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Laser Physics

Laser focusing of cold atoms: Analytical solution of the problem

В. В. Климов, Vladilen S Letokhov

Published Jan 1, 2003• 2 citations
OpenAlex

Abstract

The motion of paraxial atomic beams in a laser radiation field is studied within the framework of a parabolic equation. Exact analytical solutions of the parabolic equation are found for a variety of potentials featuring a nonuniformity in the propagation direction. Special attention is paid to the propagation of cold atomic beams in the gradient field of the TEM01* laser radiation mode. Explicit analytical expressions are found for the position of the focal points, focal spot radius, and spatial intensity distribution.

Related papers

Exact solution of the problem of laser focusing of an atomic beam

В. В. Климов, Vladilen S Letokhov

The exact solution (Green’s function) of a parabolic equation describing the motion of neutral atoms in the field of a hollow TEM 01 * mode of laser radiation is found. The positions of the focus and the width of the focal spot are found on the basis of this solution for various configurations of the laser atomic beam.

Journal of Experimental and Theoretical Physics Letters•Nov 1, 1999•3 citations

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

Focusing of an atomic beam by a J1 laser beam

Kurnyul Choi, HeeS. Lee, Henry Fenichel

Atomic beam focusing by a gradient (dipole) force of the near resonant first order Bessel beam is considered in the paraxial approximation. The first order Bessel beam (J1) is a nondivergent laser beam whose intensity profile is the square of the first-order Bessel function of the first kind. A co-propagating J1 beam, tuned above resonance, provides the minimum rate of spontaneous emission on axis where the intensity is minimum. It has a steeper intensity gradient and a longer interaction range than does TEM01*. Numerical results for the focal length and the atomic beam density distribution in the focal plane are presented. Focusing limitations due to aberrations are discussed. The results are compared with those of the TEM01* mode beam.

Annual Meeting Optical Society of America•Jan 1, 1992•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 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 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
The motion of paraxial atomic beams in a laser radiation field is studied within the framework of a parabolic equation. Exact analytical solutions of the parabolic equation are found for a variety of potentials featuring a nonuniformity in the propagation direction. Special attention is paid to the propagation of cold atomic beams in the gradient field of the TEM01* laser radiation mode. Explicit analytical expressions are found for the position of the focal points, focal spot radius, and spatial intensity distribution.
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.
Atomic beam focusing by a gradient (dipole) force of the near resonant first order Bessel beam is considered in the paraxial approximation. The first order Bessel beam (J1) is a nondivergent laser beam whose intensity profile is the square of the first-order Bessel function of the first kind. A co-propagating J1 beam, tuned above resonance, provides the minimum rate of spontaneous emission on axis where the intensity is minimum. It has a steeper intensity gradient and a longer interaction range than does TEM01*. Numerical results for the focal length and the atomic beam density distribution in the focal plane are presented. Focusing limitations due to aberrations are discussed. The results are compared with those of the TEM01* mode beam.
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.
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 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.