Shifting the spherical focus of a 4Pi focusing system

In a 4Pi focusing system radially polarized laser beams can be focused to a spherical focal spot. For many applications, e.g., for moving trapped particles or for scanning a specimen, one would like to change the position of focal spot along the optical axis without moving lenses or laser beams. We demonstrate how this can be achieved by modulating the phase of the input field at the pupil plane of the lens. The required phase modulation function is determined by spherical wave expansion of the plane wave factors in the Richards-Wolf integral.