Machine Learning-Driven Design of Mixed-Pitch Grating Couplers for Co-Packaged Optics Applications

Chuan Seng Tan; Wai Cheung Ma; Yeow Kheng Lim; Yu Dian Lim; Yun Da Chua

REVIEW 3 major objections 6 minor 13 references

A deep neural network trained on simulated spectra can translate a user's desired peak wavelength and bandwidth into a four-region mixed-pitch grating coupler design, with 84% of test designs matching the target peak wavelength within 2 nm.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-01 23:01 UTC pith:MDSEJDLG

load-bearing objection Useful FDTD-level inverse-design tool, but the accuracy claim only holds inside a 2D simulation world; three measured devices cannot carry the generalization to fabricated hardware. the 3 major comments →

arxiv 2607.15534 v1 pith:MDSEJDLG submitted 2026-07-17 physics.optics cs.SYeess.SY

Machine Learning-Driven Design of Mixed-Pitch Grating Couplers for Co-Packaged Optics Applications

Yu Dian Lim , Yun Da Chua , Wai Cheung Ma , Yeow Kheng Lim , Chuan Seng Tan This is my paper

classification physics.optics cs.SYeess.SY

keywords mixed-pitch grating couplerdeep neural networkinverse designFDTD simulationsilicon photonicsco-packaged opticsspectral matchingGDS layout

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper tries to establish that grating-coupler design can be inverted: ask for a spectrum, get a geometry. The authors model a four-region mixed-pitch grating by eight geometric parameters, generate 10,000 simulated power spectra with 2D FDTD, and train a deep neural network to map a 300-point spectrum back to those parameters. After training, a user's specified peak wavelength and full-width half-maximum are turned into a Gaussian target spectrum, the DNN suggests the grating geometry, and FDTD verifies the result before a GDS layout is emitted. A sympathetic reader would care because this replaces iterative expert design of a sensitive photonic component with a one-shot software pipeline, which matters for co-packaged optics where many channels need custom wavelength responses.

Core claim

The central claim is that the trained network can reliably suggest a suitable set of grating parameters (p1, dc1, p2, dc2, p3, dc3, p4, dc4) to match a desired peak wavelength and full-width half-maximum. In roughly 1,000 test combinations spanning peak wavelengths 1.535–1.615 µm and FWHM 0.08–0.145 µm, FDTD-verified peak wavelengths were within 2 nm of the target in 844 cases and FWHM within 10 nm in 738 cases; 822 spectra matched the target to <15% mean absolute error and 351 to <5%. The paper also reports that fabricated samples track the simulated peak wavelength to <5 nm, while measured FWHM deviates more, a gap it attributes mainly to training on 2D FDTD while the fabricated devices ar

What carries the argument

The central object is the mixed-pitch grating coupler: four adjacent grating regions, each with its own pitch and duty cycle (eight parameters total), designed so different regions couple different wavelength bands. The mechanism carrying the argument is an inverse-design deep neural network with five hidden layers of 256, 128, 64, 32, and 16 nodes; it takes a normalized 300-point power spectrum as input and outputs the eight grating parameters. The network is trained on ~10,000 parameter–spectrum pairs generated in 2D FDTD, and the same kind of FDTD simulation is used to verify suggestions. A GUI wraps the workflow so a user enters only peak wavelength and FWHM and receives a verified grati

Load-bearing premise

Everything hinges on the 2D FDTD simulation being an adequate stand-in for the real 3D fabricated device; the paper itself says training used 2D FDTD while fabricated and measured couplers are 3D.

