Solving the logarithmic Monge-Ampere equation with a RK4-Algorithm for Beam Shaping purposes of Femtosecond Laser Beams with Spatial Light Modulators

摘要

We will demonstrate a Runge Kutta based algorithm for solving the Monge-Ampere-Problem. The method is utilizing its parabolic type. We will show the exact numerical solving method down to each step. The derived solution is used in the context of laser beam shaping to reshape any given input distribution to arbitrary output distributions free of any constraints other than diffraction, which includes a true black in said distribution. The presented algorithm will give the required phase which will be used to verify the solution theoretically via diffraction integral and practically via Spatial Light Modulator (SLM).