Beam control by means of phase elements iterative control algorithms

Laser beam shaping in far-field zone by means of liquid crystal modulator (LCM) and semipassive bimorph deformable mirror (SBDM) both placed in near-field is discussed. Phase delay of LCM and SBDM is calculated by means of Gerchberg-Saxton (GS) algorithm. The analysis of GS algorithm accuracy, convergence and stability is conducted; the influence of laser radiation characteristics, optical scheme parameters and initial phase estimation on algorithm performance is considered. Hybrid combination of Hill-climbing and GS algorithm is proposed for beam-shaping quality improvement. However, GS algorithm is known to fail in the case of multimode beam formation. To broaden the GS algorithm application area, we suggest the modification of the algorithm that makes possible not only single-mode beam shaping but also multimode one. The phase delay of LCM or SBDM is calculated as the sum of each mode phase multiplied by its relative intensity. Several practical examples of singlemode and multimode beam transformations are shown.