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Inverse design and optimization of an aperiodic multi-notch fiber Bragg grating using neural networks

Qingshan Yu, Barnaby R. M. Norris, Göran Edvell, Liguo Luo, Joss Bland-Hawthorn, and Sergio G. Leon-Saval

Open Access Open Access

Abstract

Recent developments in the application of aperiodic fiber Bragg gratings (AFBGs) in astrophotonics, such as AFBG for astronomical near-infrared OH suppression and gas detection based on cross-correlation spectroscopy, have illuminated the problem that the optimization for AFBG with certain fabrication constraints has not been fully investigated and solved. Previous solutions will either sacrifice part of the spectral features or consume a significant amount of computation resources and time. Inspired by recently successful applications of artificial neural networks (ANNs) in photonics inverse design, we develop an AFBG optimization approach employing ANNs in conjunction with genetic algorithms (GAs) for the first time, to the best of our knowledge. The approach maintains the spectral notch depths and preserves the fourth-order super-Gaussian spectral features with improvements of interline loss by ${\sim}100$ times. We also implement, to our knowledge, the first inverse scattering neural network based on a tandem architecture for AFBG, using a first-order Gaussian notch profile. The neural network successfully converges but has a poor predictive capability for the phase part of the design. We discuss possible ways to overcome these limitations.

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Data availability

The data that support the findings of this study are available from the corresponding author, Q.Y., upon reasonable request.

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Figures (10)
Fig. 1.
Fig. 1. Top: first-order Gaussian versus fourth-order super-Gaussian profiles. Bottom: $q(z)$ for both cases (blue solid line for the magnitude and red dashed line for the phase).

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Fig. 2.
Fig. 2. Neural network structure for the first-order Gaussian case.

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Fig. 3.
Fig. 3. Neural network training state for first-order Gaussian case is shown in the top-left plot, with the best performance marked with a yellow circle. The title indicates the best MSE achieved. A comparison of prediction reconstructed versus ground truth spectrum is shown in the top-right plot. In the lower row, six peaks with approximately even distribution across wavelengths are presented in a zoomed view for detailed comparisons. The differences may be considered negligible compared to the original spectral features.

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Fig. 4.
Fig. 4. Neural network structure for the fourth-order super-Gaussian case.

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Fig. 5.
Fig. 5. Neural network training state for fourth-order super-Gaussian case is shown in the top-left plot, with the best performance marked with a yellow circle. The title indicates the best MSE achieved. A comparison of prediction reconstructed versus ground truth spectrum is shown in the top-right plot. In the lower row, six peaks with approximately even distribution across wavelengths are presented in a zoomed view for detailed comparisons. The differences in wavelength are ${\sim}{10^{- 2}}\,{\rm nm}$ and are still within the error budget for OH suppression application. The differences in FWHM and in reflection may be considered negligible.

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Fig. 6.
Fig. 6. GA results for first-order Gaussian profile are presented in the left plot. The $q(z)$ before and after the optimization is presented in the right-top and right-bottom plots, respectively (magnitude: blue solid line; phase: red solid line).

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Fig. 7.
Fig. 7. GA results for fourth-order Gaussian profile are presented in the left plot. The $q(z)$ before and after the optimization is presented in the right-top and right-bottom plots, respectively (magnitude: blue solid line; phase: red solid line).

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Fig. 8.
Fig. 8. Top panel illustrates a comparison of the AFBG spectrum characterized by a first-order Gaussian profile, before and after optimization. Zoomed views for two selected notches are shown in the bottom row, representing cases with the least differences (left) and largest differences (right) in terms of spectral features.

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Fig. 9.
Fig. 9. Top panel illustrates a comparison of the AFBG spectrum characterized by a fourth-order Gaussian profile, before and after optimization. Zoomed views for two selected notches are shown in the bottom row, representing cases with the least differences (left) and largest differences (right) in terms of spectral features.

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Fig. 10.
Fig. 10. Results from inverse scattering neural network compared to the ground truth accordingly.

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Equations (2)

Equations on this page are rendered with MathJax. Learn more.

q ( z ) = G − 1 { r ( z ; δ ) } ≈ ∑ l = 1 N G − 1 { r l ( z ; δ l ) } ,
f i t n e s s = A × r m s e + q max × L ,
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