What would settle it

Fabricate a batch of, say, twenty AI-designed couplers spanning the tested peak-wavelength range and measure their fiber-to-grating spectra; if most measured peaks drift more than 2 nm from target, or FWHM errors cluster well above the 10 nm threshold at the same rate as in simulation, then the DNN's accuracy is an artifact of the 2D simulation and does not transfer to real devices.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

Designs for any target peak/FWHM within the tested range can be produced from a single software run that outputs grating parameters, an FDTD check, and a GDS layout.
Mixed-pitch gratings enable multiple CPO channels with different wavelengths to couple from one shared optical input, and this pipeline tailors each channel's grating automatically.
Because the model inverts spectrum to geometry, it removes the need for designers to hand-tune pitch and duty cycle through trial-and-error FDTD iterations.
The authors' suggested next step—retraining on data that better represent measured devices—would extend the demonstrated accuracy from simulation to fabrication.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

A consequence the paper does not spell out: the tool's success metric is a Gaussian target spectrum, so the deployed pipeline generates Gaussian-like responses only; flat-top, asymmetric, or multi-peak spectral targets would need a different input representation.
The paper's own 2D-versus-3D caveat implies the reported 84%/74% success rates are simulation-bound upper bounds; without 3D-aware training data, a production chip designer should expect larger FWHM errors than the headline numbers suggest.
If the inverse-design approach generalizes, the same spectrum-to-geometry inversion could be repurposed as a general photonic compiler, taking an optical specification and emitting a mask layout for any component family with a fast forward simulator.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

Useful FDTD-level inverse-design tool, but the accuracy claim only holds inside a 2D simulation world; three measured devices cannot carry the generalization to fabricated hardware.

read the letter

Quick take: this is a serviceable engineering paper, not a scientific breakthrough. The DNN+GUI workflow for mixed-pitch grating couplers is genuinely useful for rapid FDTD-level prototyping, but the central accuracy claim is only established inside a simulation world, and the three experimental devices are too few to support the leap to fabricated hardware.

What's new: a complete inverse-design loop from user-specified peak wavelength/FWHM to GDS layout. They train a 5-hidden-layer DNN on 10,000 FDTD spectra, test on ~1,000 target combinations, and report 844/1000 peaks within 2 nm and 738/1000 FWHMs within 10 nm. Those numbers are plausible and the GUI (streamlit, deployed at inphai.com) makes the tool accessible. Credit is due for stating the 2D/3D limitation explicitly in the text instead of burying it.

The soft spot is load-bearing. All training, testing, and "verification" uses the same 2D FDTD simulator, so the success rates are self-consistency checks, not external validation. The paper itself acknowledges that the fabricated devices are measured in 3D, that the four regions actually have different sizes due to the taper, and that FWHM deviation is prominent in Figure 5. Three measured devices cannot carry the generalization. On top of that, there's no code, no data, no training hyperparameters, and no statement that the test combinations were excluded from training. These are fixable, but they block acceptance as written.

The paper is honest about what it does, and the method is straightforward enough that I don't see a hidden flaw in the simulation results. It's just overclaimed. If the authors narrow the claim to "suggests parameters that match a 2D FDTD model" or add enough measured devices to show the 2D model is a faithful proxy, the contribution stands.

Send it to peer review, because a tool like this has real value and the limitations are openly disclosed, but expect a round of revision focused on validation and reproducibility.

Referee Report

3 major / 6 minor

Summary. The manuscript presents an inverse-design workflow for a four-region mixed-pitch grating coupler. A deep neural network with five hidden layers (256, 128, 64, 32, 16 nodes) is trained on roughly 10,000 pairs of grating parameters (p1, dc1, ..., p4, dc4) and 2D-FDTD power spectra. In use, a user specifies a target peak wavelength and FWHM; a 300-point Gaussian spectrum is generated and fed to the DNN, whose output grating parameters are then verified by FDTD before GDS layout generation. On about 1,000 test combinations the paper reports 822/1000 attempts with full-spectrum MAE < 15%, 351/1000 with MAE < 5%, 844/1000 with peak-wavelength AE < 2 nm, and 738/1000 with FWHM AE < 10 nm. Three experimental spectra are compared with simulated and Gaussian spectra; peak wavelengths agree to about 5 nm, but the authors state that FWHM deviations are prominent between FDTD-simulated and experimentally measured spectra.

