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Designing nanophotonic structures using conditional-deep convolutional generative adversarial networks
Sunae So, Junsuk Rho
TL;DR
Nanophotonic design lacks a systematic alternative to laborious iterative simulations. The paper uses a conditional deep convolutional generative adversarial network to generate image-based antenna designs from input reflection spectra, including structures unconstrained by predefined shapes. Simulations of generated designs agree well with the target spectra, supporting the method’s use for rapid complex-structure design within the demonstrated setting.
Problem
Nanophotonic component design lacks a systematic protocol and conventionally relies on laborious, time-consuming iterative simulations.
Method
A cDCGAN takes a 200 × 1 input reflection spectrum and 100 × 1 random noise vector to generate a 64 × 64 design image representing a 500 nm × 500 nm nanophotonic structure.
Results
The generated designs produce reflection spectra agreeing well with inputs, with an average MAE of 0.0322 across 12 test samples and new structures beyond the training shapes.
Takeaways & Limitations
Image-based cDCGAN generation provides nanophotonic designs not constrained by predefined structural parameters and offers 24096 design degrees of freedom.
Takeaways & Limitations
The demonstrated deep-learning setting uses a fixed physical domain and wavelength; different periodicities or wavelengths require additional data collection or a new deep-learning procedure.
Abstract
from arXiv · showhide
Data-driven design approaches based on deep-learning have been introduced in nanophotonics to reduce time-consuming iterative simulations which have been a major challenge. Here, we report the first use of conditional deep convolutional generative adversarial networks to design nanophotonic antennae that are not constrained to a predefined shape. For given input reflection spectra, the network generates desirable designs in the form of images; this form allows suggestions of new structures that cannot be represented by structural parameters. Simulation results obtained from the generated designs agreed well with the input reflection spectrum. This method opens new avenues towards the development of nanophotonics by providing a fast and convenient approach to design complex nanophotonic structures that have desired optical properties.
1 Introduction
Nanophotonic design has advanced optical functionality but still lacks a systematic protocol for creating desired components efficiently. Data-driven neural-network methods reduce iterative simulation effort, while cDCGAN extends design beyond predefined structural parameterizations.
- Motivation: Precisely designed sub-wavelength antennas can provide useful optical functionalities, including cloaking, super-resolution imaging, and negative refractive index.These capabilities arise from the interaction between sub-wavelength antennas and light.
- Motivation: Nanophotonics lacks a systematic protocol for designing desired components, leaving conventional optimization dependent on laborious, time-consuming iterative simulations.
- Prior approaches: Earlier neural-network approaches predicted structural parameters after fixing shapes such as multilayers or H-antennas.Once trained, these networks provided corresponding design parameters without additional iterative simulations.
- Prior approaches: GAN-based inverse design began addressing arbitrary unit-cell patterns, but basic structures remained predefined and only structural parameters were predictable.
- Proposed direction: The paper introduces cDCGAN to generate nanophotonic designs as images, enabling essentially arbitrary structures rather than designs limited to specific predefined forms.The designs use a 64 × 64-pixel probability distribution function in a 500 nm × 500 nm domain.
2 Results and Discussions
The cDCGAN maps reflection spectra to image-based antenna designs, then evaluates those designs through simulation. Across familiar, novel, and hand-drawn spectral targets, generated structures produced responses that generally matched the desired spectra.
- 2.1 Deep-learning procedure: 10,150 silver antennae spanning six representative shapes formed the training dataset, pairing 200-point reflection spectra with 64 × 64-pixel structural images.The images represented a 500 nm × 500 nm physical domain.
- 2.1 Deep-learning procedure: The generator combines 100 × 1 random noise with a 200 × 1 input spectrum to produce a 64 × 64-pixel probability distribution function.The discriminator then distinguishes generated designs from ground-truth designs.
- 2.1 Deep-learning procedure: ρ = 0.5 was selected to balance design and adversarial losses, while validation BCE Loss converged to 5.564 × 10^-3 after 1,000 epochs.The PDF is converted into a binary design using Otsu's thresholding method.
