Shape optimization of H-plane waveguide tee junction using edge finite element method

Lee, Hong-Bae; Jung, Hyun-Kyo; Hahn, Song–Yop; Cheon, Changyul; Lee, Ki-Sik

doi:10.1109/20.376417

Cited by 20 publications

(1 citation statement)

References 3 publications

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“…Sensitivity analysis in electromagnetism has its roots in the optimal design of dynamic mechanical systems , and was applied to design waveguide structures in the late 1990s. , While AVM was formulated for simulators that solve systems of equations captured by large system matrices like FEM simulations, Chung et al demonstrated that AVM could also be applied to FDTD, which does not use system matrices and is defined on a structured Yee grid. − …”

Section: Methodsmentioning

confidence: 99%

Time Reversal Differentiation of FDTD for Photonic Inverse Design

Tang,

Lim,

Ossiander

et al. 2023

ACS Photonics

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Differentiable models enable the efficient computation of parameter gradients for continuous functions, greatly expediting the optimization of highdimensional systems. This makes them an asset for the design of nanostructured metasurfaces. The adjoint variable method (AVM) is the workhorse for photonic gradient computation but can be challenging to implement with the finite difference time domain (FDTD) electromagnetic simulation method for certain optimization problems. Automatic differentiation (AD) platforms remove the need for manual constructions while retaining favorable computational scaling, but high memory consumption limits their application to small systems. Here, we introduce a method of gradient calculation based on the direct differentiation of the FDTD update equations by leveraging the time-reversible nature of Maxwell's equations. We support open and closed systems by recording the time-dependent fields at lossy boundaries and playing them back during the time-reversed FDTD simulation. The method is generally applicable without the high memory consumption of AD by eliminating redundant memory operations performed at each time step. We demonstrate this architecture in a 3D FDTD simulation. Its computational cost is comparable to the adjoint method, and it reduces memory requirements by 98% compared to an equivalent AD calculation for calculating a 900-element gradient vector. The differentiable simulator is applied to design two systems: a color sorter with frequency-domain behavior and a resonant nanostructure array with time-domain behavior. This approach to differentiate grid-based simulators is applicable to a broad range of physics simulators, thereby broadening the scope of inverse design topology optimization across fields.

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Section: Methodsmentioning

confidence: 99%

Time Reversal Differentiation of FDTD for Photonic Inverse Design

Tang,

Lim,

Ossiander

et al. 2023

ACS Photonics

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A level set‐based topology optimization method targeting metallic waveguide design problems

Yamasaki

Nomura

Kawamoto

et al. 2011

Numerical Meth Engineering

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SUMMARYIn this paper, we propose a level set-based topology optimization method targeting metallic waveguide design problems, where the skin effect must be taken into account since the metallic waveguides are generally used in the high-frequency range where this effect critically affects performance. One of the most reasonable approaches to represent the skin effect is to impose an electric field constraint condition on the surface of the metal. To implement this approach, we develop a boundary-tracking scheme for the arbitrary Lagrangian Eulerian (ALE) mesh pertaining to the zero iso-contour of the level set function that is given in an Eulerian mesh, and impose Dirichlet boundary conditions at the nodes on the zero iso-contour in the ALE mesh to compute the electric field. Since the ALE mesh accurately tracks the zero iso-contour at every optimization iteration, the electric field is always appropriately computed during optimization. For the sensitivity analysis, we compute the nodal coordinate sensitivities in the ALE mesh and smooth them by solving a Helmholtz-type partial differential equation. The obtained smoothed sensitivities are used to compute the normal velocity in the level set equation that is solved using the Eulerian mesh, and the level set function is updated based on the computed normal velocity. Finally, the utility of the proposed method is discussed through several numerical examples.

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