相关论文: The perfect lens on a finite bandwidth
For the first time exact analytical solutions to the eikonal equations in (1+1) dimensions with a refractive index being a saturated function of intensity are constructed. It is demonstrated that the solutions exhibit collapse; an explicit…
Lipschitz constants for the width and diameter functions of a convex body in $\mathbb R^n$ are found in terms of its diameter and thickness (maximum and minimum of both functions). Also, a dual approach to thickness is proposed.
In this paper, a non-Hermitian two-dimensional photonic crystal flat lens is proposed. The negative refraction of the second band of photonic crystal is utilized to realize super-resolution imaging of the point source. Based on the…
In absence of a lens to form an image, incoherent or partially coherent light scattering off an obstructive or reflective object forms a broad intensity distribution in the far field with only feeble spatial features. We show here that…
We calculate the fidelity susceptibility chi_f for the Luttinger model and show that there is a universal contribution linear in temperature T (or inverse length 1/L). Furthermore, we develop an algorithm - based on a lattice path integral…
We measure the size-luminosity relation of photometrically-selected galaxies within the redshift range $z\sim6-9$, using galaxies lensed by six foreground Hubble Frontier Fields (HFF) clusters. The power afforded by strong gravitational…
An efficient integral equation based solver is constructed for the electrostatic problem on domains with cuboidal inclusions. It can be used to compute the polarizability of a dielectric cube in a dielectric background medium at virtually…
Motivated by modern applications like image processing and wireless sensor networks, we consider a variation of the famous Kepler Conjecture. Given any infinite set of unit balls covering the whole space, we want to know the optimal (lim…
We prove explicit stability estimates for the sphere packing problem in dimensions 8 and 24, showing that, in the lattice case, if a lattice is $\sim \varepsilon$ close to satisfying the optimal density, then it is, in a suitable sense,…
We experimentally demonstrate imaging in the longwave-infrared (LWIR) spectral band (8um to 12um) using a single polymer flat lens based upon multi-level diffractive optics. The device thickness is only 10{\mu}m, and chromatic aberrations…
We present two long-working-distance objective lenses with numerical apertures (NA) of 0.29 and 0.4 for single-atom experiments. The objective lenses are assembled entirely by the commercial on-catalog $\Phi$1'' singlets. Both the…
We consider the homogeneous Dirichlet problem for the integral fractional Laplacian $(-\Delta)^s$. We prove optimal Sobolev regularity estimates in Lipschitz domains provided the solution is $C^s$ up to the boundary. We present the…
The existence of strong lensing systems with Einstein radii (Re) covering the full mass spectrum, from ~1-2" (produced by galaxy scale dark matter haloes) to >10" (produced by galaxy cluster scale haloes) have long been predicted. Many…
We have observed two blank fields of approximately 30 by 23 arcminutes using the William Herschel Telescope. The fields have been studied as part of the CNOC2 survey, and spectroscopic redshifts are available for 1125 galaxies in the two…
The set B of geodesic rays avoiding a suitable obstacle in a complete negatively curved Riemannian manifold determines a spectrum S. While various properties of this spectrum are known, we define and study dimension functions on S in terms…
Diffraction limits the behaviour of light in optical systems and sets the smallest achievable line width at half the wavelength. With a novel subwavelength plasmonic lens to reduce the diffraction via an asymmetry and to generate and…
Leonhardt demonstrated (2009) that the 2D Maxwell Fish Eye lens (MFE) can perfectly focus 2D Helmholtz waves of arbitrary frequency, i.e., it can perfectly transport an outward (monopole) 2D Helmholtz wave field, generated by a point…
We introduce the cone of completely-positive functions, a subset of the cone of positive-type functions, and use it to fully characterize maximum-density distance-avoiding sets as the optimal solutions of a convex optimization problem. As a…
We study the expressivity of one-dimensional (1D) ReLU deep neural networks through the lens of their linear regions. For randomly initialized, fully connected 1D ReLU networks (He scaling with nonzero bias) in the infinite-width limit, we…
It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation,…