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arxiv: 2606.27099 · v1 · pith:3JS22LG2new · submitted 2026-06-25 · ⚛️ physics.optics · physics.app-ph· physics.comp-ph

Neural Networks for Inverse Design of Cascaded-Mode Near-Field Landscapes

Wannes Luts De Martelaere , Joeri Lenaerts , Vincent Ginis This is my paper

Pith reviewed 2026-06-26 02:17 UTC · model grok-4.3

classification ⚛️ physics.optics physics.app-phphysics.comp-ph
keywords neural networksinverse designnear-field landscapescascaded-mode interferencemultimode waveguidegradient-based optimizationoptical near-fields
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The pith

Multilayer neural networks approximate the mapping from modal coefficients to near-field landscapes, enabling gradient-based optimization to reconstruct target profiles.

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

The paper establishes that neural networks can learn the relationship between combinations of waveguide modes and the resulting near-field intensity patterns. Once trained on simulated examples, the networks serve as differentiable surrogates that support gradient descent to recover the modal coefficients needed for any chosen target landscape. This succeeds reliably for longitudinal variations along the propagation direction, including both simple and complex patterns, while lateral variations require extra data selection and augmentation to reach usable accuracy. A reader would care because near-field structuring supports applications in microscopy and nanoparticle control, and the method replaces repeated full-wave simulations with a single trained model inside the optimizer.

Core claim

We model the relationship between the design parameters and near-field landscapes using multilayer neural networks. After training, these networks are used for gradient-based optimization to reconstruct target near-field profiles. We implement this methodology to design longitudinal and lateral field variations. Our approach designs simple and complex longitudinal landscapes, demonstrating accurate prediction and flexibility. Lateral field reconstruction is more challenging but improved with training data selection and augmentation.

What carries the argument

Multilayer neural networks trained to approximate the forward mapping from modal coefficients to near-field intensity profiles, then inserted into a gradient-based optimizer to solve the inverse problem.

If this is right

  • Simple and complex longitudinal near-field landscapes can be designed with accurate prediction.
  • Lateral field reconstruction becomes feasible when training data are selected and augmented appropriately.
  • The same trained-network-plus-gradient-optimization pipeline applies to both longitudinal and lateral design tasks.
  • Deep learning supplies an efficient and scalable replacement for direct search over modal coefficients.

Where Pith is reading between the lines

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

  • The trained network could be reused across multiple target profiles without retraining from scratch.
  • The approach may transfer to other multimode systems where the forward map is expensive to evaluate repeatedly.
  • Experimental calibration of the network on measured rather than simulated fields would test robustness to fabrication imperfections.

Load-bearing premise

The mapping from modal coefficients to near-field landscapes is sufficiently smooth and can be learned accurately from a finite collection of simulated training examples.

What would settle it

A target near-field profile for which the modal coefficients returned by the trained network produce a visibly different landscape when the coefficients are inserted into an independent full-wave simulation.

Figures

Figures reproduced from arXiv: 2606.27099 by Joeri Lenaerts, Vincent Ginis, Wannes Luts De Martelaere.

Figure 1
Figure 1. Figure 1: Remote near-field structuring using mode-converters. (A) A schematic of a near-field landscaping device consisting of a multimode waveguide and two sets of β-converters delineating an area of interest. A single mode is fed into the device, and by iterative interactions with the β-converters a cascade of counterpropagating modes, with different complex amplitudes, is generated. Interference between these co… view at source ↗
Figure 2
Figure 2. Figure 2: Longitudinally trained Neural Networks (A) The performance of a network trained on a four-mode cascade (three conversions). The analytically computed ground truth is shown in red, and the prediction made by the network is shown in green. (B) The same for the case of a ten-mode cascade (nine conversions). on a four-mode network for 5000 epochs. These samples were taken from the test dataset; it is thus know… view at source ↗
Figure 3
Figure 3. Figure 3: Inverse design of longitudinal fields (A) The performance of the inverse design step for landscapes from the test dataset, on a four-mode network when using a random guess for the design parameters and no limitations on the parameter space. The desired field is shown in red and the field resultant from the predicted design parameters is shown in blue. (B) The performance can be significantly improved when … view at source ↗
Figure 4
Figure 4. Figure 4: Laterally trained networks (A) To successfully train neural networks for the lateral field design, one needs to bias the training data to sufficiently expose the network to non-evanescently decaying samples during training. This can be done using various criteria to select specific training samples from a large data pool. (B) A first selection is a totally random selection. In this case, the neural network… view at source ↗
Figure 5
Figure 5. Figure 5: Inverse design of lateral fields (B) The inverse design step for lateral field design, using a neural network trained on only random data (Fig. 4B) results in poor performance. The main reason is an inadequately trained neural network. (C) When using a neural network trained on data partially selected with the Fourier criterion (Fig. 4D), performance can be improved significantly. High sensitivity to the i… view at source ↗
read the original abstract

Structuring optical near-fields is important for applications in microscopy and nanoparticle manipulation. Traditionally, near-fields are structured using antenna nanostructures that locally convert propagating far-fields into bound near-fields. Recently, a remote structuring approach was proposed using cascaded mode interference in a multimode waveguide. However, determining the complex coefficients of the optimal modal combination needed to obtain specific near-fields remains a challenge. We address this inverse design problem using artificial neural networks. We model the relationship between the design parameters and near-field landscapes using multilayer neural networks. After training, these networks are used for gradient-based optimization to reconstruct target near-field profiles. We implement this methodology to design longitudinal and lateral field variations. Our approach designs simple and complex longitudinal landscapes, demonstrating accurate prediction and flexibility. Lateral field reconstruction is more challenging but improved with training data selection and augmentation. This work establishes deep learning as an efficient and scalable framework for cascaded-mode near-field inverse design.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 0 minor

