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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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Frequency- and Time-domain Green function methods for electromagnetic simulation, optimization, and design
We present a family of numerical methods for the solution of Maxwell’s equations, with application to simulation, optimization, and design. In particular, a novel rectangular-polar integral equation solver is mentioned which can produce solutions to the time harmonic Maxwell’s equations, with high order accuracy, for general 2D and 3D structures, with an extension to time domain problems on the basis of a time re-centering synthesis technique. An effective integral equation acceleration method, the IFGF method (Interpolated Factored Green Function), is used, which evaluates the action of Green function-based integral operators for an 𝑁𝑁-point surface discretization at a computational cost of 𝑂(𝑁log𝑁) operations without recourse to the FFT—thus, lending itself to effective distributed memory parallelization. Computational illustrations include applications to photonic optimization and design.
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- Award ID(s):
- 2109831
- PAR ID:
- 10645623
- Editor(s):
- ACES
- Publisher / Repository:
- https://ieeexplore.ieee.org/abstract/document/10580702/keywords#keywords
- Date Published:
- Format(s):
- Medium: X
- Location:
- https://ieeexplore.ieee.org/abstract/document/10580702/keywords#keywords
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
