Creation of identical multiple focal spots with three-dimensional arbitrary shifting

We propose a simple and flexible method to create identical multiple focal spots with three-dimensional arbitrary shifting without moving lenses or laser beams. The incident cylindrical vector (CV) beam superposed with predesigned phase and amplitude modulations is tightly focused by a single lens. The multiple focal spots with predetermined number and positions are generated and the identical intensity distribution as well as the polarization distribution for each individual focal spot is demonstrated. We also present a three-dimensional dynamic shifting with four identical focal spots along Pyramid-like trajectory by continuously regulating the phase and amplitude modulations on the incident CV beam. Furthermore, multiple focal spots with unique intensity profile can also be achieved when proper diffractive optical element (DOE) is associated in the focusing system. These engineered focal fields may find potential applications in 3D laser printing, moving multiple particles trapping and manipulations.