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Recent developments in the computational automated design of electromagnetic devices, otherwise known as inverse design, have significantly enhanced the design process for nanophotonic systems. Inverse design can both reduce design time considerably and lead to high-performance, nonintuitive structures that would otherwise have been impossible to develop manually. Despite the successes enjoyed by structure optimization techniques, most approaches leverage electromagnetic solvers that require significant computational resources and suffer from slow convergence and numerical dispersion. Recently, a fast simulation and boundary-based inverse design approach based on boundary integral equations was demonstrated for two-dimensional nanophotonic problems. In this work, we introduce a new full-wave three-dimensional simulation and boundary-based optimization framework for nanophotonic devices also based on boundary integral methods, which achieves high accuracy even at coarse mesh discretizations while only requiring modest computational resources. The approach has been further accelerated by leveraging GPU computing, a sparse block-diagonal preconditioning strategy, and a matrix-free implementation of the discrete adjoint method. As a demonstration, we optimize three different devices: a 1:2 1550 nm power splitter and two nonadiabatic mode-preserving waveguide tapers. To the best of our knowledge, the tapers, which span 40 wavelengths in the silicon material, are the largest silicon photonic waveguiding devices to have been optimized using full-wave 3D solution of Maxwell’s equations.
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Gradient-based Design of Computational Granular Crystals
There is growing interest in engineering uncon- ventional computing devices that leverage the in- trinsic dynamics of physical substrates to perform fast and energy-efficient computations. Granu- lar metamaterials are one such substrate that has emerged as a promising platform for building wave-based information processing devices with the potential to integrate sensing, actuation, and computation. Their high-dimensional and non- linear dynamics result in nontrivial and some- times counter-intuitive wave responses that can be shaped by the material properties, geometry, and configuration of individual grains. Such highly tunable rich dynamics can be utilized for mechan- ical computing in special-purpose applications. However, there are currently no general frame- works for the inverse design of large-scale granu- lar materials. Here, we build upon the similarity between the spatiotemporal dynamics of wave propagation in material and the computational dy- namics of Recurrent Neural Networks to develop a gradient-based optimization framework for har- monically driven granular crystals. We showcase how our framework can be utilized to design basic logic gates where mechanical vibrations carry the information at predetermined frequencies. We compare our design methodology with classic gradient-free methods and find that our approach discovers higher-performing configurations with less computational effort. Our findings show that a gradient-based optimization method can greatly expand the design space of metamaterials and pro- vide the opportunity to systematically traverse the parameter space to find materials with the desired functionalities.
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- Award ID(s):
- 2118810
- PAR ID:
- 10541864
- Publisher / Repository:
- arXiv
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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