Related papers: Optimal Diffractive Focusing of Quantum Waves
The problem of a beam of quantum particles falling through a diffractive screen is studied. The solutions for single and double slits are obtained explicitly when the potential is approximated by a linear function. It is found that the…
{The problem of laser beam concentration in a focal spot via wavefront variations is formulated as a maximization of the $beam$ $propagation$ $functional$ defined as the light power passing through aperture of an arbitrary shape located in…
We study a fully discrete finite element method for variable-order time-fractional diffusion equations with a time-dependent variable order. Optimal convergence estimates are proved with the first-order accuracy in time (and second order…
In this paper it is shown how one can use Bessel beams to obtain a stationary localized wavefield with high transverse localization, and whose longitudinal intensity pattern can assume any desired shape within a chosen interval 0 < z < L of…
Diffraction-free optical beams propagate freely without change in shape and scale. Monochromatic beams that avoid diffractive spreading require two-dimensional transverse profiles, and there are no corresponding solutions for profiles…
It is shown that the Schrodinger equation for a large family of pairs of two-dimensional quantum potentials possess wavefuctions for which the amplitude and the phase are interchangeable, producing two different solutions which are dual to…
Beam displacement measurements are widely used in optical sensing and communications; however, their performance is affected by numerous intrinsic and extrinsic factors including beam profile, propagation loss, and receiver architecture.…
This work presents the first optical trapping experimental demonstration of micro-particles with Frozen Waves. Frozen Waves are an efficient method to model longitudinally the intensity of non-diffracting beams obtained by superposing…
We present a formalism of x-ray dynamical diffraction from volume diffractive optics with large numerical aperture and high aspect ratio, in an analogy to the Takagi-Taupin equations for strained single crystals. We derive a set of basic…
Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of…
Diffraction phenomena usually can be formulated in terms of a potential that induces the redistribution of a wave's momentum. Using an atomic Bose-Einstein condensate coupled to the orbitals of a state-selective optical lattice, we…
quantum theory of generalized $\mathrm{X}$ waves with orbital angular momentum in dispersive media, and the interaction of quantized $\mathrm{X}$ waves in quadratic nonlinear media were studied in (J. opt,20,065201(2018)). We present a kind…
We study the wave equation in a bounded domain or on a compact Riemannian manifold with boundary. Assume that we are given the hyperbolic Neumann-to-Dirichlet map on the boundary corresponding to physical boundary measurements. We consider…
Bragg Diffraction of matter waves is an established technique used in the most accurate quantum sensors. It is also the method of choice to operate large-momentum-transfer, high-sensitivity atom interferometers. It suffers, however, from an…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
We derive the invariant imbedding equations for plane electromagnetic waves propagating in stratified magnetic media, where both dielectric and magnetic permeabilities vary in one spatial direction in an arbitrary manner. These equations…
Wave propagation through random continuous media remains an important fundamental problem with applications ranging from remote sensing to quantum communication. Typically, such media are characterized by smooth refractive index…
This paper proposes a frequency/time hybrid integral-equation method for the time dependent wave equation in two and three-dimensional spatial domains. Relying on Fourier Transformation in time, the method utilizes a fixed…
In this paper, we develop a theoretical analysis to efficiently handle superpositions of waves with concentrated wavevector and frequency spectra, allowing an easy analytical description of fields with interesting transverse profiles.…
Quantum entanglement and squeezing have significantly improved phase estimation and imaging in interferometric settings beyond the classical limits. However, for a wide class of non-interferometric phase imaging/retrieval methods vastly…