which, when combined with the field due to the primary (object) source, mimics the behavior of a perfect drain. Issues of causality are briefly discussed. We also demonstrate that passive outlets are not a good alternative to time-reversed sources for broadband drain-like behavior and that, even if they were, they could not do a better job than conventional optical systems at providing high resolution.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90834/1/2040-8986_13_2_024017.pd

An exactly solvable model of an avalanche-type measuring device

A quantum many-body model is presented with features similar to those of certain particle detectors. The energy spectrum contains a single, thermodynamically metastable “ready” state and macroscopically-distinct, ground “pointer” states. Transitions into classical-like states can be triggered by a single particle with the help of the thermal bath. Schrödinger cat states are associated with superpositions of inequivalent vacua, thus suggestion a relationship between wave function collapse and the dynamics of symmetry breaking in phase transformations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/58113/2/epl_76_4_541.pd

Erratum: “Analytical solution of the almost-perfect-lens problem” [Appl. Phys. Lett. 84, 1290 (2004)]

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71175/2/APPLAB-85-11-2144-1.pd

Analytical solution of the almost-perfect-lens problem

The problem of imaging for a slab of a lossless left-handed material with refractive index n = −(1−σ)1/2n=−(1−σ)1/2 is solved analytically for ∣σ∣≪1. The electromagnetic field behavior is determined largely by singularities arising from the excitation of surface polaritons with wave vector q→±∞.q→±∞. Depending on the sign of σ, the near-field is either odd or even with respect to the lens middle plane. Consistent with other nonanalytical studies, the resolution depends logarithmically on ∣σ∣. With minor alterations, these results apply as well to the electrostatic limit. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70534/2/APPLAB-84-8-1290-1.pd

Perturbed Periodic Lattices: Sharp Crossover Between Effective-Mass-Like States and Wannier-Stark-Like Ladders

The concept of Wannier-Stark ladders, describing the equally spaced spectrum of a tightly-bound particle in a constant electric field, is generalized to account for arbitrary slowly-varying potentials. It is shown that an abrupt transition exists that separates Wannier-Stark-like from effective-mass-like behavior when the depth of the perturbation becomes equal to the width of the band of extended states. For potentials bounded from below, the spectrum bifurcates above the critical energy while the wavefunctions detach from the effective-mass region and split into two pieces