Significance. If the validation concerns are resolved, the work would be a practical demonstration of machine-learning inverse design for a component relevant to co-packaged optics. The strengths are concrete: an 8-parameter mixed-pitch design space, integration of the trained model into a publicly accessible GUI with automatic GDS output, and a candid discussion of the 2D-versus-3D simulation discrepancy. However, the central quantitative claims are established only within the same 2D-FDTD simulation world used to generate the training data. The three experimental spectra, which already show large FWHM deviations, are too few to transfer the reported accuracy to fabricated devices. The paper therefore needs either additional 3D-FDTD or experimental validation, or a clearly scoped claim restricted to 2D-FDTD design suggestions.

major comments (3)

[Methodology (Fig. 2); Results and Discussion (Fig. 3)] The manuscript never states that the ~1,000 test combinations are disjoint from the 10,000 training examples. Because the FDTD verification uses the same simulator that generated the training spectra, any overlap would inflate the reported success rates (844/1000 peak AE <2 nm; 738/1000 FWHM AE <10 nm) and would make the results a memory check rather than a generalization test. Please specify the sampling procedure for the training set and confirm explicitly that no test grating-parameter/spectrum pair was included in training. Also clarify whether each 'tested' case involved a new FDTD run after training.
[Results and Discussion, Fig. 5] The tool is advertised as designing couplers from both peak wavelength and FWHM, yet the only experimental evidence consists of three measured spectra. The authors themselves state that 'the deviation of FWHM is especially prominent when comparing between FDTD-simulated and experimentally measured spectrum' and attribute this to the 2D-FDTD model versus 3D fabricated devices with unequal region sizes. Since FWHM is one of two user-specified targets, this experimental limitation is load-bearing. The abstract and conclusion should not claim that the software designs mixed-pitch grating couplers from user-specified FWHM values without either additional 3D-FDTD or wafer-level validation, or an explicit scope restriction to 2D-FDTD behavior.
[Methodology (training setup)] No training hyperparameters are reported: loss function, optimizer, learning rate, batch size, number of epochs, validation split, normalization, and random seed are all absent. Without these details, the reported success rates cannot be reproduced, and it is impossible to assess whether the quoted accuracies reflect robust training or a particular initialization. Please provide the full training configuration and, ideally, make the code and trained weights publicly available alongside the GUI.

minor comments (6)

[Results and Discussion, first paragraph] The sentence 'model performs better at higher peak wavelengths between 1.57 to 1.6 µm. and FWHM between 0.95 to 0.115 µm' appears to contain a typo: the FWHM range should likely be 0.095 to 0.115 µm.
[Fig. 3] The labels 'Region with <5% error' and 'Region with <15% error' are mentioned in the text but are not clearly visible in the current figure; please enlarge or annotate the relevant regions.
[Fig. 5] The three measured spectra lack scale bars and error bars. Please state the number of measured devices and the exact normalization procedure used for the experimental spectra.
[Discussion] The phrase 'First, the 10,000 grating parameters-spectrum pair used for model training (ref. Figure 2)' is missing a verb; please rephrase.
[Abstract and Results] The exact number of test cases should be stated rather than '~1,000' throughout; this would allow readers to compute binomial confidence intervals for the reported success rates.
[References] The reference list is heavily application-specific. A citation to a standard methodology for evaluating ML models (e.g., data splitting, cross-validation) would help ground the evaluation protocol.

Circularity Check

0 steps flagged

No significant circularity: the DNN is an inverse surrogate trained and tested on the same FDTD simulator, which is a normal self-consistency benchmark; the acknowledged 2D/3D mismatch is an external-validity limitation, not a circular step.

