J. Eur. Opt. Society-Rapid Publ. 21, 17( 2025) 179
Figure 6. Flow chart of the iterative wave-optical propagation algorithm( IWPA) coupled with a solver for the direct heat conduction problem( DHCP) and the inverse heat conduction problem( IHCP) to minimize the deviation from a given target temperature field. The algorithm stops after a set number of iterations or when the difference between the resulting temperature field and the target temperature field is below a predefined value( cf. Fig. 1).
Figure
7. Schematic representation of light propagation through a diffractive neural network with three pixelated phase masks as network layers.
neural network and the layers are( fully) connected via the wave-optical propagation of light in the optical system( cf. Fig. 7). Initially developed for optical computing, DNNs allow to solve classical machine vision tasks at the speed of light [ 45, 46 ]. In the field of beam shaping, DNNs have been used for the shaping of tophat distributions with terahertz radiation and for multi-directional beam steering [ 47, 48 ].
We developed a framework to extend the area of application of DNNs to laser beam shaping with DOEs and / or LCoS-SLMs for laser material processing. By implementing the training structure for the DNNs in PyTorch Lightning, we are able to utilize the rapid advances in machine learning technology of the last decades for high fidelity laser beam shaping [ 22, 49 ]. Like the IWPA, DNNs can be used for practically arbitrary optical systems( cf. Sect. 2). DNNs also enable to simultaneously optimize two or more phase masks in an optical system and therefore provide full amplitude and phase control of the complex electric field. This allows for the direct optimization of 3D light fields with e. g. different complex intensity distributions in different target planes and intensity distributions with increased depth of field [ 49, 50 ]. Akin to neural networks for classification tasks, DNNs can also be trained to generate a constant output for similar but varying input values. This allows to create optical systems that are robust to changes of the input beam or misalignments of elements in the optical system [ 49, 51 ]. Finally, DNNs allow to consider and compensate for technology dependent influences like pixel crosstalk in LCoS-SLMs( cf. Fig. 8)[ 22 ].
Further details on the implementation and application of DNNs are outside of the scope of this overview and we refer the reader to [ 22, 49 – 51 ].
6 Conclusion
Laser beam shaping allows to tailor the spatial energy distribution of a laser beam to the specific application. The use of beam shaping elements based on the phase manipulation of an incoming laser beam requires so-called phase retrieval algorithms to determine suitable phase manipulations( phase masks) for a given beam shaping task. Well established phase retrieval algorithms like the iterative Fourier transform algorithm( IFTA), however, impose heavy limitations on the beam shaping system. IFTA-based approaches set the target plane for laser beam shaping to the focal plane behind a focusing lens or a plane