Neural Network Predicts Misalignment in Multi-Pass Laser Amplifiers

Published in Applied Physics B, the study presents the first step toward an intelligent thin-disk multi-pass amplifier, a system designed to autonomously monitor and correct optical errors. By creating a digital twin of an experimental laser system, the team generated over 200,000 training datasets to teach a neural network to identify the specific tilts of individual optical elements. The results confirm that artificial intelligence methods are suitable for ensuring the stable operation of complex optical systems, where even minute misalignments can lead to significant power loss or equipment damage.

Thin-disk multi-pass amplifiers are highly efficient architectures for amplifying laser radiation, capable of reaching average powers of up to 10 kilowatts and peak powers of 689 gigawatts. These systems work by repeatedly folding a seed beam over a thin laser-active medium, allowing for flexible repetition rates ranging from continuous wave to gigahertz frequencies. However, this architecture involves long free-space beam paths, often around 200 meters, and requires a large number of optical elements to fold the beam. Consequently, the systems are sensitive to various disturbances, including thermally induced air wedges, thermal lenses, and mechanical stresses that cause mirrors to tilt.

Such misalignments can have severe consequences for the laser beam. Depending on which optical element is misaligned, the beam may undergo complex displacements that result in power loss, degraded beam quality, or even physical damage to the system. While existing approaches use highly stable mechanical structures, retro-reflecting mirror pairs, and beam rotators to improve ruggedness, mechanical and thermal effects during operation cannot be completely excluded. The researchers therefore proposed an intelligent system that uses sensors to detect emerging problems and actuators to correct them, with artificial intelligence handling the interpretation of observations and decision-making.

To develop this artificial intelligence, the team first needed to prove its capability in an idealized simulative environment. They implemented a digital twin of their experimental system using a specifically developed ray-tracing simulation tool called Sodiray. This digital twin allowed them to generate training data by simulating the propagation of the beam through the amplifier under various misalignment conditions. The digital twin included a laser disk, a central mirror, two retro-reflecting mirror pairs, and an array of 40 folding mirrors. The simulation accounted for the specific propagation scheme, where the disk is passed over 20 times and the central mirror 8 times.

The training data generation process involved randomly selecting a number of optical elements to tilt, ranging from one to all 47 elements in the system. For each selected element, the tilt magnitudes around the x and z axes were chosen randomly using a normal distribution centered at zero with a standard deviation of 0.087 milliradians. This approach ensured that the training data represented a diverse range of realistic misalignment scenarios. The ray-tracing tool then calculated the resulting beam shifts on the surfaces of all optics, which served as the observational data for the neural network. In total, 235,000 datasets were created, with 2,000 reserved for evaluation and the remainder split into training, test, and validation sets.

The neural network used was a multilayer shallow network with two hidden layers containing 300 neurons each. The input layer contained 178 neurons, corresponding to the beam position shifts on all optics for both axes, while the output layer had 94 neurons to predict the tilts of the 47 optical elements. The network was trained using scaled conjugate gradient backpropagation in MATLAB. After 10,000 epochs of training, which took approximately 16 hours on a CPU, the performance of the network converged. The network was trained to determine the tilt of all optical elements based solely on the observed beam movements, effectively learning to reverse-engineer the misalignments from the beam’s behavior.

Evaluation of the network’s performance showed high accuracy in predicting the applied tilts. When compared to a best-guess approach that always predicts zero tilt, the neural network demonstrated a significantly lower root mean squared error. For datasets with a small number of misaligned optics, the best-guess approach performed reasonably well because most optics were correctly identified as aligned. However, as the number of misaligned optics increased, the error of the best-guess approach rose drastically, while the neural network maintained a much lower and more stable error rate. This indicates that the network successfully learned the complex relationship between beam shifts and optical tilts.

The homogeneity of the predictions was also evaluated to ensure that the network did not simply guess for some optics while being accurate for others. For 98.8% of the predictions, the deviation between the predicted and actual misalignment was smaller than 0.087 milliradians. The network performed particularly well for the laser disk and the central mirror, with 99% of predictions for the disk having a deviation smaller than 0.023 milliradians. The predictions for the array mirrors were also highly accurate, with 99% of predictions for an exemplary mirror having a deviation smaller than 0.028 milliradians.

One notable exception was the last mirror in the array, A40, for which the network could not predict the tilt accurately. This is because A40 is the final optic in the propagation scheme, and there is no subsequent beam propagation data to inform the network about its alignment. The network effectively defaulted to a best-guess prediction for this mirror, which served as a sanity check during development. The predictions for the retro-reflecting mirror pairs were also less accurate, attributed to the close distance between these optics, which causes minor beam deviations that are difficult to distinguish from other effects.

The study highlights the potential of digital twins and artificial intelligence in managing complex optical systems. By simulating the system’s behavior, researchers can train neural networks without the need for extensive and time-consuming experimental data collection. This approach allows for the direct use of ground truth data, reducing the risk of errors in the training process. The successful simulation-based training provides a foundation for future practical implementations, where the neural network will be integrated with real-world sensors and actuators.

Future work will focus on moving from the idealized simulation to a real-world system. This involves developing observational systems that can accurately detect beam positions on all optics using a minimal number of cameras. The researchers plan to use image processing to extract the necessary data from camera feeds. Additionally, the integration of actuators, such as piezo-based tip-tilt mechanisms, will be pursued to correct the misalignments identified by the neural network. The goal is to create a fully autonomous system that can maintain optimal alignment during operation.

Further theoretical investigations are needed to determine which beam passes are essential for the neural network’s predictions, as accessing data from all reflections may be impractical in a real system. The digital twin will also need to be enhanced to account for manufacturing tolerances and the state of the initial alignment. By addressing these challenges, the researchers aim to develop a robust intelligent amplifier that can operate reliably under real-world conditions, ensuring high performance and safety for high-power laser applications.

Subject of Research: Determination of misalignment in a multi-pass amplifier using a neural network

Article Title: Determination of misalignment in a multi-pass amplifier using a neural network

Article References: Bienert, F., Schmittner, C., Röcker, C., Michalowski, A., Graf, T., & Abdou Ahmed, M. (2026). Determination of misalignment in a multi-pass amplifier using a neural network. Applied Physics B, 132(7), Article 89. https://doi.org/10.1007/s00340-026-08698-x

Image Credits: AI Generated

DOI: 10.1007/s00340-026-08698-x

Keywords: Determination, misalignment, multi-pass, amplifier, neural, network, scientific research