full rationale

The paper's central claim is that a trained DNN can map a user-specified Gaussian spectrum (derived from a desired peak wavelength and FWHM) to eight grating parameters, and that the resulting FDTD-simulated spectrum matches the requested spectrum. This is not circular by construction: the DNN is trained on 10,000 parameter–spectrum pairs generated by FDTD, and its performance is evaluated on ~1,000 held-out target spectra using the same FDTD simulator. That evaluation measures the DNN's ability to invert the FDTD forward model on new inputs; success is not guaranteed and is reported as empirical hit rates (844/1000 with peak AE < 2 nm, etc.). There is no equation in which the prediction target is defined in terms of the fitted parameters, nor is any fitted parameter renamed as a prediction. The only serious concern is external validity: the paper explicitly states that training and verification use a 2D FDTD model while fabricated devices are 3D, and that experimental FWHM deviations are prominent. That is a limitation of the surrogate model's fidelity to real devices, not a circular derivation. Self-citations (refs. [6]–[8]) are used only for measurement details and prior mixed-pitch grating work; they are not load-bearing for the DNN's accuracy claim, and no uniqueness theorem or ansatz is imported from the authors' prior work. Therefore no circular step exists, and the appropriate score is 0.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

The central result rests on a trained empirical surrogate plus a simulator. No new physical entity is proposed; the key unpaid inputs are the FDTD simulator's fidelity, the Gaussian target representation, and hand-chosen model/data settings.

free parameters (4)

DNN architecture hyperparameters = 5 hidden layers: 256, 128, 64, 32, 16 nodes
Chosen without reported search or ablation; the exact capacity affects the reported accuracies.
Spectrum discretization = 300 values
The Gaussian target and FDTD spectra are represented as 300 points; resolution affects MAE and AE measurements.
Training set size = ~10,000
Selected to balance simulation time and accuracy; no scaling or saturation analysis is reported.
FDTD modeling choices = 2D; 80 nm partial etch; 220 nm SOI; 2 µm SiO2 cladding; material indices/mesh unspecified
These choices determine the spectral response used as training labels; the paper does not report mesh size, simulation time, or boundary conditions.

axioms (6)

domain assumption FDTD simulation is a sufficiently accurate model of the fiber-to-grating coupling spectrum for training and evaluation.
Used throughout: all 10,000 training labels and verification curves come from FDTD; no independent ground truth for most test cases.
domain assumption 2D FDTD adequately represents the 3D fabricated grating structure.
Acknowledged as only approximate in Results: 'the FDTD simulation was done using a two-dimensional (2D) model. However, the grating couplers were fabricated and measured in three-dimensional (3D) manner.' This is the weakest load-bearing premise.
domain assumption The desired power spectrum can be described as a Gaussian parameterized only by peak wavelength and FWHM.
User-defined targets in the methodology are generated as Gaussian spectra with 300 values; real grating coupler spectra are not necessarily Gaussian.
domain assumption The mapping from 300-point spectrum to 8 grating parameters is well-posed and learnable from ~10,000 samples.
No uniqueness or generalization analysis is provided; degenerate spectra could map to multiple parameter sets.
standard math Grating equation Λ = λ0/(neff - nclad sin θ) relates pitch to wavelength.
Standard design equation from [5], used in Introduction to motivate pitch selection.
standard math Standard DNN training procedure (backpropagation, supervised regression) works as implemented.
No formal guarantees; standard empirical ML assumption.

pith-pipeline@v1.3.0-alltime-deepseek · 4886 in / 13194 out tokens · 131356 ms · 2026-08-01T23:01:19.109583+00:00 · methodology

0 comments

read the original abstract

A mixed-pitch grating coupler which can couple a wide range of wavelengths is preferred in its application in co-packaged optics (CPO). However, the design and optimization of such grating coupler is complex. In this work, we developed software with integrated deep neural network (DNN) model to automatically design the mixed-pitch grating coupler from user-specified peak wavelengths and full-width half-maximum (FWHM) values. We first trained the DNN model with 10,000 rows of grating parameters-power spectrum datasets, where the power spectrum was simulated using finite-difference time domain (FDTD) technique. Upon training, we tested the model using ~1,000 different combinations of peak wavelengths and FWHM values. Among the combinations, 822 attempts have <15% error, while 351 attempts have <5% error when comparing the user-specified and FDTD-verified spectrum. Meanwhile, comparing the user-specified and FDTD-verified peak wavelengths, 844 attempts have peak wavelengths with absolute error (AE) < 2 nm. For FWHMs, 738 attempts have FWHM values with AE < 10 nm. We have also developed a graphical-user interface (GUI) to ease the usage of this software.

