Deep Learning Assisted Modeling for $χ^{(2)}$ Nonlinear Optics

TL;DR

The paper tackles the high computational cost of simulating $χ^{(2)}$ nonlinear optics, especially when resolving fast oscillations with SSFM, by introducing an LSTM-based surrogate trained on high-fidelity SSFM data from a start-to-end laser model for noncollinear SFG. The authors implement a sequence-to-sequence LSTM with 2048 hidden units to predict multi-slice field evolution for the triple-field vector $(A_1,A_2,A_3)$, using a weighted $MSE$ loss that emphasizes the SFG channel $A_2$ and a composite metrics-based evaluation to balance shape and energy fidelity. They demonstrate a >250× speedup on GPU while maintaining high fidelity and discuss practical considerations for real-time optimization, digital-twin integration, and generalization to other $χ^{(2)}$ processes. Overall, the work establishes a data-driven surrogate framework that connects high-fidelity physics simulations with real-time photonics control and design workflows, enabling rapid design iterations and adaptive optimization in complex nonlinear optical systems.

Abstract

Modeling second-order ($χ^{(2)}$) nonlinear optical processes remains computationally expensive due to the need to resolve fast field oscillations and simulate wave propagation using methods like the split-step Fourier method (SSFM). This can become a bottleneck in real-time applications, such as high-repetition-rate laser systems requiring rapid feedback and control. We present an LSTM-based surrogate model trained on SSFM simulations generated from a start-to-end model of the photocathode drive laser at SLAC National Accelerator Laboratory's Linac Coherent Light Source II. The model achieves over 250x speedup while maintaining high fidelity, enabling future real-time optimization and laying the foundation for data-integrated modeling frameworks and digital twins of laser systems.

Figures (5)

• Figure 1: $\chi^{(2)}$ Processes and Neural Network Architecture. a) schematic of SHG, SFG, and DFG $\chi^{(2)}$ processes; b) input-output block diagram of $\chi^{(2)}$ nonlinear medium; c) associated wave vectors for $\chi^{(2)}$ processes; d) single-layer 10-input LSTM architecture with output fully connected layers and internal workings of LSTM block; and e) noncollinear SFG process with input and output fields as well as encapsulated LSTM network for discretized replacement.
• Figure 2: Data Generation and Preparation for LSTM. a) start-to-end model of laser system hirschman2024design used to generate the data and b) the three-stage processing, including downsampling and cutting, restructuring into one vector, and normalization.
• Figure 3: Evaluation Error Distribution. Histograms and statistics for the combined error metric of temporal intensity for a) SFG, b) SHG1, and c) SHG2, respectively, and d) two randomly selected examples from the test data set from within each error quartile of the SFG error distribution (shaded) accompanied by the temporal and spectral predicted and true intensity profiles for the SFG signal and the corresponding SHG1 signal.
• Figure 4: Minimal spectral amplitude shaping example. Example pulled from the top error quartile of SFG error distribution with primarily phase shaping. Shows frequency domain (left column) and time domain (right column) for SFG (top row) and SHG1 (bottom row) for ground truth simulation (black) versus ML inference prediction (light blue), along with the associated residuals.
• Figure 5: Large spectral amplitude shaping example. Example pulled from top error quartile of SFG error distribution with amplitude and phase shaping. Shows frequency domain (left column) and time domain (right column) for SFG (top row) and SHG1 (bottom row) for ground truth simulation (black) versus ML inference prediction (light blue) along with the associated residuals.