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The equation in the title describes the number of bright images of a point source under lensing by an elliptic object with isothermal density. We prove that this equation has at most 6 solutions. Any number of solutions from 1 to 6 can…

Complex Variables · Mathematics 2018-01-08 Walter Bergweiler , Alexandre Eremenko

Exact time-dependent solutions of Maxwell's equations in Maxwell's fish eye show that perfect imaging is not an artifact of a drain at the image, although a drain is required for subwavelength resolution.

Optics · Physics 2015-05-19 Ulf Leonhardt , Thomas G. Philbin

It is shown that perfect absorption and giant amplification can be realized when a wave impinges on a special metamaterial layer with zero real parts of the permittivity and permeability. The imaginary parts of the permittivity and…

Optics · Physics 2011-05-26 Y. Jin , S. S. Xiao , N. A. Mortensen , S. L. He

This comment is devoted to the paper "Exact solutions of nonlinear diffusion-convection-reaction equation: A Lie symmetry approach" (CNSNS, vol. 67 (2019), 253-263) in which several results are not new because were derived much earlier.…

Analysis of PDEs · Mathematics 2021-06-29 Roman Cherniha

Lorentz [of the Lorentz transforms and Lorentz contractions fame] contended against Einstein that there had to be a medium in which electro-magnetic waves exist and propagate, and that that would of necessity be an absolute frame of…

General Physics · Physics 2007-12-03 Roger Ellman

We first define what we mean by gravitational lensing equations in a general space-time. A set of exact relations are then derived that can be used as the gravitational lens equations in all physical situations. The caveat is that into…

General Relativity and Quantum Cosmology · Physics 2008-12-18 Simonetta Frittelli , Ezra T. Newman

Two exact lens equations have been recently shown to be equivalent to each other, being consistent with the gravitational deflection angle of light from a source to an observer, both of which can be within a finite distance from a lens…

General Relativity and Quantum Cosmology · Physics 2021-05-26 Keita Takizawa , Hideki Asada

Fresnel lenses offer the possibility of concentrating the flux of X-rays or gamma-rays flux falling on a geometric area of many square metres onto a focal point which need only be a millimetre or so in diameter (and which may even be very…

Astrophysics · Physics 2008-11-26 G. K. Skinner

We introduce an analytic approach to study gravitational lensing in the presence of a distribution of hadrons. The situation is analogous to the propagation of photons in a medium with a nontrivial Cooper-pair condensate, where the photon…

General Relativity and Quantum Cosmology · Physics 2026-05-12 Fabrizio Canfora , Cristóbal Corral , Borja Diez

In a recent article, Banerji et al. introduced a novel quantum state of light, coined as the perfect quantum optical vortex state [Phys. Rev. A 94, 053838 (2016)] due to its mathematical similarity with the classical perfect vortex beam.…

Quantum Physics · Physics 2017-10-25 David Barral , Jesús Liñares

We analyze the performance of a planar lens based on realistic negative index material in a generalized geometry. We demonstrate that the conventional superlens design (where the lens is centered between the object and the image) is not…

Optics · Physics 2016-09-08 Viktor A. Podolskiy , Nicholas A. Kuhta , Graeme W. Milton

A large number of cosmological studies now suggest that roughly two-thirds of the critical energy density of the Universe exists in a component with negative pressure. If the equation of state of such an energy component varies with time,…

Astrophysics · Physics 2010-04-06 Asantha R. Cooray , Dragan Huterer

We investigate the resolution and absorption losses of a Ag/GaP multilayer superlens. For a fixed source to image distance the resolution is independent of the position of the lens but the losses depend strongly on the lens placement. The…

Reconstructing lens potentials and lensed sources can easily become an underconstrained problem, even when the degrees of freedom are low, due to degeneracies, particularly when potential perturbations superimposed on a smooth lens are…

Astrophysics of Galaxies · Physics 2022-07-27 Georgios Vernardos , Leon V. E. Koopmans

In gravitational lensing, the concept of optical depth assumes the lens is dark. Several microlensing detections have now been made where the lens may be bright. Relations are developed between apparent and absolute optical depth in the…

Astrophysics · Physics 2009-10-30 Robert J. Nemiroff

In this paper,three external fields interacting with the four-level Y-type atomic system described by the density-matrix approach is investigated .The results show that the left-handedness with zero absorption are achieved.And the zero…

Quantum Physics · Physics 2024-03-29 Shun-Cai Zhao , Zheng-Dong Liu , Qi-Xuan Wu

This paper revisits the controversy concerning whether gravitational lensing effects make a significant difference to estimation of distance to the Cosmic Microwave Background last scattering surface in cosmology. A recent paper by Kaiser…

General Relativity and Quantum Cosmology · Physics 2018-06-26 George F R Ellis , Ruth Durrer

The transmission of evanescent waves in a gain-compensated perfect lens is discussed. In particular, the impact of gain saturation is included in the analysis, and a method for calculating the fields of such nonlinear systems is developed.…

In a recent communication, Parimi et al. (Nature 426, 404 (2003)) reported the experimental results on imaging by a flat lens made of photonic crystals. They attributed the observed focusing to the negative refraction expected for the…

Materials Science · Physics 2007-05-23 Chao-Hsien Kuo , Zhen Ye

The standard theory of weak gravitational lensing relies on the infinitesimal light beam approximation. In this context, images are distorted by convergence and shear, the respective sources of which unphysically depend on the resolution of…

General Relativity and Quantum Cosmology · Physics 2017-11-08 Pierre Fleury , Julien Larena , Jean-Philippe Uzan