Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Laser lenses for neutral atomic beams

Gregg M. Gallatin, P. L. Gould

Published Nov 1, 1990• 0 citations
Publisher

Abstract

The focusing of a neutral atomic beam using near-resonant laser light is considered. The results of a path integral solution to the Schrodinger in the stationary phase approximation are presented. The details of the derivation of the propagation kernel are presented elsewhere [1]. This approach is general and allows us to deal with "thick" laser lenses. Numerical results for the focusing of a Gaussian atomic beam are presented. These results show that spot diameters on the order of 20 Angstroms are obtainable for many reasonable choices of laser and atomic beam parameters, and that for most of these cases the thin lens approximation is not valid.

DOI
10.1117/12.22988

Related papers

Laser focusing of atomic beams

Gregg M. Gallatin, P. L. Gould

The focusing of an atomic beam using near-resonant laser light is considered. Path-integral techniques are employed to transform the problem into a standard diffraction integral. This approach is general and allows us to deal with thick laser lenses. Starting from the basic form of the potential energy for an atom in a laser beam, we derive the propagation kernel for the atomic wave function for the particular case of a TEM01*, or doughnut, mode laser beam. Both the full three-dimensional propagation kernel and its paraxial approximation are discussed. We show that the paraxial case can be obtained from the three-dimensional case by a stationary-phase approximation of the propagation equation. Numerical results for the focusing of a Gaussian atomic beam are presented. These results show that spot diameters on the order of 20 Å are obtainable for many reasonable choices of laser and atomic beam parameters and that for most of these cases the thin-lens approximation is not valid. The effects of the lowest-order aberrations are also briefly discussed. Spherical aberration is found to contribute significantly to the focal spot diameter, at least for the doughnut mode laser beam considered here.

Journal of the Optical Society of America B•Mar 1, 1991•72 citations

Laser focusing of atomic beams

Gregg M. Gallatin, P. L. Gould

Recently, the focusing of an atomic beam using a laser has been considered by Balykin and Letokhov.1 Their calculations explicitly assume the thin lens approximation. Here, using path integral techniques, we derive the focal length and lowest-order aberrations of the laser atomic beam lens as a function of both laser and atomic beam parameters without making the thin lens approximation. Starting from the basic form of the potential energy for an atom in a laser beam, the propagation kernel is derived for the TEM(01)* or donut mode beam. From this result the focal length and lowest-order aberrations can be found for any atomic beam profile. We consider in particular a Gaussian atomic beam. Both the full 3-D propagation kernel and its paraxial approximation are discussed. We show how the paraxial case can be obtained from the 3-D case via a stationary phase approximation of the propagation equation.

Annual Meeting Optical Society of America•Jan 1, 1989•0 citations

Laser focusing of atoms: a particle-optics approach

Jabez J. McClelland, Michael R. Scheinfein

The use of a TEM01*-mode laser beam has been proposed as a means of focusing an atomic beam to nanometer- scale spot diameters. We have analyzed the classical trajectories of atoms through a TEM01*-mode laser beam, using methods developed for particle optics. The differential equation that describes the properties of the: first- order paraxial lens hi exactly the same form as the bell-shaped magnetic Newtonian lens that was first analyzed by Glaser for the focusing of electrons in an electron-microscope objective. We calculate the first-order properties of the lens, obtaining cardinal elements that are valid over the entire operating range of the lens including the thick and the immersion regimes. Contributions to the spot size are discussed, including four aberrations plus diffraction and atomic-beam-collimation effects. Explicit expressions for spherical chromatic, spontaneous-emission, and dipole-fluctuation aberrations are obtained. Examples are discussed for a sodium atomic beam, showing that subnanometer-diameter spots may be achieved with reasonable laser and atomic- beam parameters. Optimization of the lens is also discussed.

