Source-linked AI summary
Deep Learning Reconstruction of Ultra-Short Pulses
Tom Zahavy, Alex Dikopoltsev, Oren Cohen, Shie Mannor, Mordechai Segev
TL;DR
Characterizing ultrashort pulses is difficult when no shorter measurement event is available, and existing FROG recovery methods degrade at low SNR. The paper introduces DeepFROG, which combines a differentiable FROG model with a CNN inverse mapping and supervised plus unsupervised learning. Simulations and experiments indicate improved recovery of weak pulses and state-of-the-art performance on measured data.
Problem
Existing pulse-recovery methods deteriorate at low SNR, while ultrashort-pulse characterization matters for studying physical and chemical phenomena.
Method
DeepFROG combines a fixed differentiable FROG Net with a trainable CNN inverse mapping, using supervised simulated data and unsupervised learning on measurements.
Results
Simulations indicate recovery of very weak pulses, and experiments achieve state-of-the-art results on measured pulses while overtaking the existing reconstruction approach.
Takeaways & Limitations
The approach demonstrates applicability to experimental FROG data and potential for reducing reconstruction error at low SNR.
Takeaways & Limitations
FROG reconstruction remains unique only up to trivial ambiguities, which can destabilize DNN training unless removed from the dataset.
Abstract
from arXiv · showhide
Ultra-short laser pulses with femtosecond to attosecond pulse duration are the shortest systematic events humans can create. Characterization (amplitude and phase) of these pulses is a key ingredient in ultrafast science, e.g., exploring chemical reactions and electronic phase transitions. Here, we propose and demonstrate, numerically and experimentally, the first deep neural network technique to reconstruct ultra-short optical pulses. We anticipate that this approach will extend the range of ultrashort laser pulses that can be characterized, e.g., enabling to diagnose very weak attosecond pulses.
Introduction
Ultra-short pulses enable measurements of physical and chemical phenomena, but characterizing them can require an even shorter pulse. Existing recovery methods struggle with weak signals, motivating a deep-neural-network approach that reports improved reconstruction at low SNR and on experimental data.
- Ultra-short pulses are used across material processing, medical imaging, and research on light and matter.
- Replica-based techniques address the need to measure a pulse when no shorter event is available, but one-dimensional phase retrieval is not always injective.
- FROG addresses this ambiguity by formulating a two-dimensional phase-retrieval problem with only trivial ambiguities.
- PCGPA and Ptychographic FROG reconstruct pulses but deteriorate at low SNR, making weak ultrashort pulses difficult to recover.
- The paper proposes supervised CNN reconstruction of FROG measurements, differentiable FROG modeling, and unsupervised learning on experimental data.
- Simulations indicate recovery of very weak pulses, while experiments report state-of-the-art reconstruction that overtakes the existing approach.
Problem formulation
The paper formulates SHG-FROG reconstruction as mapping measured spectrograms of pulse autocorrelations to the complex pulse that produced them. Because FROG solutions have trivial ambiguities that destabilize regression, the data are mapped into a singular ambiguity group.
- SHG-FROG measures the Fourier intensity of products between an unknown pulse and time-shifted replicas across frequency and delay.
- The reconstruction task maps the measured FROG trace I_measured(ω_i,τ_j) to the pulse that created it.
- Figure 1 pairs the experimental measurement setup with example pulse amplitudes, phases, and corresponding FROG traces.
- Ambiguity removal: FROG reconstruction is unique up to trivial ambiguities including constant phase shift, conjugate inversion, and translation.
- Ambiguity removal: Removing these ambiguities by mapping the dataset into a singular group improved neural-network performance in practice.
Methods
DeepFROG combines a fixed differentiable FROG Net with a trainable CNN that learns the inverse mapping from measurements to pulses. The reported architecture comparison favors DenseNet and Multires, with Multires reaching good results faster.
- DeepFROG uses a fixed FROG Net for forward measurement and gradient computation, together with a trainable CNN inverse model.
- The CNN weights are optimized with Adam by minimizing the L1 loss between the measurement and reconstruction.
- CNN(I; w) denotes the CNN output for input I and weights w.
- Three architectures were tested: a typical CNN, Multires with multiple filter sizes, and DenseNet with dense connectivity.
- DenseNet and Multires performed best overall, while Multires reached good results in less time.
Experiments
The study evaluates DeepFROG on simulated noisy pulses and experimental FROG measurements, combining supervised and unsupervised learning to reconstruct ultrashort pulses. DeepFROG achieves lower reconstruction error than classical methods in low-SNR simulations and on the experimental pulse.
- Sim2Sim: 60k training examples and 10k testing examples were generated by forward-propagating simulated pulses through the FROG Net.The pulses combine randomized spectral phase, a Lorentzian envelope, and a Gaussian spectrum before Fourier transformation.
- Sim2Sim: Below 20dB SNR, the noise-trained DeepFROG variant achieves lower reconstruction error than classical methods on unseen simulated pulses.At 10dB noise, DeepFROG also produces lower-error reconstructions than the compared methods.
- Sim2Real: The experimental setup creates SHG FROG measurements by duplicating, delaying, recombining, and repeatedly measuring a deformed laser pulse for different τ values.This laboratory process is the experimental equivalent of the FROG Net measurement represented by Equation 1.
- Sim2Real: Experimental reconstruction combines supervised learning on simulated data with unsupervised learning on the measured FROG trace using FROG Net gradients.The unsupervised stage makes the solution specific to the experiment without requiring the original pulse.
- Sim2Real: Unsupervised training was crucial, noise injection taught the network to filter noise, and the best deep learning method reached the lowest experimental reconstruction error.Using the true power spectrum substantially helped supervised learning but had little effect when unsupervised training was included.
Conclusions
The work presents a deep learning approach for reconstructing ultrashort laser pulses from measured FROG traces. Experiments suggest reduced reconstruction error at low SNR and demonstrate applicability to laboratory measurements.
- The authors present a deep learning approach to reconstruct ultrashort laser pulses from measured FROG traces.