Researchers have developed a deep learning-based surrogate model that significantly speeds up the simulation of nonlinear optical processes used in advanced laser systems.
Simulating the complex optical behavior behind ultrafast laser systems requires enormous computational power, posing significant challenges for experiments that rely on rapid feedback.
Researchers at Stanford University and the University of California, Los Angeles (University of California Los Angeles), SLAC National Accelerator Laboratory has developed a deep learning surrogate model that dramatically speeds up these simulations while maintaining high speed. accuracy Compatible with various laser pulse shapes.
Nonlinear optics and X-ray generation
This research focuses on second-order nonlinear optics, also known as the χ² process. In these interactions, light waves exchange energy within specially designed crystals, producing new frequencies and customized pulse shapes.
These processes are important in particle accelerator facilities. SLAC’s Upgraded Linac Coherent Light Source (LCLS-II) converts infrared laser pulses first to green light and then to ultraviolet (UV) light. The UV pulse hits the cathode and releases a flux of electrons. The electron flux is later accelerated and shaped to produce an intense X-ray pulse.
The timing and shape of the UV pulse directly affects the behavior of the electron flux and the quality of the X-rays used in scientific experiments. A new surrogate model for this nonlinear χ² frequency conversion process was reported in the following paper: advanced photonics.
Traditional simulation relies on solving the nonlinear Schrödinger equation using the split-step Fourier method (SSFM). Although this approach has high accuracy, it is computationally expensive because it repeatedly switches between time-domain and frequency-domain calculations during each propagation step. In a complete laser simulation, this stage accounts for approximately 95% of the total execution time.
Deep learning replaces the slowest step
To address this bottleneck, the researchers employed long short-term memory (LSTM) neural networks, a type of recurrent neural network previously used to model pulse propagation in optical fibers. The new system was specifically designed for more complex χ² environments containing multiple interacting light fields.
The research team tested the model using noncollinear sum frequency generation (SFG). SFG is a process in which three coupled optical fields evolve simultaneously over many different pulse conditions. This setup provided a tough benchmark to evaluate performance.
One of the key design choices was to keep the computations within a fully compressed frequency domain representation. By avoiding repeated transformations between domains, this model significantly reduced computational costs.
Highly accurate millisecond simulation
This surrogate model successfully reproduced both temporal and spectral pulse profiles under a wide range of conditions, including in the presence of strong phase modulation and pronounced spectral holes.
Using batched GPU inference reduced the average simulation time to just a few milliseconds per instance, making the system orders of magnitude faster than traditional techniques. The researchers also found that if the model accurately predicted the main SFG output, the secondary light field also closely matched traditional simulations.
A broader goal is to directly integrate these alternative models into working laser systems. The modular design allows individual physical processes to be represented by separate trained surrogate blocks, allowing the creation of predictive models that work in parallel with real-time experiments.
In the future, it can be combined quickly machine learning Surrogates with live experimental systems can support tight integration with digital twins, adaptive control techniques, and diagnostic tools across different types of laser-driven research facilities.
Reference: “Deep learning supported modeling of χ”(2) “Nonlinear Optics” by Jack Hirschman, Erfan Abedi, Mingyang Wang, Hao Zhang, Abhimanyu Bortakul, Justin Baker, Andrea L. Bertozzi, Randy Lemons, and Sergio Carbajo, May 6, 2026. advanced photonics.
DOI: 10.1117/1.AP.8.3.036004
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