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We present a method to reconstruct the complete statistical mode structure and optical losses of multimode conjugated optical fields using an experimentally measured joint photon-number probability distribution. We demonstrate that this…

This work concerns the asymptotic analysis of high-frequency wave propagation in randomly layered media with fast variations and long-range correlations. The analysis takes place in the 3D physical space and weak-coupling regime. The role…

We study the paraxial wave equation with a randomly perturbed index of refraction, which can model the propagation of a wave beam in a turbulent medium. The random perturbation is a stationary and isotropic process with a general form of…

Quantum imaging has a potential of enhancing precision of the object reconstruction by using quantum correlations of the imaging field. This is especially important for imaging requiring low-intensity fields up to the level of few-photons.…

We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed,…

Conventional wisdom holds that quantum effects are fragile and can be destroyed by loss. Here, contrary to general belief, we show how to realize quantum revival of optical correlations at the single-photon level with the help of loss. We…

Modeling strong gravitational lenses in order to quantify the distortions in the images of background sources and to reconstruct the mass density in the foreground lenses has traditionally been a difficult computational challenge. As the…

In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…

The static pair correlation (distribution) function and the structure factor of particle distributions in three-dimensional homogeneous isotropic systems are explicitly restored from two-dimensional data observed in a thin slab sliced out…

We present an effective ansatz for the wave function of correlated electrons that brings closer the fields of machine learning parameterizations and tensor rank decompositions. We consider a CANDECOMP/PARAFAC (CP) tensor factorization of a…

Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments of the field to be…

Wavefield speckle patterns are generated by interference of randomly scattered coherent light. In the weak-coupling regime of the It\^o-Schr\"odinger paraxial model for long-distance wave propagation, we show the following multiscale…

Refraction at the interface between two materials is fundamental to the interaction of light with photonic devices and to the propagation of light through the atmosphere at large. Underpinning the traditional rules for the refraction of an…

A purely analytical extension of the flattened Gaussian beams [Opt. Commun. \textbf{107,} 335 (1994)] to any values of the beam order, is here proposed. Due to it, the paraxial propagation problem of axially symmetric, coherent flat-top…

A simple coherent-imaging method due to Paganin et al. is widely employed for phase-amplitude reconstruction of samples using a single paraxial x-ray propagation-based phase-contrast image. The method assumes that the sample-to-detector…

A light field records numerous light rays from a real-world scene. However, capturing a dense light field by existing devices is a time-consuming process. Besides, reconstructing a large amount of light rays equivalent to multiple light…

This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance…

We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local…

Next generation radio telescopes, like the Square Kilometre Array, will acquire an unprecedented amount of data for radio astronomy. The development of fast, parallelisable or distributed algorithms for handling such large-scale data sets…

Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in…