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Journal of Experimental and Theoretical Physics

Focusing of an atomic beam by a Fresnel atom microlens

V. I. Balykin, Vladimir G. Minogin

Published Oct 1, 2007• 1 citation
Publisher

Abstract

Focusing of an atomic beam by a Fresnel atom microlens formed by an optical field diffracted by an aperture whose size is comparable to or greater than the radiation wavelength is considered. It is shown that the dipole gradient force enables one to focus the atomic beam to a spot of about 10 nm in diameter. The focusing properties of a Fresnel atom microlens are analyzed within a model describing the dipole interaction of rubidium atoms with monochromatic radiation near the D -line.

DOI
10.1134/s1063776107090026

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Focusing of an atomic beam by a Fresnel atom microlens formed by an optical field diffracted by an aperture whose size is comparable to or greater than the radiation wavelength is considered. It is shown that the dipole gradient force enables one to focus the atomic beam to a spot of about 10 nm in diameter. The focusing properties of a Fresnel atom microlens are analyzed within a model describing the dipole interaction of rubidium atoms with monochromatic radiation near the D -line.
Atomic beam focusing by an atomic microlens formed by the optical field diffracted from a circular aperture in a metallic screen is considered for an aperture diameter smaller than the wavelength of the field. Analytic expressions are derived for the dipole gradient force acting on an atom in the field of diffracted radiation. It is shown that the action of the gradient force makes it possible to focus the atomic beam into a spot with a diameter on the order of a few nanometers. Numerical estimates are obtained for the focusing properties of the atomic microlens in the model describing the dipole interaction of Rb atoms with laser radiation in the vicinity of the D line.
We analyze focusing of atomic beams by the atom near-field microlenses produced by the laser fields diffracted on the apertures in the metallic screens. Analysis of the focusing properties of the atom microlenses is given in a model describing dipole interaction of atoms with a far-off-resonance laser light. Two types of the atom microlenses are considered: The Bethe-type microlens with aperture less than the light wavelength and the Fresnel-type microlens with aperture about the wavelength. It is shown that both types of the atom microlenses are able to produce strong dipole gradient forces which can focus the atomic beams. However, while the Bethe-atom microlens is able to produce sharp focusing of the beams the Fresnel-atom microlens possesses weak focusing property due to high anharmonicity of the gradient force. We conclude that the Bethe-atom microlens can be considered as a promising tool of the atom optics potentially able to focus atomic beams into spot sizes about nanometers.
This paper examines the focusing of an atomic beam by the near field of laser radiation diffracted by a small aperture. The wave properties of the atom are taken into consideration within the framework of an approximate Schrödinger equation. The possibility is demonstrated of focusing an atomic beam into a spot some 3 nm across, the atomic and laser beam characteristics being quite acceptable. The main contribution to the spot size is shown to be from spherical aberrations and diffraction effects, the chromatic aberrations of the atomic beam with a 5% velocity distribution broadening having a lesser effect.
A simple focusing device is proposed for de Broglie matter waves—a diffractive lens, based on the optical effect of diffractive multifocal focusing of radiation. This matter-wave lens consists of two coaxial circular apertures in which the second aperture of smaller diameter is located where the Fresnel number of the first aperture is unity. It is shown that diffraction of a de Broglie matter wave by a system of two pinholes on an optical axis exhibits the multifocal focusing effect of matter waves in the near-field (Fresnel) zone, which creates a very intense, spatially localized beam of atoms. Theoretical predictions for the focusing efficiency of a neutral atomic beam by the diffractive lens are as follows. The spot diameter is ~0.1 µm, the ratio of focal and incident intensities is ~15, the focal length of the diffractive lens is in the range ~0.13 to 6 cm, the focusing depth is in the range ~15 to 30 cm, and the energy transmitting efficiency is ~30 %. For the relatively large diameters of the pinholes, 5.0 µm, the proposed configuration acts as a matter-wave lens with a large focal length and a long focusing depth.
A simple focusing device is proposed for de Broglie matter-waves - a diffractive lens, based on the optical effect of diffractive multifocal focusing of radiation. This matter-wave lens consists of two co-axial circular apertures in which the second aperture of smaller diameter is located where the Fresnel number of the first aperture is unity. It is shown that diffraction of a de Broglie matter wave by a system of two pinholes on an optical axis exhibits the multifocal focusing effect of matter waves in the near-field (Fresnel) zone. The focusing, defocusing and refocusing phenomenon is explained as resulting from periodic phase changes at singular points, which are points where the intensity is zero and the phase is undefined. It is shown that the proposed matter-wave lens could create a very intense, spatially-localized beam of atoms. Theoretical predictions for the focusing efficiency of a neutral atomic beam by the diffractive lens are: the spot diameter is ~ 0.1 &mgr;m, the ratio of focal and incident intensities is ~ 15, the focal length of the diffractive lens is in the range ~ 0.13.6 cm, the focusing depth is in the range ~ 15.30 cm, and the energy transmitting efficiency is ~ 30%. For the relatively-large diameters of the pinholes, ⩾ 5.0 &mgr;m, the proposed configuration acts as a matter-wave lens with a large focal length and a long focusing depth.
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.