Double freeform surfaces design for laser beam shaping with Monge–Ampère equation method

This paper presents a method for designing double freeform surfaces to simultaneously control the intensity distribution and phase profile of the laser beam. Based on Snell’s law, the conservation law of energy and the constraint imposed on the optical path length between the input and output wavefronts, the double surfaces design is converted into an elliptic Monge–Ampère (MA) equation with a nonlinear boundary problem. A generalized approach is introduced to find the numerical solution of the design model. Two different layouts of the beam shaping system are introduced and detailed comparisons are also made between the two layouts. Design examples are given and the results indicate that good matching is achieved by the MA method with more than 98% of the energy efficiency. The MA method proposed in this paper provides a reasonably good means for laser beam shaping.