Optimization-free optical focal field engineering through reversing the radiation pattern from a uniform line source.

A simple and flexible method is presented for the generation of optical focal field with prescribed characteristics. By reversing the field pattern radiated from a uniform line source, for which the electric current is constant along its extent, situated at the focus of a 4Pi focusing system formed by two confocal high-NA objective lenses, the required illumination distribution at the pupil plane for creating optical focal field with desired properties can be obtained. Numerical example shows that an arbitrary length optical needle with extremely high longitudinal polarization purity and consistent transverse size of ~0.36λ over the entire depth of focus (DOF) can be created with this method. Coaxially double-focus with spot size of ~0.36λ in the transversal direction and ~λ in the axial direction separated by a prescribed spacing is illustrated as another example. The length of optical needle field and the interval between double-focus are determined by the length of uniform line source. These engineered focal fields may found potential applications in particle acceleration, optical microscopy, optical trapping and manipulations.