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The focusing of atoms interacting with both far-detuned and resonant standingwave fields in the thin lens regime is considered. The thin lens approximationis discussed quantitatively from a quantum perspective. Exact quantumexpressions for the Fourier components of the density (that include allspherical aberration) are used to study the focusing numerically. The followinglens parameters and density profiles are calculated as functions of the pulsedfield area $\theta $: the position of the focal plane, peak atomic density,atomic density pattern at the focus, focal spot size, depth of focus, andbackground density. The lens parameters are compared to asymptotic, analyticalresults derived from a scalar diffraction theory for which spherical aberrationis small but non-negligible ($\theta \gg 1$). Within the diffraction theoryanalytical expressions show that the focused atoms in the far detuned case havean approximately constant background density $0.5(1-0.635\theta ^{- 1/2})$while the peak density behaves as $% 3.83\theta ^{1/2}$, the focal distance ortime as $\theta ^{-1}(1+1.27\theta ^{- 1/2})$, the focal spot size as$0.744\theta ^{-3/4}$, and the depth of focus as $1.91\theta ^{- 3/2}$.Focusing by the resonant standing wave field leads to a new effect, a Rabi-like oscillation of the atom density. For the far-detuned lens, chromaticaberration is studied with the exact Fourier results. Similarly, thedegradation of the focus that results from angular divergence in beams orthermal velocity distributions in traps is studied quantitatively with theexact Fourier method and understood analytically using the asymptotic results.Overall, we show that strong thin lens focusing is possible with modest laserpowers and with currently achievable atomic beam characteristics.Comment: 21 pages, 11 figure

Atom focusing by far-detuned and resonant standing wave fields: Thin-lens regime