The focusing of atoms after interacting with both far-detuned and resonant standing wave fields in the thin-lens regime is considered. Exact quantum expressions for the Fourier components of the density (that include all spherical aberration) are used to study the focusing numerically. The following lens parameters and density profiles are calculated as functions of the pulsed field area theta: the position of the focal plane, peak atomic density, atomic density pattern at the focus, focal spot size, depth of focus, and background density. The lens parameters are compared to asymptotic, analytical results derived from a scalar diffraction theory for which spherical aberration is small but non-negligible (theta much greater than 1). Within the diffraction theory analytical expressions show that the focused atoms in the far-detuned case have an 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 as theta(-1)(1+1.27 theta(-1/2)) L-T/2 pi, the depth of focus as 0.304L(T)theta(-3/2), and the focal spot size 0.0592 lambda theta(-3/4), where L-T is the Talbot distance and lambda is the wavelength of the light. Focusing by the resonant standing wave held leads to a new effect, a Rabi-Like oscillation of the atom density. For the far-detuned lens, chromatic aberration is studied quantitatively with the exact Fourier results. Similarly, the degradation of the focus that results from angular divergence in beams or thermal velocity distributions in traps is studied quantitatively with the exact Fourier method and understood analytically using the asymptotic results. Overall, we show that strong thin-lens focusing is possible with modest laser powers and with currently achievable atomic beam characteristics. [S1050-2947(99)06412-4].