- 2.2 Network evaluation: The 12 test samples achieved an average MAE of 0.0322, with simulated reflection spectra agreeing well with their input spectra.Suggested PDFs showed good qualitative agreement with ground-truth designs, and were binarized before FDTD simulation.
- 2.2 Network evaluation: For unseen triangle and star structures, generated designs differed from ground truth yet produced reflection spectra similar to the input spectra.The paper attributes this to non-unique correlations between optical properties and designs; generated results tended to remain near the trained dataset space.
- 2.2 Network evaluation: For four hand-drawn Lorentzian-like spectra, MAEs were 0.0496, 0.0396, 0.0409, and 0.0408, respectively, with reasonably good overall spectral agreement.The generated shapes deviated substantially from the training shapes and were not constrained by predefined structures.
3 Conclusion
The paper demonstrates the first use of cDCGAN for designing nanophotonic structures with desired reflection properties. Unlike predefined-structure approaches, it generates new designs and could reduce manual design time and computational cost.
- cDCGAN competitively trains generator and discriminator networks to suggest nanophotonic structures with desired reflection properties.
- The method generates new designs rather than limiting suggestions to predefined structures.The designs have 64 × 64 pixels, corresponding to 24096 degrees of freedom.
- Adding layer thickness and antenna material as output parameters could enable more independent nanophotonic-device design.The paper states that this modification could reduce the time and computational cost of manual design.
A.1 Details on data preparation and deep learning procedure
The study prepares a simulation dataset of six antenna geometries and trains the model using mini-batch learning with binary cross-entropy loss. The loss uses target and input values to evaluate binary antenna-versus-air outputs.
- Data preparation: The dataset contains 10,150 simulation results from circle, square, cross, bow-tie, H-shaped, and V-shaped structures.The data are divided into training, validation, and testing subsets, with 20 test samples.
- Deep learning procedure: Mini-batch gradient descent trains the model with batches of 64 samples and averages batch losses after each 128-batch epoch.The implementation uses the Pytorch framework.
- Deep learning procedure: Binary Cross Entropy with Logits Loss evaluates predictions using target and input values for binary antenna-versus-air outputs.The target and input symbols are used to calculate the loss, with antenna represented by 1 and air by 0.
A.2 Network Optimization
The cDCGAN was optimized against conventional cGAN and across adversarial-loss ratios, with comparisons examining validation loss, generated designs, and training behavior.
- Adversarial-loss optimization: ρ = 0, ρ = 0.5, and ρ = 1 produced average test losses of 5.564e-3, 5.564e-3, and 1.0723e-2, respectively.The values correspond to the three adversarial-loss ratios in that order.
- cGAN versus cDCGAN: cDCGAN and conventional cGAN were compared using average loss on 2,140 validation data and generated-image behavior during training.The cGAN used a generator with four hidden layers.
- Adversarial-loss optimization: Figure A.2 compares suggested PDFs and simulation prediction results for circle antennas at ρ = 0, ρ = 0.5, and ρ = 1.Suggested PDFs appear in the first row and simulation results in the second row.
- Adversarial-loss optimization: ρ = 0.5 generated more authentic images than ρ = 0 despite similar average test loss.The difference is attributed to competition with the discriminator.
Funding Information
The work was financially supported by National Research Foundation grants funded by Korea’s Ministry of Science and ICT, with additional global Ph.D. fellowship support acknowledged.
- Funding Information: The work received National Research Foundation grants funded by Korea’s Ministry of Science and ICT.The listed grants include NRF-2017R1E1A1A03070501, NRF-2019R1A2C3003129, CAMM-2019M3A6B3030637, NRF-2018M3D1A1058998, and NRF-2015R1A5A1037668.
- Funding Information: S.S. acknowledges a global Ph.D. fellowship from the National Research Foundation and Ministry of Science and ICT, Korea.The fellowship identifier is NRF-2017H1A2A1043322.