Related papers: Theorem on subwavelength imaging with arrays of di…
Quantum-inspired superresolution methods surpass the Rayleigh limit in imaging, or the analogous Fourier limit in spectroscopy. This is achieved by carefully extracting the information carried in the emitted optical field by engineered…
In this letter we study the subwavelength imaging of sparse broadband sources inside a disordered medium by processing the data acquired by a single antenna. A mathematical model has been developed for solving such problem based on the idea…
A limit theorem for a sequence of diffusion processes on graphs is proved in a case when vary both parameters of the processes (the drift and diffusion coefficients on every edge and the asymmetry coefficients in every vertex), and…
In this paper we show that the extraordinary optical transmission phenomenon found before in 2D hole arrays is already present in a linear chain of subwavelength holes, which can be considered as the basic geometrical unit showing this…
In recent years, there has been a proliferation of wide-field sky surveys to search for a variety of transient objects. Using relatively short focal lengths, the optics of these systems produce undersampled stellar images often marred by a…
Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction…
We show that independent and uniformly distributed sampling points are as good as optimal sampling points for the approximation of functions from the Sobolev space $W_p^s(\Omega)$ on bounded convex domains $\Omega\subset \mathbb{R}^d$ in…
If identical photons meet at a semi-transparent mirror they appear to leave in the same direction, an effect called "two-photon interference". It has been known for some time that this effect should occur for photons generated by dissimilar…
A general expression for the optical theorem for probe sources given in terms of propagation invariant beams is derived. This expression is obtained using the far field approximation for Rayleigh regime. In order to illustrate this results…
Historically, the resolution of optical imaging systems was dictated by diffraction, and the Rayleigh criterion was long considered an unsurpassable limit. In superresolution microscopy, this limit is overcome by manipulating the emission…
In this paper, we introduce the concepts of weaknorm, quasi-weaknorm on real vector spaces. By these concepts, we introduce the concept of quasi-locally convex topological vector spaces, which include locally convex topological vector…
Imaging below the diffraction limit is always a public interest because of the restricted resolution of conventional imaging systems. To beat the limit, evanescent harmonics decaying in space must participate in the imaging process. Here,…
We study the possibility of creating spatial patterns having subwavelength size by using the so-called dark states formed by the interaction between atoms and optical fields. These optical fields have a specified spatial distribution. Our…
We obtain sufficient conditions on kernels of quantum states under which Wigner functions, optical quantum tomograms and linking their formulas are correctly defined. Our approach is based upon the Sobolev embedding theorem. The transition…
A p-adic analogue of the pseudonorm version of the birational Torelli type theorem is obtained via a comparison theorem of image closures. Among other results obtained, we have a criterion for existence of rational points of canonically…
A Central Limit Theorem is proved for linear random fields when sums are taken over finite disjoint union of rectangles. The approach does not rely upon the use of Beveridge Nelson decomposition and the conditions needed are similar to…
We obtain a new version of the Uncertainty Principle for functions with Fourier transforms supported on a lacunary set of intervals. This is a generalization of Zygmund's theorem on lacunary trigonometric series to the real line in the…
The Rayleigh's criterion infamously imposes a minimum separation between two incoherent sources for them to be distinguishable via classical methods. In this work, we demonstrate the emergence of two-photon beats from the interference of a…
This paper describes a new approach to the optimization of information extraction in multi-wavelength image cubes of cosmological fields. The objective is to create a framework for the automatic identification and tagging of sources…
Simple optical instruments are linear optical networks where the incident light modes are turned into equal numbers of outgoing modes by linear transformations. For example, such instruments are beam splitters, multiports, interferometers,…