Source-linked AI summary
Learning to decompose the modes in few-mode fibers with deep convolutional neural network
Yi An, Liangjin Huang, Jun Li, Jinyong Leng, Lijia Yang, Pu Zhou
TL;DR
Mode decomposition needs to recover both modal amplitudes and phases, while existing optimization methods can be slow and sensitive to initialization. This paper trains a CNN to infer complete mode coefficients from near-field intensity images; it reports accurate simulated and real-beam reconstructions, with GPU processing at 30 ms per frame.
Problem
Existing numerical MD methods can be slow or sensitive to initialization, and a prior CNN approach omitted modal phase information needed to reconstruct beams for verification.
Source: §1 · p. 2Method
A CNN is trained on simulated beam patterns to map near-field intensity images to mode weights and relative phases, using cosine-coded phase labels to address ambiguity.
Source: §1 · p. 2, §2.2 · p. 3Results
0.5% and 1% are the average modal-weight errors for 3-mode and 5-mode cases, respectively, while real-beam testing reached a mean correlation of 99.12%.
Source: §3.1 · p. 6, §3.2 · p. 9Takeaways & Limitations
The authors report complete mode decomposition with potential real-time performance, at 30 ms per frame on GPU.
Source: §4 · p. 10With only one intensity image, the sign of phase is ambiguous because the real and conjugated fields cannot be distinguished.
Source: §2.1 · p. 3
Abstract
from arXiv · showhide
We introduce deep learning technique to perform complete mode decomposition for few-mode optical fiber for the first time. Our goal is to learn a fast and accurate mapping from near-field beam profiles to the complete mode coefficients, including both modal amplitudes and phases. We train the convolutional neural network with simulated beam patterns, and evaluate the network on both of the simulated beam data and the real beam data. In simulated beam data testing, the correlation between the reconstructed and the ideal beam profiles can achieve 0.9993 and 0.995 for 3-mode case and 5-mode case respectively. While in the real 3-mode beam data testing, the average correlation is 0.9912 and the mode decomposition can be potentially performed at 33 Hz frequency on Graphic Processing Unit, indicating real-time processing ability. The quantitative evaluations demonstrate the superiority of our deep learning based approach.
1. Introduction
Mode decomposition estimates the amplitudes and phases of a fiber’s spatial modes, but existing approaches can require intensive measurements or slow, initialization-sensitive optimization. This paper uses a deep neural network to infer complete mode coefficients from beam images and evaluates it on simulated and real data.
1. Introduction
- Earlier imaging and measurement-based methods can be accurate but require substantial post-processing or intensive experimental measurements.Source: §1 · p. 1
- Existing numerical optimization methods can be sensitive to initial values, become trapped in local optima, and process only slowly varying beams at about 9 Hz with SPGD.Gerchberg-Saxton also requires heavy iterative calculation.Source: §1 · p. 2
- A prior CNN approach estimated modal power but omitted phase, preventing beam reconstruction for verification; a trained network can perform MD in one forward pass without initialization.The paper motivates real-time MD for monitoring mode evolution and optimizing mode-resolved devices.Source: §1 · p. 2
- The end-to-end network maps near-field intensity images to complete mode coefficients, including modal weights and relative phases, and is evaluated on simulated and real beams.The authors describe this as a deep-learning approach for few-mode fibers.Source: §1 · p. 2
2. Methods
The method represents the propagating field through fiber eigenmodes and estimates their weights and relative phases from a near-field pattern. Its CNN predicts those quantities from intensity images, using cosine-coded phase labels to address ambiguity in the training data.
2.1. Modal decomposition basics
- Mode decomposition predicts each eigenmode’s modal weight and relative phase from the near-field pattern of the fiber’s propagating field.The eigenmodes are described as linearly polarized modes under the weak-guidance approximation.Source: §2.1 · p. 2
- With one intensity image, the real and conjugated fields cannot be distinguished, creating a sign ambiguity in phase that does not invalidate MD evaluation.Accurate mode weights alone can suffice for monitoring mode-instability dynamics and modal-gain analysis.Source: §2.1 · p. 3
2.2. Deep-learning networks
- The network fine-tunes pretrained VGG-16 for regression, using max pooling in the first five blocks and adapting its input and output layers to the grayscale image and mode-label size.The authors report better performance with max pooling than with average pooling.Source: §2.2 · p. 3
- Training images are generated from theoretical eigenmode superpositions, with mode weights and relative phases forming a 2N-1-dimensional label vector.Cosine phase labels are scaled from [-1,1] to [0,1] to handle phase ambiguity, and the network uses mean-square error loss.Source: §2.2 · pp. 3–4
- The correlation metric compares reconstructed and measured beam intensities; a value of 1 indicates identical patterns, with nearly identical maxima possible for real and conjugated fields.The cited intensity difference is defined between measured and reconstructed patterns.Source: §2.2 · p. 4
3. Results and discussion
The CNN reconstructs simulated and recorded few-mode beam patterns with high correlation, while accuracy varies with mode count and input noise. On recorded 3-mode data, it achieves a mean correlation of 99.12% and processes frames at approximately 33 Hz.
3.1. Evaluating accuracy with simulated beam patterns
- 0.9993 and 0.995 are the final correlations for simulated 3-mode and 5-mode cases, respectively.The 3-mode correlation exceeded 0.998 after two epochs; the 5-mode correlation converged near 0.995 after 20 epochs.Source: §3.1 · p. 5, Figure 3 · p. 6
- Average modal-weight errors are about 0.5% and 1% for 3-mode and 5-mode cases, while phase errors are about 0.7% and 1.3%.The reported phase-error definition accounts for the possible opposite sign of the predicted phase when only one beam profile is used.Source: Table 2 · p. 6, §3.1 · p. 6, Table 3 · p. 7
- As mode count increases, accuracy decreases; for 10 modes, correlation is about 0.95 and weight and phase errors are about 2.3% and 4.9%.The authors conclude the scheme is robust for six or fewer modes; for eight or more, they note finite resolution and increasing pattern ambiguity, and suggest far-field input or CNN-initialized SPGD. At 224 × 224 resolution, 5-mode errors decrease to 0.93% for weights and 1.26% for phase, but training takes 24 hours.Source: §3.1 · p. 7, Figure 5 · p. 8
- At noise intensity 0.32, reconstructed-pattern correlation remains over 0.99 and modal-weight and phase errors remain below 1.8%.The noise test used 5-mode patterns with pixel values multiplied by 1 + N(0,1)·σ.Source: Figure 6 · p. 8, §3.1 · p. 8
3.2. Processing recorded frames of CCD
- 99.12% mean correlation was achieved on recorded 3-mode data, and processing 16 frames took 480 ms, about 33 Hz.The captured frames were cropped and resized to 128 × 128 before inference.Source: §3.2 · p. 9, Figure 8 · p. 10
4. Conclusion
The paper proposes a deep-learning method for complete mode decomposition in few-mode fibers, with potential real-time performance and high accuracy. On GPU, decomposition takes 30 ms per frame; future work will investigate near- and far-field patterns and multi-mode fibers.
4. Conclusion
- 30 ms per frame on GPU is the reported mode-decomposition speed.The authors describe the method as having potential real-time performance.Source: §4 · p. 10
- The authors report that quantitative evaluations on simulated and real beam patterns demonstrate the method's superiority.They describe this as a first step toward deep-learning-based mode decomposition.Source: §4 · p. 10
- Future work will investigate using near- and far-field beam patterns and extending the strategy to multi-mode fibers.Source: §4 · p. 10