Journal of the Optical Society of America B•Sep 1, 1991•93 citations

Laser Focusing of Atoms: A Particle Optics Approach

Jabez J. McClelland, Michael R. Scheinfein

The use of a TEMoi*-mode laser beam has been proposed as a means of focusing an atomic beam to nanometerscale spot diameters. We have analyzed the classical trajectories of atoms through a TEM01*-mode laser beam, using methods developed for particle optics. The differential equation that describes the properties of the firstorder paraxial lens has exactly the same form as the bell-shaped magnetic Newtonian lens that was first analyzed by Glaser for the focusing of electrons in an electron-microscope objective. We calculate the first-order properties of the lens, obtaining cardinal elements that are valid over the entire operating range of the lens, including the thick and the immersion regimes. Contributions to the spot size are discussed, including four aberrations plus diffraction and atomic-beam-collimation effects. Explicit expressions for spherical, chromatic, spontaneous-emission, and dipole-fluctuation aberrations are obtained. Examples are discussed for a sodium atomic beam, showing that subnanometer-diameter spots may be achieved with reasonable laser and atomicbeam parameters. Optimization of the lens is also discussed.

•Jan 1, 1990•0 citations

An Atomic Lens Using a Focusing Hollow Beam

XIAYong, YINJian-Ping, WANGYu-Zhu

We propose a new method to generate a focused hollow laser beam by using an azimuthally distributed 2π-phase plate and a convergent thin lens,and calculate the intensity distribution of the focused hollow beam in free propagation space.The relationship between the waist w0 of the incident collimated Gaussian beam and the dark spot size of the focused hollow beam at the focal point,and the relationship between the focal lenght f of the thin lens and the dark spot size are studied respectively.The optical potential of the blue-detuned focused hollow beam for^85 Rb atoms is calculated.Our study shows that when the larger waist w of the incident Gaussian beam and the shorter focal length f of the lens are chosen,we can obtain an extremely small dark spot size of the focused hollow beam,which can be used to form an atomic lens with a resolution of sereval angstroms.

Chinese Physics Letters•Jan 1, 2003•0 citations

Focusing of Atomic Beams

V. I. Balykin, Vladilen S Letokhov

The principal element in any sort of optics is a lens. It is essential to create laser field configurations capable of focusing neutral atomic beams. There are two possibilities for focusing an atomic beam by laser light: by using the gradient force or by using the light pressure force. The force effecting the focusing of an atom in a beam should be proportional to the atomic displacement. This criterion must be satisfied for the force to produce the true “image”: if this criteria is not met, the image is blurred, i.e. there are aberrations. An approach to treat the focusing of atomic beam by laser light is to use the path integral technique to calculate the evolution of atomic wave function as it propagates in laser field. A particle-optical approach also can be used for treatment of focusing of atoms by laser light. The quadratic radial dependence of the potential is a necessary condition for focusing of atoms.