discussion (0)

Reference graph

Works this paper leans on

13 extracted references · 4 canonical work pages

[1]

Co-packaged optics (CPO): status, challenges, and solutions,

M. Tan et al., “Co-packaged optics (CPO): status, challenges, and solutions,” Dec. 01, 2023, Higher Education Press Limited Company. doi: 10.1007/s12200-022-00055-y

work page doi:10.1007/s12200-022-00055-y 2023
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M. Mehta, “Broadcom’s journey to CPO at scale: performance KPIs & fiber reliability,” Broadcom. Accessed: Nov. 21, 2024. [Online]. Available: https://www.broadcom.com/blog/broadcom-s-journey-to- cpo-at-scale-performance-kpis-fiber-reliability

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A. Hayakawa, H. Ebe, Y. Chen, and T. Mori, “Silicon Photonics optical transceiver for high-speed, high-density and low-power LSI interconnect,” Fujitsu Scientific and Technical Journal, vol. 52, no. 1, pp. 19–26, 2016

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G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction. West Sussex: John Wiley & Sons, Ltd, 2004. doi: 10.1002/0470014180

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Y. D. Lim, P. Zhao, L. Guidoni, J. Likforman, and C. S. Tan, “Next-Value Prediction of Beam Waists From Mixed Pitch Grating Using Simplified Transformer Model,” IEEE Photonics J., vol. 16, no. 5, pp. 1–9, 2024, doi: 10.1109/JPHOT.2024.3442169

arXiv 2024
[7]

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Y. D. Lim, P. Zhao, L. Guidoni, J. P. Likforman, and C. S. Tan, “Development of Mixed Pitch Grating for the Optical Addressing of Trapped Sr+ Ions with Data Analysis Techniques,” Opt. Express, vol. 31, no. 15, pp. 23801– 23812, 2023, doi: 10.1109/JPHOT.2023.3281134

arXiv 2023
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Y. D. Lim, H. Y. Li, P. Zhao, J. Tao, L. Guidoni, and C. S. Tan, “Design and Fabrication of Grating Couplers for the Optical Addressing of Trapped Ions,” IEEE Photonics J., vol. 13, no. 4, pp. 1–6, 2021, doi: 10.1109/jphot.2021.3094646

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doi:10.1038/s41598-017-16505-z 2017
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T. Sharma et al., “Coupling performance enhancement using SOI grating coupler design,” Opt. Commun., vol. 427, no. July, pp. 452–456, 2018, doi: 10.1016/j.optcom.2018.06.012

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I. Demirtzioglou et al., “Apodized silicon photonic grating couplers for mode-order conversion,” Photonics Res., vol. 7, no. 9, p. 1036, 2019, doi: 10.1364/prj.7.001036

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Y. D. Lim, “AI-Native Design: Mixed Pitch Grating Coupler | InPhAI Demo,” YouTube. Accessed: Jun. 11,
[2026]

Available: https://www.youtube.com/watch?v=L4-jOLQg2Tk

[Online]. Available: https://www.youtube.com/watch?v=L4-jOLQg2Tk

[1] [1]

Co-packaged optics (CPO): status, challenges, and solutions,

M. Tan et al., “Co-packaged optics (CPO): status, challenges, and solutions,” Dec. 01, 2023, Higher Education Press Limited Company. doi: 10.1007/s12200-022-00055-y

work page doi:10.1007/s12200-022-00055-y 2023

[2] [2]

MediaTek launches next-generation ASIC design platform with co-packaged optics solutions at OFC 2024,

MediaTek, “MediaTek launches next-generation ASIC design platform with co-packaged optics solutions at OFC 2024,” MediaTek. Accessed: Nov. 21, 2024. [Online]. Available: https://corp.mediatek.com/news-events/press- releases/mediatek-launches-next-generation-asic-design- platform-with-co-packaged-optics-solutions-at-ofc-2024

