Journal ArticleDOI
Helmholtz–Gauss waves
TLDR
In this article, a detailed study of the propagation of an arbitrary nondiffracting beam whose disturbance in the plane z = 0 is modulated by a Gaussian envelope is presented.Abstract:
A detailed study of the propagation of an arbitrary nondiffracting beam whose disturbance in the plane z=0 is modulated by a Gaussian envelope is presented. We call such a field a Helmholtz–Gauss (HzG) beam. A simple closed-form expression for the paraxial propagation of the HzG beams is written as the product of three factors: a complex amplitude depending on the z coordinate only, a Gaussian beam, and a complex scaled version of the transverse shape of the nondiffracting beam. The general expression for the angular spectrum of the HzG beams is also derived. We introduce for the first time closed-form expressions for the Mathieu–Gauss beams in elliptic coordinates and for the parabolic Gauss beams in parabolic coordinates. The properties of the considered beams are studied both analytically and numerically.read more
Citations
More filters
Journal ArticleDOI
Localized Light Waves: Paraxial and Exact Solutions of the Wave Equation (a Review)
TL;DR: In this article, simple explicit localized solutions are systematized over the whole space of a linear wave equation, which models the propagation of optical radiation in a linear approximation, and a similarity between these exact solutions and harmonic in time fields obtained in the paraxial approximation based on the Leontovich-Fock parabolic equation has been studied.
Journal ArticleDOI
Diffraction-free pulsed optical beams via space-time correlations.
TL;DR: It is shown here that imposing a judicious correlation between spatial and spectral degrees of freedom of a pulsed beam can render its transverse spatial profile independent of location along the propagation axis, thereby arresting the spread of the time-averaged beam.
Journal ArticleDOI
Lorentz beams and symmetry properties in paraxial optics
Omar El Gawhary,Sergio Severini +1 more
TL;DR: In this article, a new tridimensional scalar optical beams are introduced, called Lorentz beams, which are obtained by multiplying the original Lorenttz beam by a Gaussian apodization function.
Journal ArticleDOI
On the concept of “tractor beams”
Sergey Sukhov,Aristide Dogariu +1 more
TL;DR: It is demonstrated the existence of a class of optical beams where the nonconservative forces can be locally oriented in a direction opposite to the propagation wave vector.
References
More filters
Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Journal ArticleDOI
Tables of Integrals, Series, and Products
Journal ArticleDOI
Diffraction-free beams.
TL;DR: The first experimental investigation of nondiffracting beams, with beam spots as small as a few wavelengths, can exist and propagate in free space, is reported.
Journal ArticleDOI
Exact solutions for nondiffracting beams. I. The scalar theory
TL;DR: In this paper, exact nonsingular solutions of the scalar-wave equation for beams that are non-diffracting were presented, which means that the intensity pattern in a transverse plane is unaltered by propagating in free space.