Shaping of light beams along curves in three dimensions

We present a method for efficient and versatile generation of beams whose intensity and phase are prescribed along arbitrary 3D curves. It comprises a non-iterative beam shaping technique that does not require solving inversion problems of light propagation. The generated beams have diffraction-limited focusing with high intensity and controlled phase gradients useful for applications such as laser micro-machining and optical trapping. Its performance and feasibility are experimentally demonstrated on several examples including multiple trapping of micron-sized particles.