Optical properties of mirrors for focusing of non-normal incidence atom beams

Calculations of focal properties and third-order aberration coefficients are presented for atom mirrors based on elastically deformed single-crystal surfaces. Biaxial loading of the mirrors is achieved by a combination of a uniform applied pressure and rectangular boundary conditions. The results are calculated for readily available single-crystal wafers of Si(111) with a thickness of 50 μm and a usable free standing diameter of 18 mm. Focusing of beams at non-normal incidence requires the principal radii of curvature, in planes normal to the mirror plane, to be different. The ratio of these principal radii of curvature is shown to be insensitive to the applied pressure and can be varied by a factor greater than 10 by changing the boundary conditions from square (1:1) to rectangular (1:2).