Creation of identical multiple focal spots with prescribed axial distribution

We present a scheme for the construction of coaxially equidistant multiple focal spots with identical intensity profiles for each individual focus and a predetermined number and spacing. To achieve this, the radiation field from an antenna is reversed and then gathered by high numerical aperture objective lenses. Radiation patterns from three types of line sources, i.e., the electric current, magnetic current and electromagnetic current distributions, with cosine-squared taper are respectively employed to generate predominately longitudinally polarized bright spots, azimuthally polarized doughnuts, and focal spots with a perfect spherically symmetric intensity distribution. The required illuminations at the pupil plane of a 4Pi focusing configuration for the creation of these identical multiple focal spots can be easily derived by solving the inverse problem of the antenna radiation field. These unique focal field distributions may find potential applications in laser direct writing and optical microscopy, as well as multiple-particle trapping, alignment, and acceleration along the optical axis.