Reverse engineering approach to focus shaping.

We propose and experimentally demonstrate an inverse design for the complete shaping of the optical focal field with the prescribed distribution of intensity, phase, and polarization. The input field that yields the desired focal field is obtained through a fast noniterative calculation procedure, in which the focal field is configured at will and then back-propagates to the input plane. The experiments have verified that all parameters of the focal field can be controlled simultaneously and independently. Furthermore, using this inverse design, we generate in focal region a kind of "perfect polarization vortex" field that has a shape independent of the topological charge of vortex. This target-oriented scheme holds the potential for applications requiring a complex focal field.