J. Eur. Opt. Society-Rapid Publ. 2025, 21, 17 Ó The Author( s), published by EDP Sciences, 2025 https:// doi. org / 10.1051 / jeos / 2025013 Available online at: https:// jeos. edpsciences. org
EOSAM 2024 Guest editors: Luca De Stefano and Raffaele Velotta
Journal of the European Optical Society-Rapid Publications
RESEARCH ARTICLE
Beyond the IFTA – Phase mask generation for 3D laser beam shaping, tailored temperature distributions and optical amplifiers
Oskar Hofmann 1, a,*
, Paul Buske 1, a, Robin Kurth 1, a, Annika Bonhoff 1, and Carlo Holly 1, 2
1 Chair for Technology of Optical Systems( TOS) – RWTH Aachen University, Steinbachstr. 15, 52074 Aachen, Germany 2 Fraunhofer Institute for Laser Technology( ILT), Steinbachstr. 15, 52074 Aachen, Germany
Received 31 January 2025 / Accepted 25 March 2025
Abstract. The iterative Fourier transform algorithm( IFTA) is the most widely used algorithm for the generation of phase masks for laser beam shaping in the field of laser material processing. But its simplicity and efficiency also come with heavy limitations. We here present an overview of our research into application adapted laser beam shaping beyond the capabilities of traditional phase retrieval algorithms for beam shaping. The presented algorithms enable, among others, the explicit optimization of phase masks for the generation of target light volumes and for tailored temperature distributions within a work piece. Furthermore, we demonstrate the consideration and pre-compensation of non-linear effects in an optical amplifier for laser beam shaping with subsequent amplification.
Keywords: Beam shaping, Phase retrieval, Phase mask, Non-linear amplification, Inverse heat conduction problem.
Nomenclature
IFTA DOE SLM LCoS DNN IWPA DHCP IHCP
1 Introduction
Iterative Fourier Transform Algorithm Diffractive Optical Element Spatial Light Modulator Liquid Crystal on Silicon Diffractive Neural Network Iterative Wave-optical Propagation Algorithm Direct Heat Conduction Problem Inverse Heat Conduction Problem
Laser beam shaping, i. e. the targeted modification of the intensity profile of a laser beam on a target plane or inside a volume, has a wide variety of applications in research and industrial use. For example, in the field of laser material processing, process adapted intensity distributions enable a targeted energy input into the work piece to achieve desired temperature distributions, phase transitions or ablation results [ 1 – 3 ]. A variety of beam shaping technologies are employed to achieve the required energy redistribution within a laser beam from the output of a given laser
a These authors contributed equally to this work. * Corresponding author: oskar. hofmann @ tos. rwth-aachen. de source to the desired intensity distribution: For static laser beam shaping, freeform optics [ 4, 5 ] and diffractive optical elements( DOEs) [ 6, 7 ] in particular have become well established and enable the generation of practically any physically possible intensity distribution. For dynamically switchable beam shaping elements, also known as spatial light modulators( SLMs) [ 8, 9 ], the so-called liquid crystal on silicon( LCoS) technology is currently the de-facto standard for laser applications [ 9, 10 ].
LCoS-SLMs imprint a locally varying phase modulation( phase mask) onto the incoming beam which, if chosen correctly, diffracts the beam into the desired intensity distributioninaplanebehindtheLCoS-SLM. However, the determination of a suitable phase mask for a given beam shaping task is usually an ill-posed problem. The transformation of a given input beam into a target intensity distribution may not be possible at all, i. e. no solution exists. And if a solution exists, there are always infinitely many solutions as the phase in the target plane remains a free parameter [ 11 – 14 ]. To find one solution, if one exists, so-called phase retrieval algorithms are used. The iterative Fourier transform algorithm( IFTA), also called Gerchberg-Saxton algorithm, is probably the most widely used phase retrieval algorithm in the field of spatial laser beam shaping [ 15, 16 ].
The main assumption for the IFTA is that the waveoptical propagation of the beam from the phase mask to the target plane can be described with a single Fourier transform of the complex electric field [ 6, 17 ]. This is based on the Fourier transform relation between a plane in front
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