Related papers: Optimal Diffractive Focusing of Quantum Waves
A Fourier transformation in a fractional dimensional space of order $\la$ ($0<\la\leq 1$) is defined to solve the Schr\"odinger equation with Riesz fractional derivatives of order $\a$. This new method is applied for a particle in a…
A non-perturbative quantization of a paraxial electromagnetic field is achieved via a generalized dispersion relation imposed on the longitudinal and the transverse components of the photon wave vector. The theoretical formalism yields a…
The challenge of imaging low-density objects in an electron microscope without causing beam damage is significant in modern TEM. This is especially true for life science imaging, where the sample, rather than the instrument, still…
We describe the minimal diffraction-free and dispersion-free, superluminal wave packets (X-waves and generic superluminal localized waves) that can carry a given amount of units $m$ of orbital angular momentum (OAM) per photon. Even if…
In this article, we study wave dynamics in the fractional nonlinear Schr\"odinger equation with a modulated honeycomb potential. This problem arises from recent research interests in the interplay between topological materials and nonlocal…
Light and sound waves have the fascinating property that they can move objects through the transfer of linear or angular momentum. This ability has led to the development of optical and acoustic tweezers, with applications ranging from…
We propose a framework for the design and analysis of optimization algorithms in variational quantum Monte Carlo, drawing on geometric insights into the corresponding function space. The framework translates infinite-dimensional…
This paper shows analytically and numerically that a vortex plate coupled to a neutral density filter can deliver a true optical derivative when placed at the focal plane of a $2f$ lens pair. This technique turns spatial variations in…
It has been known through some examples that parameters of an electromagnetic medium can be so defined that there is no dispersion equation (Fresnel equation) to restrict the choice of the wave vector of a plane wave in such a medium, i.e.,…
We consider standing waves of the nonlinear Schr\"odinger equation $i\partial_t u = -\Delta_\alpha u + |u|^{p-1}u$ in the defocusing case in dimensions $N=2$ and $N=3$. Here, $-\Delta_\alpha$ denotes the Laplacian with a point interaction.…
Light injected into a spherical dielectric body may be confined very efficiently via the mechanism of total internal reflection. The frequencies that are most confined are called resonances. If the shape of the body deviates from the…
Various methods have been introduced to measure the orbital angular momentum (OAM) of light, from fork holograms to Dove prism interferometers, from tilted lenses to triangular apertures - each with their own benefits and limitations. Here…
Diffractive optical elements that divide an input beam into a set of replicas are used in many optical applications ranging from image processing to communications. Their design requires time-consuming optimization processes, which, for a…
We consider the initial/boundary value problem for the fractional diffusion and diffusion-wave equations involving a Caputo fractional derivative in time. We develop two "simple" fully discrete schemes based on the Galerkin finite element…
We analyze the instability of an unpolarized uniform quantum plasma consisting of two oppositely charged fermionic components with varying mass ratios, against charge and spin density waves (CDWs and SDWs). Using density functional theory,…
Grating magneto-optical traps are an enabling quantum technology for portable metrological devices with ultracold atoms. However, beam diffraction efficiency and angle are affected by wavelength, creating a single-optic design challenge for…
A theory for the characterization of the fourth moment of electromagnetic wave beams is presented in the case when the source is partially coherent. A Gaussian-Schell model is used for the partially coherent random source. The white-noise…
The study points out that the traditional solutions to wave equation of dissipative wave and motion equation of block for a multi-degree-of-freedom mass spring damper system are the possible solutions, which are not necessarily objective…
In this paper, we give the quantum wave equations of single photon when it is in the free or medium space. With these equations, we can study light interference and diffraction with quantum approach. Otherwise, they can be applied in…
Precise modeling of extended sources is a central challenge in modern optical engineering, laser physics, and computational lithography. Unlike ideal point sources or completely incoherent thermal radiation sources, real-world light sources…