CRC Press eBooks•Apr 23, 2020•0 citations
The focusing of a neutral atomic beam using near-resonant laser light is considered. The results of a path integral solution to the Schrodinger in the stationary phase approximation are presented. The details of the derivation of the propagation kernel are presented elsewhere [1]. This approach is general and allows us to deal with "thick" laser lenses. Numerical results for the focusing of a Gaussian atomic beam are presented. These results show that spot diameters on the order of 20 Angstroms are obtainable for many reasonable choices of laser and atomic beam parameters, and that for most of these cases the thin lens approximation is not valid.
The focusing of an atomic beam using near-resonant laser light is considered. Path-integral techniques are employed to transform the problem into a standard diffraction integral. This approach is general and allows us to deal with thick laser lenses. Starting from the basic form of the potential energy for an atom in a laser beam, we derive the propagation kernel for the atomic wave function for the particular case of a TEM01*, or doughnut, mode laser beam. Both the full three-dimensional propagation kernel and its paraxial approximation are discussed. We show that the paraxial case can be obtained from the three-dimensional case by a stationary-phase approximation of the propagation equation. Numerical results for the focusing of a Gaussian atomic beam are presented. These results show that spot diameters on the order of 20 Å are obtainable for many reasonable choices of laser and atomic beam parameters and that for most of these cases the thin-lens approximation is not valid. The effects of the lowest-order aberrations are also briefly discussed. Spherical aberration is found to contribute significantly to the focal spot diameter, at least for the doughnut mode laser beam considered here.
Recently, the focusing of an atomic beam using a laser has been considered by Balykin and Letokhov.1 Their calculations explicitly assume the thin lens approximation. Here, using path integral techniques, we derive the focal length and lowest-order aberrations of the laser atomic beam lens as a function of both laser and atomic beam parameters without making the thin lens approximation. Starting from the basic form of the potential energy for an atom in a laser beam, the propagation kernel is derived for the TEM(01)* or donut mode beam. From this result the focal length and lowest-order aberrations can be found for any atomic beam profile. We consider in particular a Gaussian atomic beam. Both the full 3-D propagation kernel and its paraxial approximation are discussed. We show how the paraxial case can be obtained from the 3-D case via a stationary phase approximation of the propagation equation.
The use of a TEM01*-mode laser beam has been proposed as a means of focusing an atomic beam to nanometer- scale spot diameters. We have analyzed the classical trajectories of atoms through a TEM01*-mode laser beam, using methods developed for particle optics. The differential equation that describes the properties of the: first- order paraxial lens hi exactly the same form as the bell-shaped magnetic Newtonian lens that was first analyzed by Glaser for the focusing of electrons in an electron-microscope objective. We calculate the first-order properties of the lens, obtaining cardinal elements that are valid over the entire operating range of the lens including the thick and the immersion regimes. Contributions to the spot size are discussed, including four aberrations plus diffraction and atomic-beam-collimation effects. Explicit expressions for spherical chromatic, spontaneous-emission, and dipole-fluctuation aberrations are obtained. Examples are discussed for a sodium atomic beam, showing that subnanometer-diameter spots may be achieved with reasonable laser and atomic- beam parameters. Optimization of the lens is also discussed.
The use of a TEMoi*-mode laser beam has been proposed as a means of focusing an atomic beam to nanometerscale spot diameters. We have analyzed the classical trajectories of atoms through a TEM01*-mode laser beam, using methods developed for particle optics. The differential equation that describes the properties of the firstorder paraxial lens has exactly the same form as the bell-shaped magnetic Newtonian lens that was first analyzed by Glaser for the focusing of electrons in an electron-microscope objective. We calculate the first-order properties of the lens, obtaining cardinal elements that are valid over the entire operating range of the lens, including the thick and the immersion regimes. Contributions to the spot size are discussed, including four aberrations plus diffraction and atomic-beam-collimation effects. Explicit expressions for spherical, chromatic, spontaneous-emission, and dipole-fluctuation aberrations are obtained. Examples are discussed for a sodium atomic beam, showing that subnanometer-diameter spots may be achieved with reasonable laser and atomicbeam parameters. Optimization of the lens is also discussed.
We propose a new method to generate a focused hollow laser beam by using an azimuthally distributed 2π-phase plate and a convergent thin lens,and calculate the intensity distribution of the focused hollow beam in free propagation space.The relationship between the waist w0 of the incident collimated Gaussian beam and the dark spot size of the focused hollow beam at the focal point,and the relationship between the focal lenght f of the thin lens and the dark spot size are studied respectively.The optical potential of the blue-detuned focused hollow beam for^85 Rb atoms is calculated.Our study shows that when the larger waist w of the incident Gaussian beam and the shorter focal length f of the lens are chosen,we can obtain an extremely small dark spot size of the focused hollow beam,which can be used to form an atomic lens with a resolution of sereval angstroms.
The principal element in any sort of optics is a lens. It is essential to create laser field configurations capable of focusing neutral atomic beams. There are two possibilities for focusing an atomic beam by laser light: by using the gradient force or by using the light pressure force. The force effecting the focusing of an atom in a beam should be proportional to the atomic displacement. This criterion must be satisfied for the force to produce the true “image”: if this criteria is not met, the image is blurred, i.e. there are aberrations. An approach to treat the focusing of atomic beam by laser light is to use the path integral technique to calculate the evolution of atomic wave function as it propagates in laser field. A particle-optical approach also can be used for treatment of focusing of atoms by laser light. The quadratic radial dependence of the potential is a necessary condition for focusing of atoms.