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High Power Laser and Particle Beams

Aberration analysis of atom lens generated by a laser standing wave

Zhang Chunmei

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

Atom lens generated by a laser standing wave can be used to focus an atomic beam to nanometer dimensions. Aberrations exist in atom lens owing to the influence of velocity spread, beam spread, wave nature of atoms and so on. Two theoretical models were built to describe atom lens. Spherical aberration, chromatic aberration and the aberration caused by angular spread were analyzed with semi-classical model, and diffractive aberration was analyzed using quantum model. Simulation results show that aberration originates mainly from beam spread, and diffractive aberration is larger than spherical aberration and chromatic aberration. Three solutions of optimization of experimental parameters, adding beam mask and using etching technologies for improving atom lithography quality are presented.

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Atom lens generated by a laser standing wave can be used to focus an atomic beam to nanometer dimensions. Aberrations exist in atom lens owing to the influence of velocity spread, beam spread, wave nature of atoms and so on. Two theoretical models were built to describe atom lens. Spherical aberration, chromatic aberration and the aberration caused by angular spread were analyzed with semi-classical model, and diffractive aberration was analyzed using quantum model. Simulation results show that aberration originates mainly from beam spread, and diffractive aberration is larger than spherical aberration and chromatic aberration. Three solutions of optimization of experimental parameters, adding beam mask and using etching technologies for improving atom lithography quality are presented.
The two-level atom focusing in a Gaussian standing wave laser field was analyzed from the perspective of both classical mechanics and wave mechanics. The effects of source imperfection such as velocity spread and beam spread on atom focusing were analyzed by numerically integrating the classical equation of atomic motion. The ideal focal plane can be easily determined by the variation of atomic density at the minimal potential of the standing wave laser field as a function of traveling distance. In the absence of source imperfection, the contribution of diffractive aberration originating from the wave nature of the atom to broadening of feature width is larger than that of spherical aberration. Several methods for improving atom lithography experiments were presented.
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.
The focusing of atoms to nanometer-scale dimensions by a near-resonant standing-wave light field is examined from a particle optics perspective. The classical equation of motion for atoms traveling through the lens formed by a node of the standing wave is derived and converted to a spatial trajectory equation. A paraxial solution is obtained, which results in simple expressions for the focal properties of the lens, useful for estimating its behavior. Aberrations are also discussed, and an exact numerical solution of the trajectory equation is presented. The effects on focal linewidth of angular collimation and velocity spread in the atomic beam are investigated, and it is shown that angular collimation has a much more significant effect than velocity spread, even when the velocity spread is thermal.
We analyze by direct numerical simulations the effects of the wave nature of an atom on lithography with a laser standing wave. Specific calculations are done for chromium atom deposition with the experimental parameters given in the literature. In the absence of source imperfections and atomic motion during and after the deposition most of the feature width comes from diffractive aberration. Spontaneous emission broadens the linewidth further, giving a full width at half maximum about 8.9 nm and a contrast about 26:1. These are what may be achieved ultimately with the said experimental parameters and show that the nonclassical properties of the atom cannot simply be ignored. We then suggest some strategies for improving atom lithography experiments.
We start from the intensity distribution of a standing wave (SW) laser field and deduce the classical equation of atomic motion. The image distortion is analyzed using transfer function approach. Atomic flux density distribution as a function of propagation distance is calculated based on Monte-Carlo scheme and trajectory tracing method. Simulation results have shown that source imperfection, especially beam spread, plays an important role in broadening the feature width, and the focus depth of atom lens for real atomic source is longer than that for perfect source. The ideal focal plane can be easily determined by the variation of atomic density at the minimal potential of the laser field as a function of traveling distance.
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.