Simple Method of Light Field Calculation for Shaping of 3D Light Curves

We propose a method for generating three-dimensional light fields with given intensity and phase distributions using purely phase transmission functions. The method is based on a generalization of the well-known approach to the design of diffractive optical elements that focus an incident laser beam into an array of light spots in space. To calculate purely phase transmission functions, we use amplitude encoding, which made it possible to implement the designed elements using a single spatial light modulator. The generation of light beams in the form of rings, spirals, Lissajous figures, and multi-petal "rose" distributions uniformly elongated along the optical axis in the required segment is demonstrated. It is also possible to control the three-dimensional structure of the intensity and phase of the shaped light fields along the propagation axis. The experimentally generated intensity distributions are in good agreement with the numerically obtained results and show high potential for the application of the proposed method in laser manipulation with nano- and microparticles, as well as in laser material processing.