Related papers: Paraxial beam propagation from Airy-type initial c…
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. An analytic function is identified which matches the discontinuity in the initial condition and also satisfies the…
The photon density operator function is used to calculate light beam propagation through turbulent atmosphere. A kinetic equation for the photon distribution function is derived and solved using the method of characteristics. Optical wave…
With exotic propagation properties, optical Airy beams have been well studied for innovative applications in communications, biomedical imaging, micromachining, and so on. Here we extend those studies to the quantum domain, creating quantum…
We propose a quantum algorithm that simulates the propagation of a light field through a weakly inhomogeneous medium. The wave equation in the paraxial approximation in inhomogeneous material takes the form of the Schr\"odinger equation…
A concise method of deriving expressions for Gaussian-like solutions of the paraxial and d'Alembert equations is presented. This method is based on the Hankel transform. Choosing some Gaussian base functions with slight modifications of the…
An approximation is elaborated for the paraxial propagation of diffracted beams, with both one- and two-dimensional cross sections, which are released from apertures with sharp boundaries. The approximation applies to any beam under the…
Accelerating Airy beams, known for their non-diffracting nature, self-healing properties, and curved propagation trajectories, are solutions to the paraxial wave equation. In this work, we theoretically and experimentally investigate…
In practice, Airy beams can only be reproduced in an approximate manner, with a limited spatial extension and hence a finite energy content. To this end, different procedures have been reported in the literature, based on a convenient…
A new class of nonparaxial accelerating optical waves is introduced. These are beams with a Bessel-like profile that are capable of shifting laterally along fairly arbitrary trajectories as the wave propagates in free space. The concept…
This work provides a mathematical derivation of a quasi-stationary model for multimode parametric down-conversion, which was presented in [Gatti et al., Sci. Rep. 13, 16786] with heuristic arguments. The model is here derived from the 3D+1…
Beam propagation beyond the paraxial approximation is studied in an optically written waveguide structure. The waveguide structure that leads to diffractionless light propagation, is imprinted on a medium consisting of a five-level atomic…
Quantitative phase imaging has become a topic of considerable interest in the microscopy community. We have recently described one such technique based on the use of a partitioned detection aperture, which can be operated in a single shot…
We analyze the propagation dynamics of radially polarized symmetric Airy beams (R-SABs) in a (2+1)-dimensional optical system with fractional diffraction, modeled by the fractional Schr\"odinger equation (FSE) characterized by the L\'evy…
The self-accelerating beams such as the Airy beam show great potentials in many applications including optical manipulation, imaging and communication. However, their superior features during linear propagation could be easily corrupted by…
This work opens a series of papers where we develop a general quasioptical theory for mode-converting electromagnetic beams in plasma and implement it in a numerical algorithm. Here, the basic theory is introduced. We consider a general…
Circular-Beams were introduced as a very general solution of the paraxial wave equation carrying Orbital Angular Momentum. Here we study their properties, by looking at their normalization and their expansion in terms of Laguerre-Gauss…
The distributions of the $k$-th largest level at the soft edge scaling limit of Gaussian ensembles are some of the most important distributions in random matrix theory, and their numerical evaluation is a subject of great practical…
We present a detailed study of two novel methods for shaping the light optical wavefront by employing a transmissive spatial light modulator (SLM). Conventionally, optical Airy beams are created by employing SLMs in the so-called all phase…
In this work, we present the theoretical and experimental study of the propagation of Airy beams when passing through two convex lenses with different focal distances. The theoretical analysis is presented from a matrix optical model for an…
Evolution formulas of the density operator, the photon number distribution, and the Wigner function are derived for the problem on the optical fields propagation in realistic environments. The method of deriving these formulas is novel and…