Vector polymorphic beam.

A scalar polymorphic beam is designed with independent control of its intensity and phase along a strongly focused laser curve of arbitrary shape. This kind of beam has been found crucial in the creation of freestyle laser traps able to confine and drive the motion of micro/nano-particles along reconfigurable 3D trajectories in real time. Here, we present and experimentally prove the concept of vector polymorphic beam adding the benefit of independent design of the light polarization along arbitrary curves. In particular, we consider polarization shaped tangential and orthogonal to the curve that are of high interest in optical manipulation and laser micromachining. The vector polymorphic beam is described by a surprisingly simple closed-form expression and can be easily generated by using a computer generated hologram.