Related papers: The perfect lens on a finite bandwidth
Achieving exact unidirectional invisibility in a finite frequency band has been an outstanding problem for many years. We offer a simple solution to this problem in two dimensions that is based on our solution to another more basic open…
We consider a wide variety of scattering problems including scattering by Dirichlet, Neumann, and penetrable obstacles. We consider a radial perfectly-matched layer (PML) and show that for any PML width and a steep-enough scaling angle, the…
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.…
As a lens capable of sending images of deep sub-wavelength objects to the far field, the hyperlens has garnered significant attention for its super-resolution and magnification capabilities. However, traditional hyperlenses require extreme…
Let $F$ be a number field, $\pi$ either a unitary cuspidal automorphic representation of $\mathrm{GL}(2)/F$ or a unitary Eisenstein series, and $\chi$ a unitary Hecke character of analytic conductor $C(\chi).$ We develop a regularized…
We present a general scheme for the computation of the time dependent (TD) quadratic susceptibility ($\chi^{(2)}$) of an extended insulator obtained by applying the `$2n+1$' theorem to the action functional as defined in TD density…
We show the optimal coherence of $2d$ lines in $\mathbb{C}^{d}$ is given by the Welch bound whenever a skew Hadamard of order $d+1$ exists. Our proof uses a variant of Hadamard doubling that converts any equiangular tight frame of size…
The stiffness exponents in the glass phase for lattice spin glasses in dimensions $d=3,...,6$ are determined. To this end, we consider bond-diluted lattices near the T=0 glass transition point $p^*$. This transition for discrete bond…
Lens modeling is the key to successful and meaningful automated strong galaxy-scale gravitational lens detection. We have implemented a lens-modeling "robot" that treats every bright red galaxy (BRG) in a large imaging survey as a potential…
At visible and infrared frequencies, metals show tantalizing promise for strong subwavelength resonances, but material loss typically dampens the response. We derive fundamental limits to the optical response of absorptive systems, bounding…
Broadband super-resolution imaging is important in optical field. To achieve super-resolution imaging, various lenses from superlens to solid immersion lens have been designed and fabricated in recent years. However, the imaging is…
In the search for the nature of dark energy most cosmological probes measure simple functions of the expansion rate. While powerful, these all involve roughly the same dependence on the dark energy equation of state parameters, with…
Among the family of hard convex lens-shaped particles (lenses), the one with aspect ratio equal to 2/3 is `optimal' in the sense that the maximally random jammed (MRJ) packings of such lenses achieve the highest packing fraction $\phi_{\rm…
The question is considered about possibility of overcoming diffraction limit at device, named superlens. This device is a flat slab, executed from material with index of refraction n,equal n=-1. It is shown, what this device really can…
In this paper we provide explicit upper and lower bounds on certain $L^2$ $n$-widths, i.e., best constants in $L^2$ approximation. We further describe a numerical method to compute these $n$-widths approximately, and prove that this method…
We use our catalog of photometric redshifts in the Hubble Deep Field (HDF) to estimate the Luminosity Function (LF) of galaxies up to z=2. Using the obtained LF and a relationship between luminosity and halo size, we calculate the expected…
A generalized lens equation for weak gravitational fields in Schwarzschild metric and valid for finite distances of source and observer from the light deflecting body is suggested. The magnitude of neglected terms in the generalized lens…
We prove under general assumptions that solutions of the thin obstacle or Signorini problem in any space dimension achieve the optimal regularity $C^{1,1/2}$. This improves the known optimal regularity results by allowing the thin obstacle…
This paper introduces a measure, called Lipschitz widths, of the optimal performance possible of certain nonlinear methods of approximation. It discusses their relation to entropy numbers and other well known widths such as the Kolmogorov…
Optimal weighted Sobolev-Lorentz embeddings with homogeneous weights in open convex cones are established, with the exact value of the optimal constant. These embeddings are non-compact, and this paper investigates the structure of their…