2024

[3] [3]

Broadcom’s journey to CPO at scale: performance KPIs & fiber reliability,

M. Mehta, “Broadcom’s journey to CPO at scale: performance KPIs & fiber reliability,” Broadcom. Accessed: Nov. 21, 2024. [Online]. Available: https://www.broadcom.com/blog/broadcom-s-journey-to- cpo-at-scale-performance-kpis-fiber-reliability

2024

[4] [4]

Silicon Photonics optical transceiver for high-speed, high-density and low-power LSI interconnect,

A. Hayakawa, H. Ebe, Y. Chen, and T. Mori, “Silicon Photonics optical transceiver for high-speed, high-density and low-power LSI interconnect,” Fujitsu Scientific and Technical Journal, vol. 52, no. 1, pp. 19–26, 2016

2016

[5] [5]

G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction. West Sussex: John Wiley & Sons, Ltd, 2004. doi: 10.1002/0470014180

work page doi:10.1002/0470014180 2004

[6] [6]

Next-Value Prediction of Beam Waists From Mixed Pitch Grating Using Simplified Transformer Model,

Y. D. Lim, P. Zhao, L. Guidoni, J. Likforman, and C. S. Tan, “Next-Value Prediction of Beam Waists From Mixed Pitch Grating Using Simplified Transformer Model,” IEEE Photonics J., vol. 16, no. 5, pp. 1–9, 2024, doi: 10.1109/JPHOT.2024.3442169

arXiv 2024

[7] [7]

Development of Mixed Pitch Grating for the Optical Addressing of Trapped Sr+ Ions with Data Analysis Techniques,

Y. D. Lim, P. Zhao, L. Guidoni, J. P. Likforman, and C. S. Tan, “Development of Mixed Pitch Grating for the Optical Addressing of Trapped Sr+ Ions with Data Analysis Techniques,” Opt. Express, vol. 31, no. 15, pp. 23801– 23812, 2023, doi: 10.1109/JPHOT.2023.3281134

arXiv 2023

[8] [8]

Design and Fabrication of Grating Couplers for the Optical Addressing of Trapped Ions,

Y. D. Lim, H. Y. Li, P. Zhao, J. Tao, L. Guidoni, and C. S. Tan, “Design and Fabrication of Grating Couplers for the Optical Addressing of Trapped Ions,” IEEE Photonics J., vol. 13, no. 4, pp. 1–6, 2021, doi: 10.1109/jphot.2021.3094646

arXiv 2021

[9] [9]

High-efficiency grating-couplers: Demonstration of a new design strategy,

R. Marchetti et al., “High-efficiency grating-couplers: Demonstration of a new design strategy,” Sci. Rep., vol. 7, no. 1, pp. 1–9, 2017, doi: 10.1038/s41598-017-16505-z

doi:10.1038/s41598-017-16505-z 2017

[10] [10]

Coupling performance enhancement using SOI grating coupler design,

T. Sharma et al., “Coupling performance enhancement using SOI grating coupler design,” Opt. Commun., vol. 427, no. July, pp. 452–456, 2018, doi: 10.1016/j.optcom.2018.06.012

work page doi:10.1016/j.optcom.2018.06.012 2018

[11] [11]

Apodized silicon photonic grating couplers for mode-order conversion,

I. Demirtzioglou et al., “Apodized silicon photonic grating couplers for mode-order conversion,” Photonics Res., vol. 7, no. 9, p. 1036, 2019, doi: 10.1364/prj.7.001036

work page doi:10.1364/prj.7.001036 2019

[12] [12]

AI-Native Design: Mixed Pitch Grating Coupler | InPhAI Demo,

Y. D. Lim, “AI-Native Design: Mixed Pitch Grating Coupler | InPhAI Demo,” YouTube. Accessed: Jun. 11,

[13] [2026]

Available: https://www.youtube.com/watch?v=L4-jOLQg2Tk

[Online]. Available: https://www.youtube.com/watch?v=L4-jOLQg2Tk