Summary. The paper claims that multilayer neural networks can serve as accurate surrogates for the forward map from modal coefficients to near-field intensity landscapes generated by cascaded-mode interference in multimode waveguides. After supervised training on simulated data, these networks enable gradient-based optimization to solve the inverse problem of recovering coefficients that produce user-specified target near-field profiles. The method is applied to both longitudinal and lateral field structuring; the abstract states that it successfully designs simple and complex longitudinal landscapes with accurate prediction and flexibility, while lateral reconstruction improves with training-data selection and augmentation. The work positions deep learning as an efficient framework for this class of inverse-design tasks in near-field optics.

Significance. If the surrogate accuracy and end-to-end validation claims hold, the approach would supply a practical, scalable alternative to direct optimization or exhaustive search for cascaded-mode near-field design, which is relevant to microscopy and particle manipulation. The use of a differentiable NN surrogate for gradient-based inversion is a standard and potentially useful technique in photonics inverse design; however, the manuscript supplies no quantitative evidence (test-set error, out-of-distribution performance, or post-optimization full-wave verification) that would allow the reader to assess whether the reported designs are artifacts of the surrogate or solutions of the true problem.

major comments (3)
  1. [Abstract] Abstract: the central claim that the trained networks 'demonstrate accurate prediction and flexibility' for longitudinal landscapes is unsupported by any reported quantitative metric (e.g., MSE, MAE, or R² on held-out coefficient vectors) or by any comparison of NN-optimized coefficients re-evaluated in the original full-wave simulator versus the target.
  2. [Abstract] Abstract / Methods (implied): no information is given on training-set cardinality relative to the dimensionality of the modal-coefficient space, network depth/width, regularization, or validation strategy. Without these details it is impossible to judge whether the NN approximation is sufficiently faithful for its gradients to reliably solve the true inverse problem.
  3. [Abstract] Abstract: the statement that lateral-field reconstruction 'is more challenging but improved with training data selection and augmentation' is presented without any quantitative before/after metrics or description of the selection criterion, leaving the improvement claim untestable.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed comments on the need for quantitative support and methodological transparency. We agree that the abstract and methods require strengthening with explicit metrics and details to allow readers to evaluate the surrogate fidelity and inverse-design performance. We will revise accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the trained networks 'demonstrate accurate prediction and flexibility' for longitudinal landscapes is unsupported by any reported quantitative metric (e.g., MSE, MAE, or R² on held-out coefficient vectors) or by any comparison of NN-optimized coefficients re-evaluated in the original full-wave simulator versus the target.

    Authors: We agree the abstract should contain quantitative support. The manuscript body includes visual comparisons and qualitative agreement between NN predictions and targets, but explicit test-set error metrics and post-optimization full-wave verification results are not reported. We will add these (test MSE, MAE, and simulator re-evaluation of optimized coefficients) to the abstract and a new validation subsection. revision: yes

  2. Referee: [Abstract] Abstract / Methods (implied): no information is given on training-set cardinality relative to the dimensionality of the modal-coefficient space, network depth/width, regularization, or validation strategy. Without these details it is impossible to judge whether the NN approximation is sufficiently faithful for its gradients to reliably solve the true inverse problem.

    Authors: The Methods section describes the multilayer network and supervised training but omits precise dataset cardinality, architecture dimensions, regularization, and validation protocol. We will expand Methods with these hyperparameters (training-set size relative to coefficient dimension, layer widths, regularization type, and hold-out/cross-validation strategy) to demonstrate surrogate fidelity. revision: yes

  3. Referee: [Abstract] Abstract: the statement that lateral-field reconstruction 'is more challenging but improved with training data selection and augmentation' is presented without any quantitative before/after metrics or description of the selection criterion, leaving the improvement claim untestable.

    Authors: We acknowledge the lateral-reconstruction claim lacks before/after metrics and selection details. We will revise the abstract to report quantitative error reductions and add a description of the data-selection and augmentation procedure (including the criterion used) to the Methods section. revision: yes

Circularity Check

0 steps flagged

No circularity: standard NN surrogate trained on external simulations

full rationale

The paper trains multilayer neural networks on simulated forward data to approximate the map from modal coefficients to near-field profiles, then applies gradient-based optimization on the trained surrogate. No equations, self-citations, or fitted parameters are described that reduce the reported designs or predictions to the inputs by construction. The approach follows conventional supervised learning for inverse design and remains self-contained against external full-wave benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that a neural network can serve as a differentiable surrogate for the forward modal-interference model. No new physical entities are introduced. Free parameters are the network weights, which are fitted to simulated data. Axioms are standard supervised-learning assumptions (sufficient training coverage, smooth mapping).

free parameters (1)
  • neural_network_weights
    All trainable parameters of the multilayer networks; fitted during supervised training on simulated modal-to-field pairs.
axioms (1)
  • domain assumption The forward mapping from modal coefficients to near-field intensity is deterministic and can be simulated accurately enough to serve as ground truth for supervised learning.
    Invoked implicitly when the abstract states that networks are trained on the relationship between design parameters and near-field landscapes.

pith-pipeline@v0.9.1-grok · 5699 in / 1529 out tokens · 23396 ms · 2026-06-26T02:17:19.597110+00:00 · methodology

discussion (0)

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Reference graph

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