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J. Eur. Opt. Society-Rapid Publ. 21, 17( 2025)
Figure
4. Simulation results for beam shaping with subsequent amplification using phase masks calculated via the iterative Fourier transform algorithm( IFTA) and the iterative wave-optical propagation algorithm( IWPA). RMSD denotes the normalized root mean square deviation from the target intensity distribution.
Figure
5. Corresponding phase masks for the intensity distributions shown in Figure 4.( a) Phase mask calculated via IFTA without consideration of the non-linear amplification;( b) Phase mask calculated via IWPA with consideration and compensation for the nonlinear amplification.
temperature distribution. As the temperature distribution non-linearly depends on the intensity distribution, a larger deviation from the target intensity distribution can result in a smaller deviation from the target temperature distribution.
To directly optimize for a minimal deviation regarding the target temperature distribution we coupled the IWPA with our IHCP solver( cf. Fig. 6). In each iteration step, the DHCP is solved to calculate the resulting temperature field based on the current intensity distribution in the target plane. Based on the difference to the target temperature field a new adapted temperature field is calculated. The IHCP solver then calculates a new target intensity distribution for the adapted temperature field which is fed back to the normal IWPA iteration. The calculation of the adapted temperature field is required as the algorithm would otherwise always use the“ normal” IHCP result for the target temperature field leading to the aforementioned minimal deviation from the resulting intensity distribution. The adapted temperature field, when chosen correctly, allows to push the algorithm out of minima regarding deviations from the target intensity and towards or into minima regarding the deviation from the target temperature. One approach to calculate the adapted temperature field is to overcompensate the remaining differences between the current and the target temperature field. This approach is already being used successfully to adjust target intensity distributions to improve the convergence for the IFTA and IWPA [ 6, 21 ].
We are currently in the process of verifying the results of this algorithm and plan to publish the results together with a more detailed description of the algorithm in an upcoming publication.
5 Diffractive neural networks
Diffractive neural networks( DNNs) are a physical equivalent to artificial neural networks in the field of machine learning. Each optical element represents a layer in the