Related papers: Supergrowth and sub-wavelength object imaging
The inherent non-linearity of intensity correlation functions can be used to spatially distinguish identical emitters beyond the diffraction limit, as achieved, for example, in Super-Resolution Optical Fluctuation Imaging (SOFI). Here, we…
We address an important issue of a dynamic homogenisation in vector elasticity for a doubly periodic mass-spring elastic lattice. The notion of logarithmically growing resonant waves is used in a complete analysis of star-shaped wave forms…
It has been advocated that medical imaging systems and reconstruction algorithms should be assessed and optimized by use of objective measures of image quality that quantify the performance of an observer at specific diagnostic tasks. One…
We consider the inverse problem of determining the geometry of penetrable objects from scattering data generated by one incident wave at a fixed frequency. We first study an orthogonality sampling type method which is fast, simple to…
In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wave function, and the linearized inverse scattering problem…
Super-resolution imaging refers to imaging techniques that surpass the Rayleigh resolution limit. One standard way to achieve super-resolution is by structuring the phase of the field illuminating the object. Although super-resolution…
We derive upper bounds to free-space concentration of electromagnetic waves, mapping out the limits to maximum intensity for any spot size and optical beam-shaping device. For sub-diffraction-limited optical beams, our bounds suggest the…
Lenses that can collect the perfect image of an object must restore propagative and evanescent waves. However, for efficient information transfer, e.g., in compressed sensing, it is often desirable to detect only the fast spatial variations…
We present a theoretical framework for understanding the wavefunctions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong…
Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…
We show that for a large class of stochastic flows the spatial derivative grows at most exponentially fast even if one takes the supremum over a bounded set of initial points. We derive explicit bounds on the growth rates that depend on the…
The local number variance associated with a spherical sampling window of radius $R$ enables a classification of many-particle systems in $d$-dimensional Euclidean space according to the degree to which large-scale density fluctuations are…
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…
In this paper, ultra-broad band optical signal amplification are analyzed and demonstrated by utilizing supercontinuum generation propagating over the photonic crystal fiber. The coupled nonlinear Schroodinger equation containing parametric…
The evolution of both quantum and classical ensembles may be described via the probability density P on configuration space, its canonical conjugate S, and an_ensemble_ Hamiltonian H[P,S]. For quantum ensembles this evolution is, of course,…
Quantum simulations with ultracold atoms typically create atomic wavefunctions with structures at optical length scales, where direct imaging suffers from the diffraction limit. In analogy to advances in optical microscopy for biological…
Context. The overdensity inside a cosmological sub-volume and the tidal fields from its surroundings affect the matter distribution of the region. The resulting difference between the local and global power spectra is characterized by the…
The last decade has seen numerous efforts to achieve imaging resolution beyond that of the Abbe-Rayleigh diffraction limit. The main direction of research aiming to break this limit seeks to exploit the evanescent components containing fine…
We study the growth of typical groups from the family of $p$-groups of intermediate growth constructed by the second author. We find that, in the sense of category, a generic group exhibits oscillating growth with no universal upper bound.…
In a recent paper, we exhibit a link between the average local growth of Laplace eigenfunctions on surfaces and the size of their nodal set. In that paper, the average local growth is computed using the uniform - or $L^\infty$ - growth…