Focusing properties of Gaussian beams passing through a bifocal lens

Starting from Collins integral, t he focusing characteristics of Gaussian beams passing through a bifocal lens are studied. Analytical expressions for the axial intensity, waist widths and posit ions in the x and y directions are derived for the unapertured case. It is pointed out by detailed numerical calculations that the point of maximum intensity along the axis is located closer to one waist or at the position of one waist, but it can not exceed the larger focal point of the lens. Moreover, the shift relative to the waist position increases with increasing aperture effect.